Quantifying non-ergodic dynamics of force-free granular gases.

PubMed

Bodrova, Anna; Chechkin, Aleksei V; Cherstvy, Andrey G; Metzler, Ralf

2015-09-14

Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient ε. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of ε on the impact velocity of particles.

Persistence and ergodicity of plant disease model with markov conversion and impulsive toxicant input

NASA Astrophysics Data System (ADS)

Zhao, Wencai; Li, Juan; Zhang, Tongqian; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Taking into account of both white and colored noises, a stochastic mathematical model with impulsive toxicant input is formulated. Based on this model, we investigate dynamics, such as the persistence and ergodicity, of plant infectious disease model with Markov conversion in a polluted environment. The thresholds of extinction and persistence in mean are obtained. By using Lyapunov functions, we prove that the system is ergodic and has a stationary distribution under certain sufficient conditions. Finally, numerical simulations are employed to illustrate our theoretical analysis.

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

Ergodicity of a singly-thermostated harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, William Graham; Sprott, Julien Clinton; Hoover, Carol Griswold

2016-03-01

Although Nosé's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nosé-Hoover (harmonic) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space is occupied by regular conservative tori. Oscillator ergodicity has previously been achieved by controlling two oscillator moments with two thermostat variables. Here we use computerized searches in conjunction with visualization to find singly-thermostated motion equations for the oscillator which are consistent with Gibbs' canonical distribution. Such models are the simplest able to bridge the gap between Gibbs' statistical ensembles and Newtonian single-particle dynamics.

Granular Contact Forces: Proof of "Self-Ergodicity" by Generalizing Boltzmann's Stosszahlansatz and H Theorem

NASA Technical Reports Server (NTRS)

Metzger, Philip T.

2006-01-01

Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann's stosszahlansatz (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann's H functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is self-ergodic. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized H Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling.

Local conditional entropy in measure for covers with respect to a fixed partition

NASA Astrophysics Data System (ADS)

Romagnoli, Pierre-Paul

2018-05-01

In this paper we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle with respect to the notion of conditional entropy defined by Misiurewicz (1976 Stud. Math. 55 176–200) for the case of open covers. This in particular extends the work done in Romagnoli (2003 Ergod. Theor. Dynam. Syst. 23 1601–10), Glasner and Weiss (2006 Handbook of Dynamical Systems vol 1B (Amsterdam: Elsevier)) and Huang et al (2006 Ergod. Theor. Dynam. Syst. 26 219–45).

Mixing, ergodicity and slow relaxation phenomena

NASA Astrophysics Data System (ADS)

Costa, I. V. L.; Vainstein, M. H.; Lapas, L. C.; Batista, A. A.; Oliveira, F. A.

2006-11-01

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.

Evaluating gambles using dynamics

NASA Astrophysics Data System (ADS)

Peters, O.; Gell-Mann, M.

2016-02-01

Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.

Preserving the Boltzmann ensemble in replica-exchange molecular dynamics.

PubMed

Cooke, Ben; Schmidler, Scott C

2008-10-28

We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic.

Three dimensional cross-correlation dynamic light scattering by non-ergodic turbid media.

PubMed

Haro-Pérez, C; Ojeda-Mendoza, G J; Rojas-Ochoa, L F

2011-06-28

We investigate dynamic light scattering by non-ergodic turbid media with an adapted version of the method proposed by Pusey and van Megen [Physica A 157, 705 (1989)]. Our formulation follows the derivation of the original method by extending it to the three dimensional cross-correlation scheme (3DDLS). The main finding is an expression to obtain the dynamic structure factor from light scattering that takes into account the system turbidity and the peculiarities of the 3D geometry. From 3DDLS measurements in well-controlled solid-like systems of different turbidity, we confirm that our results can be interpreted reasonably well by the theoretical approach described here. Good agreement is found with earlier reported results on similar systems.

Ergodicity breaking and ageing of underdamped Brownian dynamics with quenched disorder

NASA Astrophysics Data System (ADS)

Guo, Wei; Li, Yong; Song, Wen-Hua; Du, Lu-Chun

2018-03-01

The dynamics of an underdamped Brownian particle moving in one-dimensional quenched disorder under the action of an external force is investigated. Within the tailored parameter regime, the transiently anomalous diffusion and ergodicity breaking, spanning several orders of magnitude in time, have been obtained. The ageing nature of the system weakens as the dissipation of the system increases for other given parameters. Its origin is ascribed to the highly local heterogeneity of the disorder. Two kinds of approximations (in the stationary state), respectively, for large bias and large damping are derived. These results may be helpful in further understanding the nontrivial response of nonlinear dynamics, and also have potential applications to experiments and activities of biological processes.

Dynamic divertor control using resonant mixed toroidal harmonic magnetic fields during ELM suppression in DIII-D

NASA Astrophysics Data System (ADS)

Jia, M.; Sun, Y.; Paz-Soldan, C.; Nazikian, R.; Gu, S.; Liu, Y. Q.; Abrams, T.; Bykov, I.; Cui, L.; Evans, T.; Garofalo, A.; Guo, W.; Gong, X.; Lasnier, C.; Logan, N. C.; Makowski, M.; Orlov, D.; Wang, H. H.

2018-05-01

Experiments using Resonant Magnetic Perturbations (RMPs), with a rotating n = 2 toroidal harmonic combined with a stationary n = 3 toroidal harmonic, have validated predictions that divertor heat and particle flux can be dynamically controlled while maintaining Edge Localized Mode (ELM) suppression in the DIII-D tokamak. Here, n is the toroidal mode number. ELM suppression over one full cycle of a rotating n = 2 RMP that was mixed with a static n = 3 RMP field has been achieved. Prominent heat flux splitting on the outer divertor has been observed during ELM suppression by RMPs in low collisionality regime in DIII-D. Strong changes in the three dimensional heat and particle flux footprint in the divertor were observed during the application of the mixed toroidal harmonic magnetic perturbations. These results agree well with modeling of the edge magnetic field structure using the TOP2D code, which takes into account the plasma response from the MARS-F code. These results expand the potential effectiveness of the RMP ELM suppression technique for the simultaneous control of divertor heat and particle load required in ITER.

Information, Consistent Estimation and Dynamic System Identification.

DTIC Science & Technology

1976-11-01

Washington,DC 232129 Tj-CUOSITORING AGENCY NAMIE 6 AOORESS(lI dittevmet Itroo CuooottaaII Offics) IS.- SECURITY CLASS. (of this *.part) SCHEDULE ’B...representative model from a given model set, applicable to infinite and even non-compact model sets. S-UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOrj(*whe...ergodicity. For a thorough development of ergodic theory the reader is referred to, e.g., Doob [1953], Halmos [1956] and Chacon and Ornstein [1959

Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures

NASA Astrophysics Data System (ADS)

Bochi, Jairo; Bonatti, Christian; Díaz, Lorenzo J.

2016-06-01

We give explicit C 1-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which the center Lyapunov exponent vanishes uniformly. The conditions of the criterion are met on a C 1-dense and open subset of the set of diffeomorphisms having a robust cycle. As a corollary, there exists a C 1-open and dense subset of the set of non-Anosov robustly transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic measures with positive entropy. The criterion is based on a notion of a blender defined dynamically in terms of strict invariance of a family of discs.

Control and Data Acquisition for the Spherical Tokamak MEDUSA-CR

NASA Astrophysics Data System (ADS)

Soto, Christian; Gonzalez, Jeferson; Carvajal, Johan; Ribeiro, Celso

2013-10-01

The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R < 0.14 m, a < 0.10 m, BT < 0.5 T, Ip < 40 kA, 3 ms pulse) is being recommissioned in Costa Rica Institute of Technology. The main objectives of the MEDUSA-CR project are training and to clarify several issues in relevant physics for conventional and mainly STs, including beta studies in bean-shaped ST plasmas, transport, heating and current drive via Alfvén wave, and natural divertor STs with ergodic magnetic limiter. We present here the control and data acquisition systems for MEDUSA-CR device which are based on National Instruments (NI) software (LabView) and hardware on loan to our laboratory via NI-Costa Rica. The interface with the energy, gas fueling, and security systems are also presented. VIE-ITCR, IAEA-CRP contract 17592, National Instruments of Costa Rica.

Energy, Vacuum, Gas Fueling, and Security Systems for the Spherical Tokamak MEDUSA-CR

NASA Astrophysics Data System (ADS)

Gonzalez, Jeferson; Soto, Christian; Carvajal, Johan; Ribeiro, Celso

2013-10-01

The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R < 0.14 m, a < 0.10 m, BT < 0.5 T, Ip < 40 kA, 3 ms pulse) is being recommissioned in Costa Rica Institute of Technology. The main objectives of the MEDUSA-CR project are training and to clarify several issues in relevant physics for conventional and mainly STs, including beta studies in bean-shaped ST plasmas, transport, heating and current drive via Alfvén wave, and natural divertor STs with ergodic magnetic limiter. We present here the energy, vacuum, gas fueling, and security systems for MEDUSA-CR device. The interface with the control and data acquisition systems based on National Instruments (NI) software (LabView) and hardware (on loan to our laboratory via NI-Costa Rica) are also presented. VIE-ITCR, IAEA-CRP contract 17592, National Instruments of Costa Rica.

Enhanced visible and near-infrared capabilities of the JET mirror-linked divertor spectroscopy system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lomanowski, B. A., E-mail: b.a.lomanowski@durham.ac.uk; Sharples, R. M.; Meigs, A. G.

2014-11-15

The mirror-linked divertor spectroscopy diagnostic on JET has been upgraded with a new visible and near-infrared grating and filtered spectroscopy system. New capabilities include extended near-infrared coverage up to 1875 nm, capturing the hydrogen Paschen series, as well as a 2 kHz frame rate filtered imaging camera system for fast measurements of impurity (Be II) and deuterium Dα, Dβ, Dγ line emission in the outer divertor. The expanded system provides unique capabilities for studying spatially resolved divertor plasma dynamics at near-ELM resolved timescales as well as a test bed for feasibility assessment of near-infrared spectroscopy.

Theory of Advanced Magnetic Divertors

NASA Astrophysics Data System (ADS)

Kotschenreuther, Michael; Valanju, Prashant; Mahajan, Swadesh; Covele, Brent

2013-10-01

The magnetic field structure in the SOL is the most important determinant of divertor physics. A comprehensive analytical and numerical methodology is developed to investigate SOL magnetic fields in the backdrop of two advanced divertor geometries- the X-divertor (XD) proposed and discussed in 2004, and the snowflake divertor (SFD) of 2007-2010. The analysis shows that XD and SFD represent very distinct and readily distinguishable magnetic geometries, epitomized through a differentiating metric, the Divertor Index (DI). In terms of this simple metric, the XD (DI > 1) and the SFD (DI < 1) fall on opposite sides of the standard divertor SD (DI = 1). Amongst other things, DI signifies the rate of convergence (divergence) of the flux surfaces near the divertor plate; the flux surfaces of SFD are more convergent contracting) than the SD while the XD flux surfaces are less convergent, in fact, divergent (flaring). These different SOL magnetics imply different physics, particularly with respect to detachment dynamics. It is also shown that some experiments on NSTX and DIII-D match both the prescription and the predictions of the 2004 XD paper. Work supported under US-DOE projects DE-FG02-04ER54742 and DE-FG02-04ER54754.

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior

PubMed Central

da Cunha, C. R.; Mineharu, M.; Matsunaga, M.; Matsumoto, N.; Chuang, C.; Ochiai, Y.; Kim, G.-H.; Watanabe, K.; Taniguchi, T.; Ferry, D. K.; Aoki, N.

2016-01-01

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene. PMID:27609184

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior.

PubMed

da Cunha, C R; Mineharu, M; Matsunaga, M; Matsumoto, N; Chuang, C; Ochiai, Y; Kim, G-H; Watanabe, K; Taniguchi, T; Ferry, D K; Aoki, N

2016-09-09

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

NASA Astrophysics Data System (ADS)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence

NASA Technical Reports Server (NTRS)

Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor

2010-01-01

We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.

Reformulation of time-convolutionless mode-coupling theory near the glass transition

NASA Astrophysics Data System (ADS)

Tokuyama, Michio

2017-10-01

The time-convolutionless mode-coupling theory (TMCT) recently proposed is reformulated under the condition that one of two approximations, which have been used to formulate the original TMCT in addition to the MCT approximations done on a derivation of nonlinear memory function in terms of the intermediate-scattering function, is not employed because it causes unphysical results for intermediate times. The improved TMCT equation is then derived consistently under another approximation. It is first checked that the ergodic to non-ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long-time dynamics of both equations coincides with each other. However, it is emphasized that a difference between them appears in the intermediate-time dynamics of physical quantities. Such a difference is explored numerically in the dynamics of a non-Gaussian parameter by employing the Percus-Yevick static structure factor to calculate the nonlinear memory function.

Chaotic attractors and physical measures for some density dependent Leslie population models

NASA Astrophysics Data System (ADS)

Ugarcovici, Ilie; Weiss, Howard

2007-12-01

Following ecologists' discoveries, mathematicians have begun studying extensions of the ubiquitous age structured Leslie population model that allow some survival probabilities and/or fertility rates to depend on population densities. These nonlinear extensions commonly exhibit very complicated dynamics: through computer studies, some authors have discovered robust Hénon-like strange attractors in several families. Population biologists and demographers frequently wish to average a function over many generations and conclude that the average is independent of the initial population distribution. This type of 'ergodicity' seems to be a fundamental tenet in population biology. In this paper we develop the first rigorous ergodic theoretic framework for density dependent Leslie population models. We study two generation models with Ricker and Hassell (recruitment type) fertility terms. We prove that for some parameter regions these models admit a chaotic (ergodic) attractor which supports a unique physical probability measure. This physical measure, having full Lebesgue measure basin, satisfies in the strongest possible sense the population biologist's requirement for ergodicity in their population models. We use the celebrated work of Wang and Young 2001 Commun. Math. Phys. 218 1-97, and our results are the first applications of their method to biology, ecology or demography.

Applications of Ergodic Theory to Coverage Analysis

NASA Technical Reports Server (NTRS)

Lo, Martin W.

2003-01-01

The study of differential equations, or dynamical systems in general, has two fundamentally different approaches. We are most familiar with the construction of solutions to differential equations. Another approach is to study the statistical behavior of the solutions. Ergodic Theory is one of the most developed methods to study the statistical behavior of the solutions of differential equations. In the theory of satellite orbits, the statistical behavior of the orbits is used to produce 'Coverage Analysis' or how often a spacecraft is in view of a site on the ground. In this paper, we consider the use of Ergodic Theory for Coverage Analysis. This allows us to greatly simplify the computation of quantities such as the total time for which a ground station can see a satellite without ever integrating the trajectory, see Lo 1,2. More over, for any quantity which is an integrable function of the ground track, its average may be computed similarly without the integration of the trajectory. For example, the data rate for a simple telecom system is a function of the distance between the satellite and the ground station. We show that such a function may be averaged using the Ergodic Theorem.

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

NASA Astrophysics Data System (ADS)

Notarnicola, Simone; Iemini, Fernando; Rossini, Davide; Fazio, Rosario; Silva, Alessandro; Russomanno, Angelo

2018-02-01

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N -coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N -dimensional Anderson model. The thermodynamic limit N →∞ , in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N ≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.

Ergodic theorem, ergodic theory, and statistical mechanics

PubMed Central

Moore, Calvin C.

2015-01-01

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697

Experiments and numerical modeling of fast flowing liquid metal thin films under spatially varying magnetic field conditions

NASA Astrophysics Data System (ADS)

Narula, Manmeet Singh

Innovative concepts using fast flowing thin films of liquid metals (like lithium) have been proposed for the protection of the divertor surface in magnetic fusion devices. However, concerns exist about the possibility of establishing the required flow of liquid metal thin films because of the presence of strong magnetic fields which can cause flow disrupting MHD effects. A plan is underway to design liquid lithium based divertor protection concepts for NSTX, a small spherical torus experiment at Princeton. Of these, a promising concept is the use of modularized fast flowing liquid lithium film zones, as the divertor (called the NSTX liquid surface module concept or NSTX LSM). The dynamic response of the liquid metal film flow in a spatially varying magnetic field configuration is still unknown and it is suspected that some unpredicted effects might be lurking. The primary goal of the research work being reported in this dissertation is to provide qualitative and quantitative information on the liquid metal film flow dynamics under spatially varying magnetic field conditions, typical of the divertor region of a magnetic fusion device. The liquid metal film flow dynamics have been studied through a synergic experimental and numerical modeling effort. The Magneto Thermofluid Omnibus Research (MTOR) facility at UCLA has been used to design several experiments to study the MHD interaction of liquid gallium films under a scaled NSTX outboard divertor magnetic field environment. A 3D multi-material, free surface MHD modeling capability is under development in collaboration with HyPerComp Inc., an SBIR vendor. This numerical code called HIMAG provides a unique capability to model the equations of incompressible MHD with a free surface. Some parts of this modeling capability have been developed in this research work, in the form of subroutines for HIMAG. Extensive code debugging and benchmarking exercise has also been carried out. Finally, HIMAG has been used to study the MHD interaction of fast flowing liquid metal films under various divertor relevant magnetic field configurations through numerical modeling exercises.

Dynamically induced many-body localization

NASA Astrophysics Data System (ADS)

Choi, Soonwon; Abanin, Dmitry A.; Lukin, Mikhail D.

2018-03-01

We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe nonequilibrium phases of matter for a long time, limited only by coupling to external environment.

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

PubMed

Inaba, H

1988-01-01

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

Nonlinear dynamics and predictability in the atmospheric sciences

NASA Technical Reports Server (NTRS)

Ghil, M.; Kimoto, M.; Neelin, J. D.

1991-01-01

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Upgraded divertor Thomson scattering system on DIII-D

NASA Astrophysics Data System (ADS)

Glass, F.; Carlstrom, T. N.; Du, D.; McLean, A. G.; Taussig, D. A.; Boivin, R. L.

2016-11-01

A design to extend the unique divertor Thomson scattering system on DIII-D to allow measurements of electron temperature and density in high triangularity plasmas is presented. Access to this region is selectable on a shot-by-shot basis by redirecting the laser beam of the existing divertor Thomson system inboard — beneath the lower floor using a moveable, high-damage threshold, in-vacuum mirror — and then redirecting again vertically. The currently measured divertor region remains available with this mirror retracted. Scattered light is collected from viewchords near the divertor floor using in-vacuum, high temperature optical elements and relayed through the port window, before being coupled into optical fiber bundles. At higher elevations from the floor, measurements are made by dynamically re-focusing the existing divertor system collection optics. Nd:YAG laser timing, analysis of the scattered light spectrum via polychromators, data acquisition, and calibration are all handled by existing systems or methods of the current multi-pulse Thomson scattering system. Existing filtered polychromators with 7 spectral channels are employed to provide maximum measurement breadth (Te in the range of 0.5 eV-2 keV, ne in the range of 5 × 1018-1 × 1021 m3) for both low Te in detachment and high Te measurement up beyond the separatrix.

Upgraded divertor Thomson scattering system on DIII-D.

PubMed

Glass, F; Carlstrom, T N; Du, D; McLean, A G; Taussig, D A; Boivin, R L

2016-11-01

A design to extend the unique divertor Thomson scattering system on DIII-D to allow measurements of electron temperature and density in high triangularity plasmas is presented. Access to this region is selectable on a shot-by-shot basis by redirecting the laser beam of the existing divertor Thomson system inboard - beneath the lower floor using a moveable, high-damage threshold, in-vacuum mirror - and then redirecting again vertically. The currently measured divertor region remains available with this mirror retracted. Scattered light is collected from viewchords near the divertor floor using in-vacuum, high temperature optical elements and relayed through the port window, before being coupled into optical fiber bundles. At higher elevations from the floor, measurements are made by dynamically re-focusing the existing divertor system collection optics. Nd:YAG laser timing, analysis of the scattered light spectrum via polychromators, data acquisition, and calibration are all handled by existing systems or methods of the current multi-pulse Thomson scattering system. Existing filtered polychromators with 7 spectral channels are employed to provide maximum measurement breadth (T e in the range of 0.5 eV-2 keV, n e in the range of 5 × 10 18 -1 × 10 21 m 3 ) for both low T e in detachment and high T e measurement up beyond the separatrix.

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levnajić, Zoran; Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106; Mezić, Igor

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone,more » and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.« less

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

PubMed

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

Moments distributions of single dye molecule spectra in a low-temperature polymer: Analysis of system ergodicity

NASA Astrophysics Data System (ADS)

Anikushina, T. A.; Naumov, A. V.

2013-12-01

This article demonstrates the principal advantages of the technique for analysis of the long-term spectral evolution of single molecules (SM) in the study of the microscopic nature of the dynamic processes in low-temperature polymers. We performed the detailed analysis of the spectral trail of single tetra-tert-butylterrylene (TBT) molecule in an amorphous polyisobutylene matrix, measured over 5 hours at T = 7K. It has been shown that the slow temporal dynamics is in qualitative agreement with the standard model of two-level systems and stochastic sudden-jump model. At the same time the distributions of the first four moments (cumulants) of the spectra of the selected SM measured at different time points were found not consistent with the standard theory prediction. It was considered as evidence that in a given time interval the system is not ergodic

Toroidally symmetric plasma vortex at tokamak divertor null point

DOE PAGES

Umansky, M. V.; Ryutov, D. D.

2016-03-09

Reduced MHD equations are used for studying toroidally symmetric plasma dynamics near the divertor null point. Numerical solution of these equations exhibits a plasma vortex localized at the null point with the time-evolution defined by interplay of the curvature drive, magnetic restoring force, and dissipation. Convective motion is easier to achieve for a second-order null (snowflake) divertor than for a regular x-point configuration, and the size of the convection zone in a snowflake configuration grows with plasma pressure at the null point. In conclusion, the trends in simulations are consistent with tokamak experiments which indicate the presence of enhanced transportmore » at the null point.« less

Upgraded divertor Thomson scattering system on DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Glass, F., E-mail: glassf@fusion.gat.com; Carlstrom, T. N.; Du, D.

2016-11-15

A design to extend the unique divertor Thomson scattering system on DIII-D to allow measurements of electron temperature and density in high triangularity plasmas is presented. Access to this region is selectable on a shot-by-shot basis by redirecting the laser beam of the existing divertor Thomson system inboard — beneath the lower floor using a moveable, high-damage threshold, in-vacuum mirror — and then redirecting again vertically. The currently measured divertor region remains available with this mirror retracted. Scattered light is collected from viewchords near the divertor floor using in-vacuum, high temperature optical elements and relayed through the port window, beforemore » being coupled into optical fiber bundles. At higher elevations from the floor, measurements are made by dynamically re-focusing the existing divertor system collection optics. Nd:YAG laser timing, analysis of the scattered light spectrum via polychromators, data acquisition, and calibration are all handled by existing systems or methods of the current multi-pulse Thomson scattering system. Existing filtered polychromators with 7 spectral channels are employed to provide maximum measurement breadth (T{sub e} in the range of 0.5 eV–2 keV, n{sub e} in the range of 5 × 10{sup 18}–1 × 10{sup 21} m{sup 3}) for both low T{sub e} in detachment and high T{sub e} measurement up beyond the separatrix.« less

Linking density functional and mode coupling models for supercooled liquids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P.

2016-03-28

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicitymore » transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.« less

Generalized continued fractions and ergodic theory

NASA Astrophysics Data System (ADS)

Pustyl'nikov, L. D.

2003-02-01

In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest.

Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2016-11-01

We introduce a class of discrete random-walk model driven by global memory effects. At any time, the right-left transitions depend on the whole previous history of the walker, being defined by an urnlike memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically, each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature, the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long-time regime, they remain random objects. While their average over realizations recovers the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment, an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Numerical study of the current-convective instability driven by asymmetry of detachment in inner and outer divertors

NASA Astrophysics Data System (ADS)

Stepanenko, A. A.; Krasheninnikov, S. I.

2018-01-01

One of the possible mechanisms responsible for strong radiation fluctuations observed in recent experiments with detached plasmas at ASDEX Upgrade [Potzel et al., Nucl. Fusion 54, 013001 (2014)] can be related to the onset of the current-convective instability (CCI) driven by strong asymmetry of detachment in the inner and outer divertors of the tokamak [S. Krasheninnikov and A. Smolyakov, Phys. Plasmas 23, 092505 (2016)]. In this study, we present the physical model, used to simulate the CCI, and the first numerical results of modeling of the CCI dynamics in ASDEX Upgrade-like conditions. The simulation results provide frequency spectra of turbulent divertor plasma oscillations showing reasonably good agreement with the available experimental data.

Periodically driven ergodic and many-body localized quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ponte, Pedro; Department of Physics and Astronomy, University of Waterloo, ON N2L 3G1; Chandran, Anushya

2015-02-15

We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disorderedmore » spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.« less

A simple condition for uniqueness of the absolutely continuous ergodic measure and its application to economic models

NASA Astrophysics Data System (ADS)

Sato, Kenji; Yano, Makoto

2012-09-01

Unique existence of the absolutely continuous ergodic measure, or existence of ergodic chaos (in a strong sense), has been considered important in economics since it explains the mechanism underlying economic fluctuations. In the present study, a simple sufficient condition for ergodic chaos is proved and applied to economic models.

Upstream Density for Plasma Detachment with Conventional and Lithium Vapor-Box Divertors

NASA Astrophysics Data System (ADS)

Goldston, Rj; Schwartz, Ja

2016-10-01

Fusion power plants are likely to require detachment of the divertor plasma from material targets. The lithium vapor box divertor is designed to achieve this, while limiting the flux of lithium vapor to the main plasma. We develop a simple model of near-detachment to evaluate the required upstream plasma density, for both conventional and lithium vapor-box divertors, based on particle and dynamic pressure balance between up- and down-stream, at near-detachment conditions. A remarkable general result is found, not just for lithium-induced detachment, that the upstream density divided by the Greenwald-limit density scales as (P 5 / 8 /B 3 / 8) Tdet1 / 2 / (ɛcool + γTdet) , with no explicit size scaling. Tdet is the temperature just before strong pressure loss, 1/2 of the ionization potential of the dominant recycling species, ɛcool is the average plasma energy lost per injected hydrogenic and impurity atom, and γ is the sheath heat transmission factor. A recent 1-D calculation agrees well with this scaling. The implication is that the plasma exhaust problem cannot be solved by increasing R. Instead significant innovation, such as the lithium vapor box divertor, will be required. This work supported by DOE Contract No. DE-AC02-09CH11466.

Fast imaging of filaments in the X-point region of Alcator C-Mod

DOE PAGES

Terry, J. L.; Ballinger, S.; Brunner, D.; ...

2017-01-27

A rich variety of field-aligned fluctuations has been revealed using fast imaging of D α emission from Alcator C-Mod's lower X-point region. Field-aligned filamentary fluctuations are observed along the inner divertor leg, within the Private-Flux-Zone (PFZ), in the Scrape-Off Layer (SOL) outside the outer divertor leg, and, under some conditions, at or above the X-point. The locations and dynamics of the filaments in these regions are strikingly complex in C-Mod. Changes in the filaments’ generation appear to be ordered by plasma density and magnetic configuration. Filaments are not observed for plasmas with n/nGreenwald ≲ 0.12 nor are they observed inmore » Upper Single Null configurations. In a Lower Single Null with 0.12 ≲ n/nGreenwald ≲ 0.45 and Bx∇B directed down, filaments typically move up the inner divertor leg toward the X-point. Reversing the field direction results in the appearance of filaments outside of the outer divertor leg. With the divertor targets “detached”, filaments inside the LCFS are seen. Lastly, these studies were motivated by observations of filaments in the X-point and PFZ regions in MAST, and comparisons with those observations are made.« less

Coupled Kinetic-MHD Simulations of Divertor Heat Load with ELM Perturbations

NASA Astrophysics Data System (ADS)

Cummings, Julian; Chang, C. S.; Park, Gunyoung; Sugiyama, Linda; Pankin, Alexei; Klasky, Scott; Podhorszki, Norbert; Docan, Ciprian; Parashar, Manish

2010-11-01

The effect of Type-I ELM activity on divertor plate heat load is a key component of the DOE OFES Joint Research Target milestones for this year. In this talk, we present simulations of kinetic edge physics, ELM activity, and the associated divertor heat loads in which we couple the discrete guiding-center neoclassical transport code XGC0 with the nonlinear extended MHD code M3D using the End-to-end Framework for Fusion Integrated Simulations, or EFFIS. In these coupled simulations, the kinetic code and the MHD code run concurrently on the same massively parallel platform and periodic data exchanges are performed using a memory-to-memory coupling technology provided by EFFIS. The M3D code models the fast ELM event and sends frequent updates of the magnetic field perturbations and electrostatic potential to XGC0, which in turn tracks particle dynamics under the influence of these perturbations and collects divertor particle and energy flux statistics. We describe here how EFFIS technologies facilitate these coupled simulations and discuss results for DIII-D, NSTX and Alcator C-Mod tokamak discharges.

Statistical characterization of discrete conservative systems: The web map

NASA Astrophysics Data System (ADS)

Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino

2017-10-01

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.

Global helium particle balance in LHD

NASA Astrophysics Data System (ADS)

Motojima, G.; Masuzaki, S.; Tokitani, M.; Kasahara, H.; Yoshimura, Y.; Kobayashi, M.; Sakamoto, R.; Morisaki, T.; Miyazawa, J.; Akiyama, T.; Ohno, N.; Mutoh, T.; Yamada, H.; LHD Experiment Group

2015-08-01

Global helium particle balance in long-pulse discharges is analyzed for the first time in the Large Helical Device (LHD) with the plasma-facing components of the first wall and the divertor tiles composed of stainless steel and carbon, respectively. During the 2-min discharge sustained by ion cyclotron resonance heating (ICRH) and electron cyclotron heating (ECH), helium is observed to be highly retained in the wall (regarded as both the first wall and the divertor tiles). Almost all (about 96%) puffed helium particles (1.3 × 1022 He) are absorbed in the wall near the end of the discharge. Even though a dynamic retention is eliminated, 56% is still absorbed. The analysis is also applied to longer pulse discharges over 40 min by ICRH and ECH, indicating that the helium wall retention is dynamically changed in time. At the initial phase of the discharge, a mechanism for adsorbing helium other than dynamical retention is invoked.

Kinetic control of the coverage of oil droplets by DNA-functionalized colloids

PubMed Central

Joshi, Darshana; Bargteil, Dylan; Caciagli, Alessio; Burelbach, Jerome; Xing, Zhongyang; Nunes, André S.; Pinto, Diogo E. P.; Araújo, Nuno A. M.; Brujic, Jasna; Eiser, Erika

2016-01-01

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a “frozen” degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi–two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity. PMID:27532053

Statistical Mechanics of Turbulent Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

MHD Turbulence and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Symmetry, Statistics and Structure in MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2007-01-01

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

The ergodicity landscape of quantum theories

NASA Astrophysics Data System (ADS)

Ho, Wen Wei; Radičević, Đorđe

2018-02-01

This paper is a physicist’s review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here, we present a unified, graph-based view of all archetypical models of such universality (billiards, particles in random media, interacting spin or fermion systems). We find phenomenological relations between the onset of ergodicity (Gaussian-random delocalization of eigenstates) and the structure of the appropriate graphs, and we construct a heuristic picture of summing trajectories on graphs that describes why a generic interacting system should be ergodic. We also provide an operator-based discussion of quantum chaos and propose criteria to distinguish bases that can usefully diagnose ergodicity. The result of this analysis is a rough but systematic outline of how ergodicity changes across the space of all theories with a given Hilbert space dimension. As a particular example, we study the SYK model and report on the transition from maximal to partial ergodicity as the disorder strength is decreased.

Dynamic ELM and divertor control using resonant toroidal multi-mode magnetic fields in DIII-D and EAST

NASA Astrophysics Data System (ADS)

Sun, Youwen

2017-10-01

A rotating n = 2 Resonant Magnetic Perturbation (RMP) field combined with a stationary n = 3 RMP field has validated predictions that access to ELM suppression can be improved, while divertor heat and particle flux can also be dynamically controlled in DIII-D. Recent observations in the EAST tokamak indicate that edge magnetic topology changes, due to nonlinear plasma response to magnetic perturbations, play a critical role in accessing ELM suppression. MARS-F code MHD simulations, which include the plasma response to the RMP, indicate the nonlinear transition to ELM suppression is optimized by configuring the RMP coils to drive maximal edge stochasticity. Consequently, mixed toroidal multi-mode RMP fields, which produce more densely packed islands over a range of additional rational surfaces, improve access to ELM suppression, and further spread heat loading on the divertor. Beneficial effects of this multi-harmonic spectrum on ELM suppression have been validated in DIII-D. Here, the threshold current required for ELM suppression with a mixed n spectrum, where part of the n = 3 RMP field is replaced by an n = 2 field, is smaller than the case with pure n = 3 field. An important further benefit of this multi-mode approach is that significant changes of 3D particle flux footprint profiles on the divertor are found in the experiment during the application of a rotating n = 2 RMP field superimposed on a static n = 3 RMP field. This result was predicted by modeling studies of the edge magnetic field structure using the TOP2D code which takes into account plasma response from MARS-F code. These results expand physics understanding and potential effectiveness of the technique for reliably controlling ELMs and divertor power/particle loading distributions in future burning plasma devices such as ITER. Work supported by USDOE under DE-FC02-04ER54698 and NNSF of China under 11475224.

The Spherical Tokamak MEDUSA for Costa Rica

NASA Astrophysics Data System (ADS)

Ribeiro, Celso; Vargas, Ivan; Guadamuz, Saul; Mora, Jaime; Ansejo, Jose; Zamora, Esteban; Herrera, Julio; Chaves, Esteban; Romero, Carlos

2012-10-01

The former spherical tokamak (ST) MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R<0.14m, a<0.10m, BT<0.5T, Ip<40kA, 3ms pulse)[1] is in a process of donation to Costa Rica Institute of Technology. The main objective of MEDUSA is to train students in plasma physics /technical related issues which will help all tasks of the very low aspect ratio stellarator SCR-1(A≡R/>=3.6, under design[2]) and also the ongoing activities in low temperature plasmas. Courses in plasma physics at undergraduate and post-graduate joint programme levels are regularly conducted. The scientific programme is intend to clarify several issues in relevant physics for conventional and mainly STs, including transport, heating and current drive via Alfv'en wave, and natural divertor STs with ergodic magnetic limiter[3,4]. [1] G.D.Garstka, PhD thesis, University of Wisconsin at Madison, 1997 [2] L.Barillas et al., Proc. 19^th Int. Conf. Nucl. Eng., Japan, 2011 [3] C.Ribeiro et al., IEEJ Trans. Electrical and Electronic Eng., 2012(accepted) [4] C.Ribeiro et al., Proc. 39^th EPS Conf. Contr. Fusion and Plasma Phys., Sweden, 2012

Revealing nonergodic dynamics in living cells from a single particle trajectory

NASA Astrophysics Data System (ADS)

Lanoiselée, Yann; Grebenkov, Denis S.

2016-05-01

We propose the improved ergodicity and mixing estimators to identify nonergodic dynamics from a single particle trajectory. The estimators are based on the time-averaged characteristic function of the increments and can thus capture additional information on the process as compared to the conventional time-averaged mean-square displacement. The estimators are first investigated and validated for several models of anomalous diffusion, such as ergodic fractional Brownian motion and diffusion on percolating clusters, and nonergodic continuous-time random walks and scaled Brownian motion. The estimators are then applied to two sets of earlier published trajectories of mRNA molecules inside live Escherichia coli cells and of Kv2.1 potassium channels in the plasma membrane. These statistical tests did not reveal nonergodic features in the former set, while some trajectories of the latter set could be classified as nonergodic. Time averages along such trajectories are thus not representative and may be strongly misleading. Since the estimators do not rely on ensemble averages, the nonergodic features can be revealed separately for each trajectory, providing a more flexible and reliable analysis of single-particle tracking experiments in microbiology.

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-06-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω}. An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

NASA Astrophysics Data System (ADS)

Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

2018-01-01

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω} . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

Collision-induced evaporation of water clusters and contribution of momentum transfer

NASA Astrophysics Data System (ADS)

Calvo, Florent; Berthias, Francis; Feketeová, Linda; Abdoul-Carime, Hassan; Farizon, Bernadette; Farizon, Michel

2017-05-01

The evaporation of water molecules from high-velocity argon atoms impinging on protonated water clusters has been computationally investigated using molecular dynamics simulations with the reactive OSS2 potential to model water clusters and the ZBL pair potential to represent their interaction with the projectile. Swarms of trajectories and an event-by-event analysis reveal the conditions under which a specific number of molecular evaporation events is found one nanosecond after impact, thereby excluding direct knockout events from the analysis. These simulations provide velocity distributions that exhibit two main features, with a major statistical component arising from a global redistribution of the collision energy into intermolecular degrees of freedom, and another minor but non-ergodic feature at high velocities. The latter feature is produced by direct impacts on the peripheral water molecules and reflects a more complete momentum transfer. These two components are consistent with recent experimental measurements and confirm that electronic processes are not explicitly needed to explain the observed non-ergodic behavior. Contribution to the Topical Issue "Dynamics of Systems at the Nanoscale", edited by Andrey Solov'yov and Andrei Korol.

Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2010-01-01

Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures

High-resolution disruption halo current measurements using Langmuir probes in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Tinguely, R. A.; Granetz, R. S.; Berg, A.; Kuang, A. Q.; Brunner, D.; LaBombard, B.

2018-01-01

Halo currents generated during disruptions on Alcator C-Mod have been measured with Langmuir ‘rail’ probes. These rail probes are embedded in a lower outboard divertor module in a closely-spaced vertical (poloidal) array. The dense array provides detailed resolution of the spatial dependence (~1 cm spacing) of the halo current distribution in the plasma scrape-off region with high time resolution (400 kHz digitization rate). As the plasma limits on the outboard divertor plate, the contact point is clearly discernible in the halo current data (as an inversion of current) and moves vertically down the divertor plate on many disruptions. These data are consistent with filament reconstructions of the plasma boundary, from which the edge safety factor of the disrupting plasma can be calculated. Additionally, the halo current ‘footprint’ on the divertor plate is obtained and related to the halo flux width. The voltage driving halo current and the effective resistance of the plasma region through which the halo current flows to reach the probes are also investigated. Estimations of the sheath resistance and halo region resistivity and temperature are given. This information could prove useful for modeling halo current dynamics.

Divertor-localized fluctuations in NSTX-U L-mode discharges

NASA Astrophysics Data System (ADS)

Scotti, Filippo; Soukhanovskii, V. A.; Zweben, S.; Myra, J.; Baver, D.; Sabbagh, S. A.

2017-10-01

The 3-D structure of divertor turbulence is characterized in NSTX-U by means of fast camera imaging. Edge and divertor turbulence can be important in determining the heat flux width in fusion devices. Field-aligned filaments are found on the divertor legs via imaging of C III and D- α emission in NBI-heated diverted L-mode discharges, similar to observations in Alcator C-Mod and MAST. These flute-like fluctuations of up to 10-20% in RMS/mean are radially localized around the separatrix and limited to the region below the X-point. Poloidal and parallel correlation lengths are a few cm (10-50ρi) and several meters, respectively. For the outer leg filaments, poloidal correlation lengths decrease along the leg away from the strike point and typical effective toroidal mode numbers are in the range of 10-20. Opposite toroidal rotation is observed for inner (co-current rotation) and outer leg (counter-current rotation) filaments with apparent poloidal propagation of 1 km/s. The poloidal motion of outer leg filaments is opposite to the one typically observed for NSTX upstream blobs in the scrape-off layer. The shape, dynamics and absence of correlation with upstream turbulence suggest that these fluctuations are generated and localized in the divertor region. Supported by US DOE DE-AC52-07NA27344, DE-AC02-09CH11466, DE-FG02- 02ER54678, DE-FG02-99ER54524.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lumsdaine, A.; Bjorholm, T.; Harris, J.

The Wendelstein 7-X stellarator is in final stages of commissioning, and will begin operation in late 2015. In the first phase, the machine will operate with a limiter, and will be restricted to low power and short pulse. But in 2019, plans are for an actively cooled divertor to be installed, and the machine will operate in steady state at full power. Recently, plasma simulations have indicated that, in this final operational phase, a bootstrap current will evolve in certain scenarios. This will cause the sensitive ends of the divertor target to be overloaded beyond their qualified limit. A highmore » heat flux scraper element (HHF-SE) has been proposed in order to take up some of the convective flux and reduce the load on the divertor. In order to examine whether the HHF-SE will be able to effectively reduce the plasma flux in the divertor region of concern, and to determine how the pumping effectiveness will be affected by such a component, it is planned to include a test divertor unit scraper element (TDU-SE) in 2017 during an earlier operational phase. Several U.S. fusion energy science laboratories have been involved in the design, analysis (structural and thermal finite element, as well as computational fluid dynamics), plasma simulation, planning, prototyping, and diagnostic development around the scraper element program (both TDU-SE and HHF-SE). As a result, this paper presents an overview of all of these activities and their current status.« less

Overview of design and analysis activities for the W7-X scraper element

DOE PAGES

Lumsdaine, A.; Bjorholm, T.; Harris, J.; ...

2016-08-18

The Wendelstein 7-X stellarator is in final stages of commissioning, and will begin operation in late 2015. In the first phase, the machine will operate with a limiter, and will be restricted to low power and short pulse. But in 2019, plans are for an actively cooled divertor to be installed, and the machine will operate in steady state at full power. Recently, plasma simulations have indicated that, in this final operational phase, a bootstrap current will evolve in certain scenarios. This will cause the sensitive ends of the divertor target to be overloaded beyond their qualified limit. A highmore » heat flux scraper element (HHF-SE) has been proposed in order to take up some of the convective flux and reduce the load on the divertor. In order to examine whether the HHF-SE will be able to effectively reduce the plasma flux in the divertor region of concern, and to determine how the pumping effectiveness will be affected by such a component, it is planned to include a test divertor unit scraper element (TDU-SE) in 2017 during an earlier operational phase. Several U.S. fusion energy science laboratories have been involved in the design, analysis (structural and thermal finite element, as well as computational fluid dynamics), plasma simulation, planning, prototyping, and diagnostic development around the scraper element program (both TDU-SE and HHF-SE). As a result, this paper presents an overview of all of these activities and their current status.« less

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.

Equality of the Spectral and Dynamical Definitions of Reflection

NASA Astrophysics Data System (ADS)

Breuer, Jonathan; Ryckman, Eric; Simon, Barry

2010-04-01

For full-line Jacobi matrices, Schrödinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of m-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x = -∞ as t → -∞ goes entirely to x = ∞ as t → ∞. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

Chirikov, Boris V.

1993-01-01

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Efficiency bounds for nonequilibrium heat engines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehta, Pankaj; Polkovnikov, Anatoli, E-mail: asp@bu.edu

2013-05-15

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodicmore » engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. -- Highlights: ► Derived efficiency bounds for heat engines working with a single reservoir. ► Analyzed both ergodic and non-ergodic engines. ► Showed that non-ergodic engines can be more efficient. ► Extended fundamental thermodynamic relation to arbitrary nonequilibrium processes.« less

Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

NASA Astrophysics Data System (ADS)

Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua

2018-06-01

Allee effect can interact with environment stochasticity and is active when population numbers are small. Our goal of this paper is to investigate such effect on population dynamics. More precisely, we develop and investigate a stochastic single species model with Allee effect under regime switching. We first prove the existence of global positive solution of the model. Then, we perform the survival analysis to seek sufficient conditions for the extinction, non-persistence in mean, persistence in mean and stochastic permanence. By constructing a suitable Lyapunov function, we show that the model is positive recurrent and ergodic. Our results indicate that the regime switching can suppress the extinction of the species. Finally, numerical simulations are carried out to illustrate the obtained theoretical results, where a real-life example is also discussed showing the inclusion of Allee effect in the model provides a better match to the data.

On the analogues of Szegő's theorem for ergodic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirsch, W; Pastur, L A

2015-01-31

Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.

Ergodic Transition in a Simple Model of the Continuous Double Auction

PubMed Central

Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

2014-01-01

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen. PMID:24558377

Ergodic transition in a simple model of the continuous double auction.

PubMed

Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico

2014-01-01

We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen.

A statistical evaluation of non-ergodic variogram estimators

USGS Publications Warehouse

Curriero, F.C.; Hohn, M.E.; Liebhold, A.M.; Lele, S.R.

2002-01-01

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.

Advanced divertor configurations with large flux expansion

NASA Astrophysics Data System (ADS)

Soukhanovskii, V. A.; Bell, R. E.; Diallo, A.; Gerhardt, S.; Kaye, S.; Kolemen, E.; LeBlanc, B. P.; McLean, A.; Menard, J. E.; Paul, S. F.; Podesta, M.; Raman, R.; Ryutov, D. D.; Scotti, F.; Kaita, R.; Maingi, R.; Mueller, D. M.; Roquemore, A. L.; Reimerdes, H.; Canal, G. P.; Labit, B.; Vijvers, W.; Coda, S.; Duval, B. P.; Morgan, T.; Zielinski, J.; De Temmerman, G.; Tal, B.

2013-07-01

Experimental studies of the novel snowflake divertor concept (D. Ryutov, Phys. Plasmas 14 (2007) 064502) performed in the NSTX and TCV tokamaks are reviewed in this paper. The snowflake divertor enables power sharing between divertor strike points, as well as the divertor plasma-wetted area, effective connection length and divertor volumetric power loss to increase beyond those in the standard divertor, potentially reducing heat flux and plasma temperature at the target. It also enables higher magnetic shear inside the separatrix, potentially affecting pedestal MHD stability. Experimental results from NSTX and TCV confirm the predicted properties of the snowflake divertor. In the NSTX, a large spherical tokamak with a compact divertor and lithium-coated graphite plasma-facing components (PFCs), the snowflake divertor operation led to reduced core and pedestal impurity concentration, as well as re-appearance of Type I ELMs that were suppressed in standard divertor H-mode discharges. In the divertor, an otherwise inaccessible partial detachment of the outer strike point with an up to 50% increase in divertor radiation and a peak divertor heat flux reduction from 3-7 MW/m2 to 0.5-1 MW/m2 was achieved. Impulsive heat fluxes due to Type-I ELMs were significantly dissipated in the high magnetic flux expansion region. In the TCV, a medium-size tokamak with graphite PFCs, several advantageous snowflake divertor features (cf. the standard divertor) have been demonstrated: an unchanged L-H power threshold, enhanced stability of the peeling-ballooning modes in the pedestal region (and generally an extended second stability region), as well as an H-mode pedestal regime with reduced (×2-3) Type I ELM frequency and slightly increased (20-30%) normalized ELM energy, resulting in a favorable average energy loss comparison to the standard divertor. In the divertor, ELM power partitioning between snowflake divertor strike points was demonstrated. The NSTX and TCV experiments are providing support for the snowflake divertor as a viable solution for the outstanding tokamak plasma-material interface issues.

Snowflake divertor configuration studies for NSTX-Upgrade

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soukhanovskii, V A

2011-11-12

Snowflake divertor experiments in NSTX provide basis for PMI development toward NSTX-Upgrade. Snowflake configuration formation was followed by radiative detachment. Significant reduction of steady-state divertor heat flux observed in snowflake divertor. Impulsive heat loads due to Type I ELMs are partially mitigated in snowflake divertor. Magnetic control of snowflake divertor configuration is being developed. Plasma material interface development is critical for NSTX-U success. Four divertor coils should enable flexibility in boundary shaping and control in NSTX-U. Snowflake divertor experiments in NSTX provide good basis for PMI development in NSTX-Upgrade. FY 2009-2010 snowflake divertor experiments in NSTX: (1) Helped understand controlmore » of magnetic properties; (2) Core H-mode confinement unchanged; (3) Core and edge carbon concentration reduced; and (4) Divertor heat flux significantly reduced - (a) Steady-state reduction due to geometry and radiative detachment, (b) Encouraging results for transient heat flux handling, (c) Combined with impurity-seeded radiative divertor. Outlook for snowflake divertor in NSTX-Upgrade: (1) 2D fluid modeling of snowflake divertor properties scaling - (a) Edge and divertor transport, radiation, detachment threshold, (b) Compatibility with cryo-pump and lithium conditioning; (2) Magnetic control development; and (3) PFC development - PFC alignment and PFC material choice.« less

Calculations of Helium Bubble Evolution in the PISCES Experiments with Cluster Dynamics

NASA Astrophysics Data System (ADS)

Blondel, Sophie; Younkin, Timothy; Wirth, Brian; Lasa, Ane; Green, David; Canik, John; Drobny, Jon; Curreli, Davide

2017-10-01

Plasma surface interactions in fusion tokamak reactors involve an inherently multiscale, highly non-equilibrium set of phenomena, for which current models are inadequate to predict the divertor response to and feedback on the plasma. In this presentation, we describe the latest code developments of Xolotl, a spatially-dependent reaction diffusion cluster dynamics code to simulate the divertor surface response to fusion-relevant plasma exposure. Xolotl is part of a code-coupling effort to model both plasma and material simultaneously; the first benchmark for this effort is the series of PISCES linear device experiments. We will discuss the processes leading to surface morphology changes, which further affect erosion, as well as how Xolotl has been updated in order to communicate with other codes. Furthermore, we will show results of the sub-surface evolution of helium bubbles in tungsten as well as the material surface displacement under these conditions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umansky, M. V.; Ryutov, D. D.

Reduced MHD equations are used for studying toroidally symmetric plasma dynamics near the divertor null point. Numerical solution of these equations exhibits a plasma vortex localized at the null point with the time-evolution defined by interplay of the curvature drive, magnetic restoring force, and dissipation. Convective motion is easier to achieve for a second-order null (snowflake) divertor than for a regular x-point configuration, and the size of the convection zone in a snowflake configuration grows with plasma pressure at the null point. In conclusion, the trends in simulations are consistent with tokamak experiments which indicate the presence of enhanced transportmore » at the null point.« less

Developing snowflake divertor physics basis in the DIII-D, NSTX and NSTX-U tokamaks aimed at the divertor power exhaust solution [Snowflake divertor experiments in the DIII-D, NSTX and NSTX-U tokamaks aimed at the development of the divertor power exhaust solution

DOE PAGES

Soukhanovskii, V. A.; Allen, S. L.; Fenstermacher, M. E.; ...

2016-06-02

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment were performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large ELMs. However, a stable partial detachment of the outer strike pointmore » was also achieved where inter-ELM peak heat flux was reduced by factors 3-5, and peak ELM heat flux was reduced by up to 80% (cf. standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower n e, and ELM energy and divertor peak heat flux reduction, especially prominent in radiative D 2-seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative D 2-seeded SF divertor at P SOL = 3 - 4 MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multi-fluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected P SOL ≃9 MW case. In conclusion, the radiative SF divertor with carbon impurity provides a wider n e operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar q peak reduction factors (cf. standard divertor).« less

Developing physics basis for the snowflake divertor in the DIII-D tokamak

DOE PAGES

Soukhanovskii, V. A.; Allen, S. L.; Fenstermacher, M. E.; ...

2018-02-01

Recent DIII-D results demonstrate that the snowflake (SF) divertor geometry (cf. standard divertor) enables significant manipulation of divertor heat transport for heat spreading and reduction in attached and radiative divertor regimes, between and during edge localized modes (ELMs), while maintaining good H-mode confinement. Snowflake divertor configurations have been realized in the DIII-D tokamak for several seconds in H-mode discharges with heating power PNBImore » $$\\leqslant$$ 4-5 MW and a range of plasma currents Ip = 0.8-1.2 MA. In this work, inter-ELM transport and radiative SF divertor properties are studied. Significant impact of geometric properties on SOL and divertor plasma parameters, including increased poloidal magnetic flux expansion, divertor magnetic field line length and divertor volume, is confirmed. In the SF-minus configuration, heat deposition is affected by the geometry, and peak divertor heat fluxes are significantly reduced. In the SF-plus and near-exact SF configurations, divertor peak heat flux reduction and outer strike point heat flux profile broadening are observed. Inter-ELM sharing of power and particle fluxes between the main and additional snowflake divertor strike points has been demonstrated. The additional strike points typically receive up to 10-15% of total outer divertor power. Measurements of electron pressure and poloidal beta !p support the theoretically proposed churning mode that is driven by toroidal curvature and vertical pressure gradient in the weak poloidal field region. A comparison of the 4-4.5 MW NBI-heated H-mode plasmas with radiative SF divertor and the standard radiative divertor (both induced with additional gas puffing) shows a nearly complete power detachment and broader divertor radiated power distribution in the SF, as compared to a partial detachment and peaked localized radiation in the standard divertor. However, insignificant difference in the detachment onset w.r.t. density between the SF and the standard divertor was found. The results complement the initial SF divertor studies in the NSTX and DIII-D tokamaks and contribute to the physics basis of the SF divertor as a power exhaust concept for future tokamaks.« less

Developing physics basis for the snowflake divertor in the DIII-D tokamak

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soukhanovskii, V. A.; Allen, S. L.; Fenstermacher, M. E.

Recent DIII-D results demonstrate that the snowflake (SF) divertor geometry (cf. standard divertor) enables significant manipulation of divertor heat transport for heat spreading and reduction in attached and radiative divertor regimes, between and during edge localized modes (ELMs), while maintaining good H-mode confinement. Snowflake divertor configurations have been realized in the DIII-D tokamak for several seconds in H-mode discharges with heating power PNBImore » $$\\leqslant$$ 4-5 MW and a range of plasma currents Ip = 0.8-1.2 MA. In this work, inter-ELM transport and radiative SF divertor properties are studied. Significant impact of geometric properties on SOL and divertor plasma parameters, including increased poloidal magnetic flux expansion, divertor magnetic field line length and divertor volume, is confirmed. In the SF-minus configuration, heat deposition is affected by the geometry, and peak divertor heat fluxes are significantly reduced. In the SF-plus and near-exact SF configurations, divertor peak heat flux reduction and outer strike point heat flux profile broadening are observed. Inter-ELM sharing of power and particle fluxes between the main and additional snowflake divertor strike points has been demonstrated. The additional strike points typically receive up to 10-15% of total outer divertor power. Measurements of electron pressure and poloidal beta !p support the theoretically proposed churning mode that is driven by toroidal curvature and vertical pressure gradient in the weak poloidal field region. A comparison of the 4-4.5 MW NBI-heated H-mode plasmas with radiative SF divertor and the standard radiative divertor (both induced with additional gas puffing) shows a nearly complete power detachment and broader divertor radiated power distribution in the SF, as compared to a partial detachment and peaked localized radiation in the standard divertor. However, insignificant difference in the detachment onset w.r.t. density between the SF and the standard divertor was found. The results complement the initial SF divertor studies in the NSTX and DIII-D tokamaks and contribute to the physics basis of the SF divertor as a power exhaust concept for future tokamaks.« less

Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins

NASA Astrophysics Data System (ADS)

Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain

2015-03-01

We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).

Quasi-equilibria in reduced Liouville spaces.

PubMed

Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon

2012-06-14

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

Snowflake divertor experiments in the DIII-D, NSTX, and NSTX-U tokamaks aimed at the development of the divertor power exhaust solution

DOE PAGES

Soukhanovskii, V. A.; Allen, S. L.; Fenstermacher, M. E.; ...

2016-11-16

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in the future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment was performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large Edge Localized Modes (ELMs). However, a stable partial detachment ofmore » the outer strike point was also achieved where inter-ELM peak heat flux was reduced by factors 3-5, and peak ELM heat flux was reduced by up to 80% (see standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower ne, and ELM energy and divertor peak heat flux reduction, especially prominent in radiative D 2-seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative D 2-seeded SF divertor at PSOL = 3 - 4 MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multifluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected PSOL ≃ 9 MW case. Furthermore, the radiative SF divertor with carbon impurity provides a wider ne operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar q peak reduction factors (see standard divertor).« less

Developing physics basis for the snowflake divertor in the DIII-D tokamak

NASA Astrophysics Data System (ADS)

Soukhanovskii, V. A.; Allen, S. L.; Fenstermacher, M. E.; Lasnier, C. J.; Makowski, M. A.; McLean, A. G.; Meyer, W. H.; Ryutov, D. D.; Kolemen, E.; Groebner, R. J.; Hyatt, A. W.; Leonard, A. W.; Osborne, T. H.; Petrie, T. W.; Watkins, J.

2018-03-01

Recent DIII-D results demonstrate that the snowflake (SF) divertor geometry (see standard divertor) enables significant manipulation of divertor heat transport for heat spreading and reduction in attached and radiative divertor regimes, between and during edge localized modes (ELMs), while maintaining good H-mode confinement. Snowflake divertor configurations have been realized in the DIII-D tokamak for several seconds in H-mode discharges with heating power P_NBI ≤slant 4 -5 MW and a range of plasma currents I_p=0.8-1.2 MA. In this work, inter-ELM transport and radiative SF divertor properties are studied. Significant impact of geometric properties on SOL and divertor plasma parameters, including increased poloidal magnetic flux expansion, divertor magnetic field line length and divertor volume, is confirmed. In the SF-minus configuration, heat deposition is affected by the geometry, and peak divertor heat fluxes are significantly reduced. In the SF-plus and near-exact SF configurations, divertor peak heat flux reduction and outer strike point heat flux profile broadening are observed. Inter-ELM sharing of power and particle fluxes between the main and additional snowflake divertor strike points has been demonstrated. The additional strike points typically receive up to 10-15% of total outer divertor power. Measurements of electron pressure and poloidal beta βp support the theoretically proposed churning mode that is driven by toroidal curvature and vertical pressure gradient in the weak poloidal field region. A comparison of the 4-4.5 MW NBI-heated H-mode plasmas with radiative SF divertor and the standard radiative divertor (both induced with additional gas puffing) shows a nearly complete power detachment and broader divertor radiated power distribution in the SF, as compared to a partial detachment and peaked localized radiation in the standard divertor. However, insignificant difference in the detachment onset w.r.t. density between the SF and the standard divertor was found. The results complement the initial SF divertor studies conducted in high-power H-mode discharges in the NSTX and DIII-D tokamaks, and, along with snowflake divertor results from TCV and other tokamaks, contribute to the physics basis of the SF divertor as a power exhaust concept for future high power density tokamaks.

The Quest for the Ultimate Anisotropic Banach Space

NASA Astrophysics Data System (ADS)

Baladi, Viviane

2017-02-01

We present a new scale U^{t,s}_p (s<-t<0 and 1≤p <∞) of anisotropic Banach spaces, defined via Paley-Littlewood, on which the transfer operator L_g φ = (g \\cdot φ) circ T^{-1} associated to a hyperbolic dynamical system T has good spectral properties. When p=1 and t is an integer, the spaces are analogous to the "geometric" spaces B^{t,|s+t|} considered by Gouëzel and Liverani (Ergod Theory Dyn Syst 26:189-217, 2006). When p>1 and -1+1/p

Quantifying time-of-flight-resolved optical field dynamics in turbid media with interferometric near-infrared spectroscopy (iNIRS) (Conference Presentation)

NASA Astrophysics Data System (ADS)

Borycki, Dawid; Kholiqov, Oybek; Zhou, Wenjun; Srinivasan, Vivek J.

2017-03-01

Sensing and imaging methods based on the dynamic scattering of coherent light, including laser speckle, laser Doppler, and diffuse correlation spectroscopy quantify scatterer motion using light intensity (speckle) fluctuations. The underlying optical field autocorrelation (OFA), rather than being measured directly, is typically inferred from the intensity autocorrelation (IA) through the Siegert relationship, by assuming that the scattered field obeys Gaussian statistics. In this work, we demonstrate interferometric near-infrared spectroscopy (iNIRS) for measurement of time-of-flight (TOF) resolved field and intensity autocorrelations in fluid tissue phantoms and in vivo. In phantoms, we find a breakdown of the Siegert relationship for short times-of-flight due to a contribution from static paths whose optical field does not decorrelate over experimental time scales, and demonstrate that eliminating such paths by polarization gating restores the validity of the Siegert relationship. Inspired by these results, we developed a method, called correlation gating, for separating the OFA into static and dynamic components. Correlation gating enables more precise quantification of tissue dynamics. To prove this, we show that iNIRS and correlation gating can be applied to measure cerebral hemodynamics of the nude mouse in vivo using dynamically scattered (ergodic) paths and not static (non-ergodic) paths, which may not be impacted by blood. More generally, correlation gating, in conjunction with TOF resolution, enables more precise separation of diffuse and non-diffusive contributions to OFA than is possible with TOF resolution alone. Finally, we show that direct measurements of OFA are statistically more efficient than indirect measurements based on IA.

Modeling of combined effects of divertor closure and advanced magnetic configuration on detachment in DIII-D by SOLPS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Si, Hang; Guo, Houyang Y.; Covele, Brent

One of the major challenges facing the design and operation of next-step high-power steady-state fusion devices is to develop a divertor solution for handling power exhaust, while ensuring acceptable divertor target plate erosion, which necessitates access to divertor detachment at relative low main plasma densities compatible with current drive and high plasma confinement. Detailed modeling with SOLPS is carried out to examine the effect of divertor closure on detachment with the normal single null divertor (SD) configuration, as well as one of the advanced divertor configurations, such as x-divertor (XD) respectively. The SOLPS modeling for a high confinement plasma in DIII-D finds that increasing divertor closure with SD reduces the upstream separatrix density at the onset of detachment frommore » $$1.18\\times {{10}^{19}}\\,{{{\\rm m}}^{-3}}$$ to $$0.88\\times {{10}^{19}}\\,{{{\\rm m}}^{-3}}$$. Furthermore, coupling the divertor closure with XD further promotes the onset of divertor detachment at a still lower upstream separatrix density, down to the value of $$0.67\\times {{10}^{19}}\\,{{{\\rm m}}^{-3}}$$, thus, showing that divertor closure and advanced magnetic configuration can work synergistically to facilitate divertor detachment.« less

Modeling of combined effects of divertor closure and advanced magnetic configuration on detachment in DIII-D by SOLPS

DOE PAGES

Si, Hang; Guo, Houyang Y.; Covele, Brent; ...

2018-04-04

One of the major challenges facing the design and operation of next-step high-power steady-state fusion devices is to develop a divertor solution for handling power exhaust, while ensuring acceptable divertor target plate erosion, which necessitates access to divertor detachment at relative low main plasma densities compatible with current drive and high plasma confinement. Detailed modeling with SOLPS is carried out to examine the effect of divertor closure on detachment with the normal single null divertor (SD) configuration, as well as one of the advanced divertor configurations, such as x-divertor (XD) respectively. The SOLPS modeling for a high confinement plasma in DIII-D finds that increasing divertor closure with SD reduces the upstream separatrix density at the onset of detachment frommore » $$1.18\\times {{10}^{19}}\\,{{{\\rm m}}^{-3}}$$ to $$0.88\\times {{10}^{19}}\\,{{{\\rm m}}^{-3}}$$. Furthermore, coupling the divertor closure with XD further promotes the onset of divertor detachment at a still lower upstream separatrix density, down to the value of $$0.67\\times {{10}^{19}}\\,{{{\\rm m}}^{-3}}$$, thus, showing that divertor closure and advanced magnetic configuration can work synergistically to facilitate divertor detachment.« less

Modeling of combined effects of divertor closure and advanced magnetic configuration on detachment in DIII-D by SOLPS

NASA Astrophysics Data System (ADS)

Si, H.; Guo, H. Y.; Covele, B.; Leonard, A. W.; Watkins, J. G.; Thomas, D.; Ding, R.

2018-05-01

One of the major challenges facing the design and operation of next-step high-power steady-state fusion devices is to develop a divertor solution for handling power exhaust, while ensuring acceptable divertor target plate erosion, which necessitates access to divertor detachment at relative low main plasma densities compatible with current drive and high plasma confinement. Detailed modeling with SOLPS is carried out to examine the effect of divertor closure on detachment with the normal single null divertor (SD) configuration, as well as one of the advanced divertor configurations, such as x-divertor (XD) respectively. The SOLPS modeling for a high confinement plasma in DIII-D finds that increasing divertor closure with SD reduces the upstream separatrix density at the onset of detachment from 1.18× {{10}19} {{m}-3} to 0.88× {{10}19} {{m}-3} . Moreover, coupling the divertor closure with XD further promotes the onset of divertor detachment at a still lower upstream separatrix density, down to the value of 0.67× {{10}19} {{m}-3} , thus, showing that divertor closure and advanced magnetic configuration can work synergistically to facilitate divertor detachment.

Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions

NASA Astrophysics Data System (ADS)

Hezari, Hamid

2018-02-01

We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.

Integrability versus Thermalizability in Isolated Quantum Systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim

2012-02-01

The purpose of this presentation is to assess the status of our understanding of the transition from integrability to thermalizability in isolated quantum systems. In Classical Mechanics, the boundary stripe between the two is relatively sharp: its integrability edge is marked by the appearance of finite Lyapunov's exponents that further converge to a unique value when the ergodicity edge is reached. Classical ergodicity is a universal property: if a system is ergodic, then every observable attains its microcanonical value in the infinite time average over the trajectory. On the contrary, in Quantum Mechanics, Lyapunov's exponents are always zero. Furthermore, since quantum dynamics necessarily invokes coherent superpositions of eigenstates of different energy, projectors to the eigenstates become more relevant; those in turn never thermalize. All of the above indicates that in quantum many-body systems, (a) the integrability-thermalizability transition is smooth, and (b) the degree of thermalizability is not absolute like in classical mechanics, but it is relative to the class of observables of interest. In accordance with these observations, we propose a concrete measure of the degree of quantum thermalizability, consistent with the expected empirical manifestations of it. As a practical application of this measure, we devise a unified recipe for choosing an optimal set of conserved quantities to govern the after-relaxation values of observables, in both integrable quantum systems and in quantum systems in between integrable and thermalizable.

Broken Ergodicity in MHD Turbulence in a Spherical Domain

NASA Technical Reports Server (NTRS)

Shebalin, John V.; wang, Yifan

2011-01-01

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

A review of radiative detachment studies in tokamak advanced magnetic divertor configurations

DOE PAGES

Soukhanovskii, V. A.

2017-04-28

The present vision for a plasma–material interface in the tokamak is an axisymmetric poloidal magnetic X-point divertor. Four tasks are accomplished by the standard poloidal X-point divertor: plasma power exhaust; particle control (D/T and He pumping); reduction of impurity production (source); and impurity screening by the divertor scrape-off layer. A low-temperature, low heat flux divertor operating regime called radiative detachment is viewed as the main option that addresses these tasks for present and future tokamaks. Advanced magnetic divertor configuration has the capability to modify divertor parallel and cross-field transport, radiative and dissipative losses, and detachment front stability. Advanced magnetic divertormore » configurations are divided into four categories based on their salient qualitative features: (1) multiple standard X-point divertors; (2) divertors with higher order nulls; (3) divertors with multiple X-points; and (4) long poloidal leg divertors (and also with multiple X-points). As a result, this paper reviews experiments and modeling in the area of radiative detachment in the advanced magnetic divertor configurations.« less

A review of radiative detachment studies in tokamak advanced magnetic divertor configurations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soukhanovskii, V. A.

The present vision for a plasma–material interface in the tokamak is an axisymmetric poloidal magnetic X-point divertor. Four tasks are accomplished by the standard poloidal X-point divertor: plasma power exhaust; particle control (D/T and He pumping); reduction of impurity production (source); and impurity screening by the divertor scrape-off layer. A low-temperature, low heat flux divertor operating regime called radiative detachment is viewed as the main option that addresses these tasks for present and future tokamaks. Advanced magnetic divertor configuration has the capability to modify divertor parallel and cross-field transport, radiative and dissipative losses, and detachment front stability. Advanced magnetic divertormore » configurations are divided into four categories based on their salient qualitative features: (1) multiple standard X-point divertors; (2) divertors with higher order nulls; (3) divertors with multiple X-points; and (4) long poloidal leg divertors (and also with multiple X-points). As a result, this paper reviews experiments and modeling in the area of radiative detachment in the advanced magnetic divertor configurations.« less

Numerical exploration of non-axisymmetric divertor closure in the small angle slot (SAS) divertor at DIII-D

NASA Astrophysics Data System (ADS)

Frerichs, H.; Schmitz, O.; Covele, B.; Feng, Y.; Guo, H. Y.; Hill, D.

2018-05-01

Numerical simulations of toroidal asymmetries in a tightly baffled small angle slot (SAS) divertor on the DIII-D tokamak show that toroidal asymmetries in divertor closure result in (non-axisymmetric) local onset of detachment within a density window of 10-15% on top of the nominal threshold separatrix density. The SAS divertor is explored at DIII-D for improving access to cold, dissipative/detached divertor conditions. The narrow width of the slot divertor coupled with a small magnetic field line-to-target angle facilitates the buildup of neutral density, thereby increasing radiative and neutrals-related (atoms and molecules) losses in the divertor. Small changes in the strike point location can be expected to have a large impact on divertor conditions. The combination of misaligned slot structure and non-axisymmetric perturbations to the magnetic field configuration causes the strike point to move along the divertor target plate, possibly leaving the divertor slot at some locations. The latter extreme case essentially introduces an opening in the divertor slot from where recycling neutrals can easily escape, and thereby degrade the performance of the slot divertor. Such a strike point dislocation is approximated by a finite gap in the divertor baffle for which 3D edge plasma and neutral gas simulations are performed with the EMC3-EIRENE code.

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

NASA Astrophysics Data System (ADS)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh

2013-10-01

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical "metric," the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes.

Plasma detachment in divertor tokamaks

NASA Astrophysics Data System (ADS)

Leonard, A. W.

2018-04-01

Observations of divertor plasma detachment in tokamaks are reviewed. Plasma detachment is characterized in terms of transport and dissipation of power, momentum and particle flux along the open field lines from the midplane to the divertor. Asymmetries in detachment onset and other characteristics between the inboard and outboard divertor plasmas is found to be primarily driven by plasma E× B drifts. The effect of divertor plate geometry and magnetic configuration on divertor detachment is summarized. Control of divertor detachment has progressed with a development of a number of diagnostics to characterize the detached state in real-time. Finally the compatibility of detached divertor operation with high performance core plasmas is examined.

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

NASA Technical Reports Server (NTRS)

Helleman, R. H. G.

1980-01-01

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

SOLPS modeling of the effect on plasma detachment of closing the lower divertor in DIII-D

DOE PAGES

Sang, C. F.; Stangeby, P. C.; Guo, H. Y.; ...

2016-12-15

SOLPS modeling has been carried out to assess the effect of tightly closing the lower divertor in DIII-D, which at present is almost fully open, on the achievement of cold dissipative/detached divertor conditions. To isolate the impact of other factors on the divertor plasma solution and to make direct comparisons, most of the parameters including the meshes were kept as similar as possible. Only the neutral baffling was modified to compare a fully open divertor with a tightly closed one. The modeling shows that the tightly closed divertor greatly improves trapping of recycling neutrals, thereby increasing radiative and charge exchangemore » losses in the divertor and reducing the electron temperature T et and deposited power density q dep at the target plate. Furthermore, the closed structure enables the divertor plasma to enter into highly dissipative and detached divertor conditions at a significantly lower upstream density. The effects of divertor closure on the neutral density and pressure, and their correlation with the divertor plasma conditions are also demonstrated. The effect of molecular D 2- ion D + elastic collisions and neutral-neutral collisions on the divertor plasma solution are assessed.« less

Comparison study of toroidal-field divertors for a compact reversed-field pinch reactor

NASA Astrophysics Data System (ADS)

Bathke, C. G.; Krakowski, R. A.; Miller, R. L.

Two divertor configurations for the Compact Reversed-Field Pinch Reactor (CRFPR) based on diverting the minority (toroidal) field have been reported. A critical factor in evaluating the performance of both poloidally symmetric and bundle divertor configurations is the accurate determination of the divertor connection length and the monitoring of magnetic islands introduced by the divertors, the latter being a three-dimensional effect. To this end the poloidal-field, toroidal-field, and divertor coils and the plasma currents are simulated in three dimensions for field-line trackings in both the divertor channel and the plasma-edge regions. The results of this analysis indicate a clear preference for the poloidally symmetric toroidal-field divertor. Design modifications to the limiter-based CRFPR design that accommodate this divertor are presented.

Dynamics of a stochastic HIV-1 infection model with logistic growth

NASA Astrophysics Data System (ADS)

Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan

2017-03-01

This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.

A statistical mechanical model of economics

NASA Astrophysics Data System (ADS)

Lubbers, Nicholas Edward Williams

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex microstructure effects to develop high-performance materials, but general microstructure quantification is an unsolved problem. Motivated by statistical physics, I envision microstructure as a low-dimensional manifold, and construct this manifold by leveraging multiple machine learning approaches including transfer learning, dimensionality reduction, and computer vision breakthroughs with convolutional neural networks.

Ergodicity, configurational entropy and free energy in pigment solutions and plant photosystems: influence of excited state lifetime.

PubMed

Jennings, Robert C; Zucchelli, Giuseppe

2014-01-01

We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.

On the relationship between cell cycle analysis with ergodic principles and age-structured cell population models.

PubMed

Kuritz, K; Stöhr, D; Pollak, N; Allgöwer, F

2017-02-07

Cyclic processes, in particular the cell cycle, are of great importance in cell biology. Continued improvement in cell population analysis methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell omics made mathematical methods based on ergodic principles a powerful tool in studying these processes. In this paper, we establish the relationship between cell cycle analysis with ergodic principles and age structured population models. To this end, we describe the progression of a single cell through the cell cycle by a stochastic differential equation on a one dimensional manifold in the high dimensional dataspace of cell cycle markers. Given the assumption that the cell population is in a steady state, we derive transformation rules which transform the number density on the manifold to the steady state number density of age structured population models. Our theory facilitates the study of cell cycle dependent processes including local molecular events, cell death and cell division from high dimensional "snapshot" data. Ergodic analysis can in general be applied to every process that exhibits a steady state distribution. By combining ergodic analysis with age structured population models we furthermore provide the theoretic basis for extensions of ergodic principles to distribution that deviate from their steady state. Copyright © 2016 Elsevier Ltd. All rights reserved.

Plasma detachment in divertor tokamaks

DOE PAGES

Leonard, A. W.

2018-02-07

In this study, observations of divertor plasma detachment in tokamaks are reviewed. Plasma detachment is characterized in terms of transport and dissipation of power, momentum and particle flux along the open field lines from the midplane to the divertor. Asymmetries in detachment onset and other characteristics between the inboard and outboard divertor plasmas is found to be primarily driven by plasmamore » $$\\vec{E}$$ x $$\\vec{B}$$ drifts. The effect of divertor plate geometry and magnetic configuration on divertor detachment is summarized. Control of divertor detachment has progressed with a development of a number of diagnostics to characterize the detached state in real-time. Finally the compatibility of detached divertor operation with high performance core plasmas is examined.« less

Plasma detachment in divertor tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leonard, A. W.

In this study, observations of divertor plasma detachment in tokamaks are reviewed. Plasma detachment is characterized in terms of transport and dissipation of power, momentum and particle flux along the open field lines from the midplane to the divertor. Asymmetries in detachment onset and other characteristics between the inboard and outboard divertor plasmas is found to be primarily driven by plasmamore » $$\\vec{E}$$ x $$\\vec{B}$$ drifts. The effect of divertor plate geometry and magnetic configuration on divertor detachment is summarized. Control of divertor detachment has progressed with a development of a number of diagnostics to characterize the detached state in real-time. Finally the compatibility of detached divertor operation with high performance core plasmas is examined.« less

Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Cosme, Jayson G.

2018-04-01

We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of the underlying mean-field trajectories. The observed prethermalization scenario can be attributed to different stages of glassy dynamics in the mode-time configuration space due to dynamical phase transition between ergodic and nonergodic trajectories.

Characterization of microstructure, viscoelasticity, heterogeneity and ergodicity in pectin-laponite-CTAB-calcium nanocomposite hydrogels.

PubMed

Joshi, Nidhi; Rawat, Kamla; Bohidar, H B

2016-01-20

In order to customize the viscoelastic properties of pectin gels, it is necessary to work on a composite platform. Herein, the gelation kinetics, and viscoelastic characterization of anionic polysaccharide pectin dispersion prepared in presence of nanoclay laponite are reported using dynamic light scattering and rheology measurements. The ratio Rg/Rh (Rg and Rh are radius of gyration and hydrodynamic radius respectively) determined from light scattering data revealed the presence of random coils of pectin chains inside the gel matrix. When nanoclay laponite was added to the pectin chains solution, two-phase separation was noticed instantaneously. Therefore, the surfactant cetyltrimethylammonium bromide [CTAB] was added to exfoliate the clay platelets in the dispersion, and also in its gel phase. The exfoliating agent cetyltrimethylammonium bromide ([CTAB]≈ cmc/10) helped to enhance the homogeneity and stability of the pectin-clay sols and gels. The storage and loss moduli (G' and G") of the composite gel changed significantly as function of nanoclay laponite content for concentration up to 0.03% (w/v) causing the softening of the gels (gel strength reduced by close to 50%) compared to pectin-calcium gel. However, as the concentration of nanoclay laponite was maintained between 0.01% and 0.03% (w/v), the gel rigidity (G') recovered by 30% (35-45 Pa). The transition from ergodic to non-ergodic state occurred during sol-gel transition owing to the presence of the nanoclay laponite. The gelation time was not too different from the ergodicity breaking time. Thus, the presence of nanoclay laponite in such minute concentration is shown to cause considerable change in the thermo-physical property of the composite gels. This material property modulation will facilitate designing of soft gels having storage modulus continuously varying in the wide range of 10-70 Pa while keeping the gelation temperature mostly unaltered. Copyright © 2015 Elsevier Ltd. All rights reserved.

Divertor scenario development for NSTX Upgrade

NASA Astrophysics Data System (ADS)

Soukhanovskii, V. A.; McLean, A. G.; Meier, E. T.; Rognlien, T. D.; Ryutov, D. D.; Bell, R. E.; Diallo, A.; Gerhardt, S. P.; Kaita, R.; Kolemen, E.; Leblanc, B. P.; Menard, J. E.; Podesta, M.; Scotti, F.

2012-10-01

In the NSTX-U tokamak, initial plans for divertor plasma-facing components (PFCs) include lithium and boron coated graphite, with a staged transition to molybdenum. Steady-state peak divertor heat fluxes are projected to reach 20-30 MW/m^2 in 2 MA, 12 MW NBI-heated discharges of up to 5 s duration, thus challenging PFC thermal limits. Based on the recent NSTX divertor experiments and modeling with edge transport code UEDGE, a favorable basis for divertor power handling in NSTX-U is developed. The snowflake divertor geometry and feedback-controlled divertor impurity seeding applied to the lower and upper divertors are presently envisioned. In the NSTX snowflake experiments with lithium-coated graphite PFCs, the peak divertor heat fluxes from Type I ELMs and between ELMs were significantly reduced due to geometry effects, increased volumetric losses and null-point convective redistribution between strike points. H-mode core confinement was maintained at H98(y,2)<=1 albeit the radiative detachment. Additional CD4 seeding demonstrated potential for a further increase of divertor radiation.

TEMPEST simulations of the plasma transport in a single-null tokamak geometry

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Bodi, K.; Cohen, R. H.; Krasheninnikov, S.; Rognlien, T. D.

2010-06-01

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. To study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. A series of TEMPEST simulations were conducted to investigate the transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. We also show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.

Small angle slot divertor concept for long pulse advanced tokamaks

NASA Astrophysics Data System (ADS)

Guo, H. Y.; Sang, C. F.; Stangeby, P. C.; Lao, L. L.; Taylor, T. S.; Thomas, D. M.

2017-04-01

SOLPS-EIRENE edge code analysis shows that a gas-tight slot divertor geometry with a small-angle (glancing-incidence) target, named the small angle slot (SAS) divertor, can achieve cold, dissipative/detached divertor conditions at relatively low values of plasma density at the outside midplane separatrix. SAS exhibits the following key features: (1) strong enhancement of the buildup of neutral density in a localized region near the plasma strike point on the divertor target; (2) spreading of the cooling front across the divertor target with the slot gradually flaring out from the strike point, thus effectively reducing both heat flux and erosion on the entire divertor target surface. Such a divertor may potentially provide a power and particle handling solution for long pulse advanced tokamaks.

Detachment experiments in new DIII-D upper divertor

NASA Astrophysics Data System (ADS)

Moser, A. L.; Leonard, A. W.; Groebner, R. J.; Guo, H.; Wang, H.; Watkins, J. G.; McLean, A. G.; Fenstermacher, M. E.; Shafer, M. W.; Briesemeister, A. R.; Hinson, E. T.

2017-10-01

Installation of the Small Angle Slot (SAS) in the upper divertor of DIII-D enables new studies of the effect of target and baffle geometry on divertor detachment. This structure provides a more-closed upper divertor as well as the SAS divertor itself. Initial SAS experiment results indicate that divertor detachment occurs at a lower line-averaged density than in the more-open, lower single null divertor configurations on DIII-D. In contrast, the increased divertor closure of the new installation did not reduce the upstream density required for detachment beyond that achieved with the previous upper divertor structure. Particle pumping in the upper divertor structure is found to produce a 10 % reduction in the pedestal density required for detachment compared to the case with no pumping. Comparisons focus on both the onset of detachment (measured by in-target Langmuir probes) as a function of upstream density, as well as the effect of the new divertor configurations on pedestal density profiles. Work supported by US DOE under DE-FC02-04ER54698, DE-AC05-00OR22725, DE-AC04-94AL85000, DE-AC52-07NA27344, and DE-SC00013911.

Intermittent many-body dynamics at equilibrium

NASA Astrophysics Data System (ADS)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Symmetry breaking, mixing, instability, and low-frequency variability in a minimal Lorenz-like system.

PubMed

Lucarini, Valerio; Fraedrich, Klaus

2009-08-01

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec(-1)) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f(3/2) power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Numerical exploration of non-axisymmetric divertor closure in the small angle slot (SAS) divertor at DIII-D

DOE PAGES

Frerichs, H.; Schmitz, O.; Covele, B.; ...

2018-02-28

Numerical simulations of toroidal asymmetries in a tightly baffled small angle slot (SAS) divertor on the DIII-D tokamak show that toroidal asymmetries in divertor closure result in (non-axisymmetric) local onset of detachment within a density window of 10-15% on top of the nominal threshold separatrix density. The SAS divertor is explored at DIII-D for improving access to cold, dissipative/detached divertor conditions. The narrow width of the slot divertor coupled with a small magnetic field line-to-target angle facilitates the buildup of neutral density, thereby increasing radiative and neutrals-related (atoms and molecules) losses in the divertor. Therefore, small changes in the strikemore » point location can be expected to have a large impact on diverter conditions. The combination of misaligned slot structure and non-axisymmetric perturbations to the magnetic field configuration causes the strike point to move along the divertor target plate, possibly leaving the diverter slot at some locations. The latter extreme case essentially introduces an opening in the divertor slot from where recycling neutrals can easily escape, and thereby degrade the performance of the slot divertor. Such a strike point dislocation is approximated by a finite gap in the divertor baffle for which three dimensional edge plasma and neutral gas simulations are performed with the EMC3-EIRENE code.« less

Numerical exploration of non-axisymmetric divertor closure in the small angle slot (SAS) divertor at DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frerichs, H.; Schmitz, O.; Covele, B.

Numerical simulations of toroidal asymmetries in a tightly baffled small angle slot (SAS) divertor on the DIII-D tokamak show that toroidal asymmetries in divertor closure result in (non-axisymmetric) local onset of detachment within a density window of 10-15% on top of the nominal threshold separatrix density. The SAS divertor is explored at DIII-D for improving access to cold, dissipative/detached divertor conditions. The narrow width of the slot divertor coupled with a small magnetic field line-to-target angle facilitates the buildup of neutral density, thereby increasing radiative and neutrals-related (atoms and molecules) losses in the divertor. Therefore, small changes in the strikemore » point location can be expected to have a large impact on diverter conditions. The combination of misaligned slot structure and non-axisymmetric perturbations to the magnetic field configuration causes the strike point to move along the divertor target plate, possibly leaving the diverter slot at some locations. The latter extreme case essentially introduces an opening in the divertor slot from where recycling neutrals can easily escape, and thereby degrade the performance of the slot divertor. Such a strike point dislocation is approximated by a finite gap in the divertor baffle for which three dimensional edge plasma and neutral gas simulations are performed with the EMC3-EIRENE code.« less

Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Anishchenko, V. S.; Boev, Ya. I.; Semenova, N. I.; Strelkova, G. I.

2015-07-01

We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich-Pesin dimension, Lyapunov exponents and the Kolmogorov-Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how the fractal dimension of chaotic attractors can be estimated using the Poincaré recurrence statistics.

Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

PubMed Central

Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter

2016-01-01

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases. PMID:27492219

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

NASA Astrophysics Data System (ADS)

Nahali, Negar; Rosa, Angelo

2018-05-01

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions.

Nonadditive entropy Sq and nonextensive statistical mechanics: Applications in geophysics and elsewhere

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2012-06-01

The celebrated Boltzmann-Gibbs (BG) entropy, S BG = -kΣi p i ln p i, and associated statistical mechanics are essentially based on hypotheses such as ergodicity, i.e., when ensemble averages coincide with time averages. This dynamical simplification occurs in classical systems (and quantum counterparts) whose microscopic evolution is governed by a positive largest Lyapunov exponent (LLE). Under such circumstances, relevant microscopic variables behave, from the probabilistic viewpoint, as (nearly) independent. Many phenomena exist, however, in natural, artificial and social systems (geophysics, astrophysics, biophysics, economics, and others) that violate ergodicity. To cover a (possibly) wide class of such systems, a generalization (nonextensive statistical mechanics) of the BG theory was proposed in 1988. This theory is based on nonadditive entropies such as S_q = kfrac{{1 - sumnolimits_i {p_i^q } }} {{q - 1}}left( {S_1 = S_{BG} } right). Here we comment some central aspects of this theory, and briefly review typical predictions, verifications and applications in geophysics and elsewhere, as illustrated through theoretical, experimental, observational, and computational results.

Random walk to a nonergodic equilibrium concept

NASA Astrophysics Data System (ADS)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

Power-law decay exponents: A dynamical criterion for predicting thermalization

NASA Astrophysics Data System (ADS)

Távora, Marco; Torres-Herrera, E. J.; Santos, Lea F.

2017-01-01

From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior ∝t-γ of the survival probability at long times. We show that the value of the power-law exponent γ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: γ ≥2 and γ <1 . Exponents γ ≥2 imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with γ <1 emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.

Magnetic configuration flexibility of snowflake divertor for HL-2M [Analysis of snowflake divertor configurations for HL-2M

DOE PAGES

Zheng, G. Y.; Xu, X. Q.; Ryutov, D. D.; ...

2014-07-09

HL-2M (Li, 2013 [1]) is a tokamak device that is under construction. Based on the magnetic coils design of HL-2M, four kinds of divertor configurations are calculated by CORSICA code (Pearlstein et al., 2001 [2]) with the same main plasma parameters, which are standard divertor, exact snowflake divertor, snowflake-plus divertor and snowflake-minus divertor configurations. The potential properties of these divertors are analyzed and presented in this paper: low poloidal field area around X-point, connection length from outside mid-plane to the primary X-point, target plate design and magnetic field shear. The results show that the snowflake configurations not only can reducemore » the heat load at divertor target plates, but also may improve the magneto-hydrodynamic stability by stronger magnetic shear at the edge. Furthermore, a new divertor configuration, named “tripod divertor”, is designed by adjusting the positions of the two X-points according to plasma parameters and magnetic coils current of HL-2M.« less

Phase transition of Boolean networks with partially nested canalizing functions

NASA Astrophysics Data System (ADS)

Jansen, Kayse; Matache, Mihaela Teodora

2013-07-01

We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the critical condition for the sensitivity of the network under a non-ergodic scenario. We use the proposed mathematical model to determine parameter values for which phase transitions from order to chaos occur. We generate Derrida plots to show that the mathematical model matches the actual network dynamics. The phase transition diagrams indicate that both order and chaos can occur, and that certain parameters induce a larger range of values leading to order versus chaos. The edge-of-chaos curves are identified analytically and numerically. It is shown that the depth of canalization does not cause major dynamical changes once certain thresholds are reached; these thresholds are fairly small in comparison to the connectivity of the nodes.

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles

PubMed Central

Wheeler, Richard John

2015-01-01

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point “snapshot” of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes—cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)—as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. PMID:26543196

Disordered crystals from first principles I: Quantifying the configuration space

NASA Astrophysics Data System (ADS)

Kühne, Thomas D.; Prodan, Emil

2018-04-01

This work represents the first chapter of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures. We are interested in the range of temperatures, where most electronic components operate, that is, room temperature and above. The aim is a predictive first-principle formalism that combines ab-initio molecular dynamics and a finite-temperature Kubo-formula for homogeneous thermodynamic phases. The input for this formula is the ergodic dynamical system (Ω , G , dP) defining the thermodynamic crystalline phase, where Ω is the configuration space for the atomic degrees of freedom, G is the space group acting on Ω and dP is the ergodic Gibbs measure relative to the G-action. The present work develops an algorithmic method for quantifying (Ω , G , dP) from first principles. Using the silicon crystal as a working example, we find the Gibbs measure to be extremely well characterized by a multivariate normal distribution, which can be quantified using a small number of parameters. The latter are computed at various temperatures and communicated in the form of a table. Using this table, one can generate large and accurate thermally-disordered atomic configurations to serve, for example, as input for subsequent simulations of the electronic degrees of freedom.

Are atmospheric surface layer flows ergodic?

NASA Astrophysics Data System (ADS)

Higgins, Chad W.; Katul, Gabriel G.; Froidevaux, Martin; Simeonov, Valentin; Parlange, Marc B.

2013-06-01

The transposition of atmospheric turbulence statistics from the time domain, as conventionally sampled in field experiments, is explained by the so-called ergodic hypothesis. In micrometeorology, this hypothesis assumes that the time average of a measured flow variable represents an ensemble of independent realizations from similar meteorological states and boundary conditions. That is, the averaging duration must be sufficiently long to include a large number of independent realizations of the sampled flow variable so as to represent the ensemble. While the validity of the ergodic hypothesis for turbulence has been confirmed in laboratory experiments, and numerical simulations for idealized conditions, evidence for its validity in the atmospheric surface layer (ASL), especially for nonideal conditions, continues to defy experimental efforts. There is some urgency to make progress on this problem given the proliferation of tall tower scalar concentration networks aimed at constraining climate models yet are impacted by nonideal conditions at the land surface. Recent advancements in water vapor concentration lidar measurements that simultaneously sample spatial and temporal series in the ASL are used to investigate the validity of the ergodic hypothesis for the first time. It is shown that ergodicity is valid in a strict sense above uniform surfaces away from abrupt surface transitions. Surprisingly, ergodicity may be used to infer the ensemble concentration statistics of a composite grass-lake system using only water vapor concentration measurements collected above the sharp transition delineating the lake from the grass surface.

A new approach to measuring tortuosity

NASA Astrophysics Data System (ADS)

Wert, Amanda; Scott, Sherry E.

2012-03-01

The detection and measurement of the tortuosity - i.e. the bending and winding - of vessels has been shown to be potentially useful in the assessment of cancer progression and treatment response. Although several metrics for tortuosity are used, no single one measure is able to capture all types of tortuosity. This report presents a new multiscale technique for measuring vessel tortuosity. The approach is based on a method - called the ergodicity defect - which gives a scale-dependent measure of deviation from ergodicity. Ergodicity is a concept that captures the manner in which trajectories or signals sample the space; thus, ergodicity and vessel tortuosity both involve the notion of how a signal samples space. Here we begin to explore this connection. We first apply the ergodicity defect tortuosity measure to both 2D and 3D synthetic data in order to demonstrate the response of the method to three types of tortuosity observed in clinical patterns. We then implement the technique on segmented vessels extracted from brain tumor MRA images. Results indicate that the method can be effectively used to detect and measure several types of vessel tortuosity.

Advanced Divertor Design and Application under Modern Superconducting Tokamak Constraints

NASA Astrophysics Data System (ADS)

Covele, Brent; Kotschenreuther, Mike; Mahajan, Swadesh; Valanju, Prashant

2013-10-01

With current ITER projections already predicting divertor exhaust heat loads in the 5-10 MW/m2 range, i.e. at the maximum tolerance, it is clear that the divertor heat load problem will only be exacerbated for future superconducting tokamaks, as well as perhaps some modern tokamaks today. Thus, an advanced divertor, such as the X-Divertor (XD), Super-X Divertor (SXD), or Snowflake (SF) will become a virtual necessity to reduce incident heat flux at the target plates. Using the 2D magnetic equilibrium code CORSICA, we explore the possibilities of creating an advanced divertor for a next-generation superconducting tokamak (Ip = 15 MA, BT = 5.3 T, R = 6.2 m) under nominal engineering constraints. Advanced divertors were achieved with no in-vessel PF coils, PF current densities below 30 MA/m2, and vertical maintenance access, all of which are favorable conditions for tokamaks today. Both the XD and SF divertors are readily achievable while maintaining core plasma performance, and the advantages and disadvantages of each are discussed in turn. Some thought is given as to how the divertor cassette will need to be modified to accommodate advanced divertors. Work supported under US-DOE projects DE-FG02-04ER54742 and DE-FG02-04ER54754.

Investigations on the heat flux and impurity for the HL-2M divertor

NASA Astrophysics Data System (ADS)

Zheng, G. Y.; Cai, L. Z.; Duan, X. R.; Xu, X. Q.; Ryutov, D. D.; Cai, L. J.; Liu, X.; Li, J. X.; Pan, Y. D.

2016-12-01

The controllability of the heat load and impurity in the divertor is very important, which could be one of the critical problems to be solved in order to ensure the success for a steady state tokamak. HL-2M has the advantage of the poloidal field (PF) coils placed inside the demountable toroidal field (TF) coils and close to the main plasma. As a result, it is possible to make highly accurate configuration control of the advanced divertor for HL-2M. The divertor target geometry of HL-2M has been designed to be compatible with different divertor configurations to study the divertor physics and support the high performance plasma operations. In this paper, the heat loads and impurities with different divertor configurations, including the standard X-point divertor, the snowflake-minus divertor and two tripod divertor configurations for HL-2M, are investigated by numerical simulations with the SOLPS5.0 code under the current design of the HL-2M divertor geometry. The plasmas with different conditions, such as the low discharge parameters with {{I}\\text{p}}   =  0.5 MA at the first stage of HL-2M and the high parameters with {{I}\\text{p}}   =  2.0 MA during the normal operations, are simulated. The heat load profiles and the impurity distributions are obtained, and the control of the peak heat load and the effect of impurity on the core plasma are discussed. The compatibility of different divertor configurations for HL-2M is also evaluated. It is seen that the excellent compatibility of different divertor configurations with the current divertor geometry has been verified. The results show that the snowflake-minus divertor and the tripod divertor with {{d}x}=30 \\text{cm} present good performance in terms of the heat load profiles and the impurity distributions under different conditions, which may not have a big effect on the core plasma. In addition, it is possible to optimize the distance between the two X-points, {{d}x} , to achieve a better performance in terms of the parameters of discharges.

"Snowflake" divertor configuration in NSTX

NASA Astrophysics Data System (ADS)

Soukhanovskii, V. A.; Ahn, J.-W.; Bell, R. E.; Gates, D. A.; Gerhardt, S.; Kaita, R.; Kolemen, E.; Kugel, H. W.; Leblanc, B. P.; Maingi, R.; Maqueda, R.; McLean, A.; Menard, J. E.; Mueller, D. M.; Paul, S. F.; Raman, R.; Roquemore, A. L.; Ryutov, D. D.; Scott, H. A.

2011-08-01

Steady-state handling of divertor heat flux is a critical issue for present and future conventional and spherical tokamaks with compact high power density divertors. A novel "snowflake" divertor (SFD) configuration that takes advantage of magnetic properties of a second-order poloidal null has been predicted to have a larger plasma-wetted area and a larger divertor volume, in comparison with a standard first-order poloidal X-point divertor configuration. The SFD was obtained in 0.8 MA, 4-6 MW NBI-heated H-mode discharges in NSTX using two divertor magnetic coils. The SFD led to a partial detachment of the outer strike point even in low-collisionality scrape-off layer plasma obtained with lithium coatings in NSTX. Significant divertor peak heat flux reduction and impurity screening have been achieved simultaneously with good core confinement and MHD properties.

Self-consistent approach to many-body localization and subdiffusion

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Herbrych, J.

2017-07-01

An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of many-body localization. Results show a qualitative agreement with the numerically obtained dynamical structure factor in the whole range of frequencies and wave vectors, as well as across the transition to nonergodic behavior. The theory reveals the singular nature of the one-dimensional problem, whereby on the ergodic side the dynamics is subdiffusive with dynamical conductivity σ (ω ) ∝|ω| α , i.e., with vanishing dc limit σ0=0 and α <1 varying with disorder, while we get α >1 in the localized phase.

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf

2011-01-01

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Numerical exploration of non-axisymmetric divertor closure in the small angle slot (SAS) divertor at DIII-D

NASA Astrophysics Data System (ADS)

Frerichs, Heinke; Schmitz, Oliver; Covele, Brent; Guo, Houyang; Hill, David; Feng, Yuhe

2017-10-01

In the Small Angle Slot (SAS) divertor in DIII-D, the combination of misaligned slot structure and non-axisymmetric perturbations to the magnetic field causes the strike point to vary radially along the divertor slot and even leave it at some toroidal locations. This effect essentially introduces an opening in the divertor slot from where recycling neutrals can easily escape, and thereby degrade performance of the slot divertor. This effect has been approximated by a finite gap in the divertor baffle. Simulations with EMC3-EIRENE show that a toroidally localized loss of divertor closure can result in non-axisymmetric divertor densities and temperatures. This introduces a density window of 10-15% on top of the nominal threshold separatrix density during which a non-axisymmetric onset of local detachment occurs, initially leaving the gap and up to 60 deg beyond that still attached. Conversely, the impact of such toroidally localized divertor perturbations on the toroidal symmetry of midplane separatrix conditions is small. This work has been funded by the U.S. Department of Energy under Early Career Award Grant DE-SC0013911, and Grant DE-FC02-04ER54698.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Calibration of a universal indicated turbulence system

NASA Technical Reports Server (NTRS)

Chapin, W. G.

1977-01-01

Theoretical and experimental work on a Universal Indicated Turbulence Meter is described. A mathematical transfer function from turbulence input to output indication was developed. A random ergodic process and a Gaussian turbulence distribution were assumed. A calibration technique based on this transfer function was developed. The computer contains a variable gain amplifier to make the system output independent of average velocity. The range over which this independence holds was determined. An optimum dynamic response was obtained for the tubulation between the system pitot tube and pressure transducer by making dynamic response measurements for orifices of various lengths and diameters at the source end.

Comparative divertor-transport study for helical devices

NASA Astrophysics Data System (ADS)

Feng, Y.; Kobayashi, M.; Sardei, F.; Masuzaki, S.; Kisslinger, J.; Morisaki, T.; Grigull, P.; Yamada, H.; McCormick, K.; Ohyabu, N.; König, R.; Yamada, I.; Giannone, L.; Narihara, K.; Wenzel, U.; Morita, S.; Thomsen, H.; Miyazawa, J.; Hildebrandt, D.; Watanabe, T.; Wagner, F.; Ashikawa, N.; Ida, K.; Komori, A.; Motojima, O.; Nakamura, Y.; Peterson, B. J.; Sato, K.; Shoji, M.; Tamura, N.; Tokitani, M.; LHD experimental Group

2009-09-01

Using the island divertors (IDs) of W7-AS and W7-X and the helical divertor (HD) of LHD as examples, the paper presents a comparative divertor transport study for three typical helical devices of different machine sizes following two distinct divertor concepts, aiming at identifying common physics issues/effects for mutual validation and combined studies. Based on EMC3/EIRENE simulations supported by experimental results, the paper first reviews and compares the essential transport features of the W7-AS ID and the LHD HD in order to build a base and framework for a predictive study of W7-X. The fundamental role of low-order magnetic islands in both divertor concepts is emphasized. Preliminary EMC3/EIRENE simulation results for W7-X are presented and discussed with respect to W7-AS and LHD in order to show how the individual field and divertor topologies affect the divertor transport and performance. For instance, a high recycling regime, which is absent from W7-AS and LHD, is predicted to exist for W7-X. The paper focuses on identifying and understanding the role of divertors for high density plasma operations in helical devices. In this regard, special attention is paid to investigating the divertor function for controlling intrinsic impurities. Impurity transport behaviour and wall-sputtering processes of CX-neutrals are studied under different divertor plasma conditions. A divertor retention effect on intrinsic impurities at high SOL collisonalities is predicted for all the three devices. The required SOL plasma conditions and the underlying mechanisms are analysed in detail. Numerical results are discussed in conjunction with the experimental observations for high density divertor plasmas in W7-AS and LHD. Different SOL transport regimes are numerically identified for the standard divertor configuration of W7-X and the possible consequences on high density plasmas are assessed. All the EMC3-EIRENE simulations presented in this paper are based on vacuum fields and comparisons with local diagnostics are made for low-ß plasmas.

TEMPEST Simulations of the Plasma Transport in a Single-Null Tokamak Geometry

DOE PAGES

X. Q. Xu; Bodi, K.; Cohen, R. H.; ...

2010-05-28

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. In order to study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. In a series of TEMPEST simulations were conducted to investigate themore » transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. Moreover, we show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.« less

TEMPEST Simulations of the Plasma Transport in a Single-Null Tokamak Geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

X. Q. Xu; Bodi, K.; Cohen, R. H.

We present edge kinetic ion transport simulations of tokamak plasmas in magnetic divertor geometry using the fully nonlinear (full-f) continuum code TEMPEST. Besides neoclassical transport, a term for divergence of anomalous kinetic radial flux is added to mock up the effect of turbulent transport. In order to study the relative roles of neoclassical and anomalous transport, TEMPEST simulations were carried out for plasma transport and flow dynamics in a single-null tokamak geometry, including the pedestal region that extends across the separatrix into the scrape-off layer and private flux region. In a series of TEMPEST simulations were conducted to investigate themore » transition of midplane pedestal heat flux and flow from the neoclassical to the turbulent limit and the transition of divertor heat flux and flow from the kinetic to the fluid regime via an anomalous transport scan and a density scan. The TEMPEST simulation results demonstrate that turbulent transport (as modelled by large diffusion) plays a similar role to collisional decorrelation of particle orbits and that the large turbulent transport (large diffusion) leads to an apparent Maxwellianization of the particle distribution. Moreover, we show the transition of parallel heat flux and flow at the entrance to the divertor plates from the fluid to the kinetic regime. For an absorbing divertor plate boundary condition, a non-half-Maxwellian is found due to the balance between upstream radial anomalous transport and energetic ion endloss.« less

Time-dependent modeling of dust injection in semi-detached ITER divertor plasma

NASA Astrophysics Data System (ADS)

Smirnov, Roman; Krasheninnikov, Sergei

2017-10-01

At present, it is generally understood that dust related issues will play important role in operation of the next step fusion devices, i.e. ITER, and in the development of future fusion reactors. Recent progress in research on dust in magnetic fusion devises has outlined several topics of particular concern: a) degradation of fusion plasma performance; b) impairment of in-vessel diagnostic instruments; and c) safety issues related to dust reactivity and tritium retention. In addition, observed dust events in fusion edge plasmas are highly irregular and require consideration of temporal evolution of both the dust and the fusion plasma. In order to address the dust-related fusion performance issues, we have coupled the dust transport code DUSTT and the edge plasma transport code UEDGE in time-dependent manner, allowing modeling of transient dust-induced phenomena in fusion edge plasmas. Using the coupled codes we simulate burst-like injection of tungsten dust into ITER divertor plasma in semi-detached regime, which is considered as preferable ITER divertor operational mode based on the plasma and heat load control restrictions. Analysis of transport of the dust and the dust-produced impurities, and of dynamics of the ITER divertor and edge plasma in response to the dust injection will be presented. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG02-06ER54852.

Ergodic theory and experimental visualization of chaos in 3D flows

NASA Astrophysics Data System (ADS)

Sotiropoulos, Fotis; Mezic, Igor

2000-11-01

In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.

Dynamics and asymptotics of correlations in a many-body localized system

NASA Astrophysics Data System (ADS)

Campbell, Steve; Power, Matthew J. M.; De Chiara, Gabriele

2017-08-01

We examine the dynamics of nearest-neighbor bipartite concurrence and total correlations in the spin-1/2 XXZ model with random fields. We show, starting from factorized random initial states, that the concurrence can suffer entanglement sudden death in the long time limit and therefore may not be a useful indicator of the properties of the system. In contrast, we show that the total correlations capture the dynamics more succinctly, and further reveal a fundamental difference in the dynamics governed by the ergodic versus many-body localized phases, with the latter exhibiting dynamical oscillations. Finally, we consider an initial state composed of several singlet pairs and show that by fixing the correlation properties, while the dynamics do not reveal noticeable differences between the phases, the long-time values of the correlation measures appear to indicate the critical region.

Divertor heat flux mitigation in the National Spherical Torus Experimenta)

NASA Astrophysics Data System (ADS)

Soukhanovskii, V. A.; Maingi, R.; Gates, D. A.; Menard, J. E.; Paul, S. F.; Raman, R.; Roquemore, A. L.; Bell, M. G.; Bell, R. E.; Boedo, J. A.; Bush, C. E.; Kaita, R.; Kugel, H. W.; Leblanc, B. P.; Mueller, D.; NSTX Team

2009-02-01

Steady-state handling of divertor heat flux is a critical issue for both ITER and spherical torus-based devices with compact high power density divertors. Significant reduction of heat flux to the divertor plate has been achieved simultaneously with favorable core and pedestal confinement and stability properties in a highly shaped lower single null configuration in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 2000] using high magnetic flux expansion at the divertor strike point and the radiative divertor technique. A partial detachment of the outer strike point was achieved with divertor deuterium injection leading to peak flux reduction from 4-6MWm-2to0.5-2MWm-2 in small-ELM 0.8-1.0MA, 4-6MW neutral beam injection-heated H-mode discharges. A self-consistent picture of the outer strike point partial detachment was evident from divertor heat flux profiles and recombination, particle flux and neutral pressure measurements. Analytic scrape-off layer parallel transport models were used for interpretation of NSTX detachment experiments. The modeling showed that the observed peak heat flux reduction and detachment are possible with high radiated power and momentum loss fractions, achievable with divertor gas injection, and nearly impossible to achieve with main electron density, divertor neutral density or recombination increases alone.

Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media

NASA Astrophysics Data System (ADS)

Russian, Anna; Dentz, Marco; Gouze, Philippe

2017-08-01

Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency Rn, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q ≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

NASA Astrophysics Data System (ADS)

Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K.

2018-02-01

We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.

Divertor detachment

NASA Astrophysics Data System (ADS)

Krasheninnikov, Sergei

2015-11-01

The heat exhaust is one of the main conceptual issues of magnetic fusion reactor. In a standard operational regime the large heat flux onto divertor target reaches unacceptable level in any foreseeable reactor design. However, about two decades ago so-called ``detached divertor'' regimes were found. They are characterized by reduced power and plasma flux on divertor targets and look as a promising solution for heat exhaust in future reactors. In particular, it is envisioned that ITER will operate in a partly detached divertor regime. However, even though divertor detachment was studied extensively for two decades, still there are some issues requiring a new look. Among them is the compatibility of detached divertor regime with a good core confinement. For example, ELMy H-mode exhibits a very good core confinement, but large ELMs can ``burn through'' detached divertor and release large amounts of energy on the targets. In addition, detached divertor regimes can be subject to thermal instabilities resulting in the MARFE formation, which, potentially, can cause disruption of the discharge. Finally, often inner and outer divertors detach at different plasma conditions, which can lead to core confinement degradation. Here we discuss basic physics of divertor detachment including different mechanisms of power and momentum loss (ionization, impurity and hydrogen radiation loss, ion-neutral collisions, recombination, and their synergistic effects) and evaluate the roles of different plasma processes in the reduction of the plasma flux; detachment stability; and an impact of ELMs on detachment. We also evaluate an impact of different magnetic and divertor geometries on detachment onset, stability, in- out- asymmetry, and tolerance to the ELMs. Supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences under Award Number DE-DE-FG02-04ER54739 at UCSD.

A review of direct experimental measurements of detachment

DOE PAGES

Boedo, J.; McLean, A. G.; Rudakov, D. L.; ...

2018-02-22

Detached divertor plasmas feature strong radial and parallel gradients of density, temperature, electric fields and flow over the divertor volume and therefore, sampling the divertor plasma directly provides crucial knowledge to the interpretation and modeling efforts. Here, we review the contribution of diagnostics that directly sample the plasma to the advancement of knowledge of the physics of detachment and detached divertors, such as the characteristics of the various regimes, discovery and quantification of drifts and identification of convection of heat and particles. We focus on wall probes, scanning probes, retarding field analyzers and Thomson Scattering (TS) in the divertor regionmore » and also include the contribution of measurements away from the divertor that provide insight on how divertor detachment affects core, edge or pedestal conditions. Wall probes are critical as they can be installed in closed volumes of difficult access to other diagnostics and measure plasma parameters at the divertor structures, which define the plasma boundary conditions and where detachment effects are more likely to be strongest.« less

A review of direct experimental measurements of detachment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boedo, J.; McLean, A. G.; Rudakov, D. L.

Detached divertor plasmas feature strong radial and parallel gradients of density, temperature, electric fields and flow over the divertor volume and therefore, sampling the divertor plasma directly provides crucial knowledge to the interpretation and modeling efforts. Here, we review the contribution of diagnostics that directly sample the plasma to the advancement of knowledge of the physics of detachment and detached divertors, such as the characteristics of the various regimes, discovery and quantification of drifts and identification of convection of heat and particles. We focus on wall probes, scanning probes, retarding field analyzers and Thomson Scattering (TS) in the divertor regionmore » and also include the contribution of measurements away from the divertor that provide insight on how divertor detachment affects core, edge or pedestal conditions. Wall probes are critical as they can be installed in closed volumes of difficult access to other diagnostics and measure plasma parameters at the divertor structures, which define the plasma boundary conditions and where detachment effects are more likely to be strongest.« less

A super-cusp divertor configuration for tokamaks

NASA Astrophysics Data System (ADS)

Ryutov, D. D.

2015-10-01

> This study demonstrates a remarkable flexibility of advanced divertor configurations created with the remote poloidal field coils. The emphasis here is on the configurations with three poloidal field nulls in the divertor area. We are seeking the structures where all three nulls lie on the same separatrix, thereby creating two zones of a very strong flux expansion, as envisaged in the concept of Takase's cusp divertor. It turns out that the set of remote coils can indeed produce a cusp divertor, with additional advantages of: (i) a large stand-off distance between the divertor and the coils and (ii) a thorough control that these coils exert over the fine features of the configuration. In reference to these additional favourable properties acquired by the cusp divertor, the resulting configuration could be called `a super-cusp'. General geometrical features of the three-null configurations produced by remote coils are described. Issues on the way to practical applications include the need for a more sophisticated control system and possible constraints related to excessively high currents in the divertor coils.

A review of direct experimental measurements of detachment

NASA Astrophysics Data System (ADS)

Boedo, J.; McLean, A. G.; Rudakov, D. L.; Watkins, J. G.

2018-04-01

Detached divertor plasmas feature strong radial and parallel gradients of density, temperature, electric fields and flow over the divertor volume and therefore, sampling the divertor plasma directly provides crucial knowledge to the interpretation and modeling efforts. We review the contribution of diagnostics that directly sample the plasma to the advancement of knowledge of the physics of detachment and detached divertors, such as the characteristics of the various regimes, discovery and quantification of drifts and identification of convection of heat and particles. We focus on wall probes, scanning probes, retarding field analyzers and Thomson scattering in the divertor region and also include the contribution of measurements away from the divertor that provide insight on how divertor detachment affects core, edge or pedestal conditions. Wall probes are critical as they can be installed in closed volumes of difficult access to other diagnostics and measure plasma parameters at the divertor structures, which define the plasma boundary conditions and where detachment effects are more likely to be strongest.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

PubMed

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Thermal Analysis of the Divertor Primary Heat Transfer System Piping During the Gas Baking Process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoder Jr, Graydon L; Harvey, Karen; Ferrada, Juan J

A preliminary analysis has been performed examining the temperature distribution in the Divertor Primary Heat Transfer System (PHTS) piping and the divertor itself during the gas baking process. During gas baking, it is required that the divertor reach a temperature of 350 C. Thermal losses in the piping and from the divertor itself require that the gas supply temperature be maintained above that temperature in order to ensure that all of the divertor components reach the required temperature. The analysis described in this report was conducted in order to estimate the required supply temperature from the gas heater.

Advantages and Challenges of Radiative Liquid Lithium Divertor

NASA Astrophysics Data System (ADS)

Ono, Masayuki

2017-10-01

Steady-state fusion power plant designs present major divertor technology challenges, including high divertor heat flux both in steady-state and during transients. In addition to these concerns, there are the unresolved technology issues of long term dust accumulation and associated tritium inventory and safety issues. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peak heat flux while maintaining essentially Li-free core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid Li divertor (RLLD) concept and its variant, the active liquid Li divertor concept (ARLLD), taking advantage of the enhanced Li radiation in relatively poorly confined divertor plasmas. It has been suggested that radiation-based liquid lithium (LL) divertor concepts with a modest Li-loop could provide a possible solution for the outstanding fusion reactor technology issues such as divertor heat flux mitigation and real time dust removal, while potentially improving the reactor plasma performance. Laboratory tests are also planned to investigate the Li-T recover efficiency and other relevant research topics of the RLLD. This work supported by DoE Contract No. DE-AC02-09CH11466.

Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Metzler, Ralf

2014-01-14

Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averagedmore » mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.« less

The effect of feedback-controlled divertor nitrogen seeding on the boundary plasma and power exhaust channel width in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Labombard, B.; Brunner, D.; Kuang, A. Q.; McCarthy, W.; Terry, J. L.

2017-10-01

The scrape-off layer (SOL) power channel width, λq, is projected to be 0.5 mm in power reactors, based on multi-machine measurements of divertor target heat fluxes in H-mode at low levels of divertor dissipation. An important question is: does λq change with the level of divertor dissipation? We report results in which feedback controlled nitrogen seeding in the divertor was used to systematically vary divertor dissipation in a series of otherwise identical L-mode plasmas at three plasma currents: 0.55, 0.8 and 1.1 MA. Outer midplane profiles were recorded with a scanning Mirror Langmuir Probe; divertor plasma conditions were monitored with `rail' Langmuir probe and surface thermocouple arrays. Despite an order of magnitude reduction in divertor target heat fluxes (q// 400 MW m-2 to 40 MW m-2) and corresponding change in divertor regime from sheath-limited through high-recycling to near-detached, the upstream electron temperature profile is found to remain unchanged or to become slightly steeper in the near SOL and to drop significantly in the far SOL. Thus heat in the SOL appears to take advantage of this impurity radiation `heat sink' in the divertor by preferentially draining via the narrow (and perhaps an increasingly narrow) λq of the near SOL. Supported by USDoE award DE-FC02-99ER54512.

3D nonlinear numerical simulation of the current-convective instability in detached diverter plasma

NASA Astrophysics Data System (ADS)

Stepanenko, Alexander; Krasheninnikov, Sergei

2017-10-01

One of the possible mechanisms responsible for strong radiation fluctuations observed in the recent experiments with detached plasmas at ASDEX Upgrade [Potzel et al., Nuclear Fusion, 2014] can be related to the onset of the current-convective instability (CCI) driven by strong asymmetry of detachment in the inner and outer tokamak divertors [Krasheninnikov and Smolyakov, PoP, 2016]. In this study we present the first results of 3D nonlinear numerical simulations of the CCI in divertor plasma for the conditions relevant to the AUG experiment. The general physical model used to simulate the CCI, qualitative estimates for the instability characteristic growth rate and transverse wavelengths derived for plasma, which is spatially inhomogeneous both across and along the magnetic field lines, are presented. The simulation results, demonstrating nonlinear dynamics of the CCI, provide the frequency spectra of turbulent divertor plasma fluctuations showing good agreement with the available experimental data. This material is based upon the work supported by the U.S. Department of Energy under Award No. DE-FG02-04ER54739 at UCSD and by the Russian Ministry of Education and Science Grant No. 14.Y26.31.0008 at MEPhI.

Divertor, scrape-off layer and pedestal particle dynamics in the ELM cycle on ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Laggner, F. M.; Keerl, S.; Gnilsen, J.; Wolfrum, E.; Bernert, M.; Carralero, D.; Guimarais, L.; Nikolaeva, V.; Potzel, S.; Cavedon, M.; Mink, F.; Dunne, M. G.; Birkenmeier, G.; Fischer, R.; Viezzer, E.; Willensdorfer, M.; Wischmeier, M.; Aumayr, F.; the EUROfusion MST1 Team; the ASDEX Upgrade Team

2018-02-01

In addition to the relaxation of the pedestal, edge localised modes (ELMs) introduce changes to the divertor and scrape-off layer (SOL) conditions. Their impact on the inter-ELM pedestal recovery is investigated, with emphasis on the electron density (n e) evolution. The typical ELM cycle occurring in an exemplary ASDEX Upgrade discharge interval at moderate applied gas puff and heating power is characterised, utilising several divertor, SOL and pedestal diagnostics. In the studied discharge interval the inner divertor target is detached before the ELM crash, while the outer target is attached. The particles and power expelled by the ELM crash lead to a re-attachment of the inner target plasma. After the ELM crash, the outer divertor target moves into a high recycling regime with large n e in front of the plate, which is accompanied by high main chamber neutral fluxes. On similar timescales, the inner target fully detaches and the high field side high density region (HFSHD) is formed reaching up to the high field side midplane. This state evolves again to the pre-ELM state, when the main chamber neutral fluxes are reduced later in the ELM cycle. Neither the timescale of the appearance of the HFSHD nor the increase of the main chamber neutral fluxes fit the timescale of the n e pedestal, which is faster. It is found that during the n e pedestal recovery, the magnetic activity at the low field side midplane is strongly reduced indicating a lower level of fluctuations. A rough estimation of the particle flux across the pedestal suggests that the particle flux is reduced in this period. In conclusion, the evolution of the n e pedestal is determined by a combination of neutral fluxes, HFSHD and reduced particle flux across the pedestal. A reduced particle flux explains the fast, experimentally observed re-establishment of the n e pedestal best, whereas neutrals and HFSHD impact on the evolution of the SOL and separatrix conditions.

Ergodicity bounds for birth-death processes with particularities

NASA Astrophysics Data System (ADS)

Zeifman, Alexander I.; Satin, Yacov; Korotysheva, Anna; Shilova, Galina; Kiseleva, Ksenia; Korolev, Victor Yu.; Bening, Vladimir E.; Shorgin, Sergey Ya.

2016-06-01

We introduce an inhomogeneous birth-death process with birth rates λk(t), death rates µk(t), and possible transitions to/from zero with rates βk(t), rk(t) respectively, and obtain ergodicity bounds for this process.

OEDGE modeling of plasma contamination efficiency of Ar puffing from different divertor locations in EAST

NASA Astrophysics Data System (ADS)

Pengfei, ZHANG; Ling, ZHANG; Zhenwei, WU; Zong, XU; Wei, GAO; Liang, WANG; Qingquan, YANG; Jichan, XU; Jianbin, LIU; Hao, QU; Yong, LIU; Juan, HUANG; Chengrui, WU; Yumei, HOU; Zhao, JIN; J, D. ELDER; Houyang, GUO

2018-04-01

Modeling with OEDGE was carried out to assess the initial and long-term plasma contamination efficiency of Ar puffing from different divertor locations, i.e. the inner divertor, the outer divertor and the dome, in the EAST superconducting tokamak for typical ohmic plasma conditions. It was found that the initial Ar contamination efficiency is dependent on the local plasma conditions at the different gas puff locations. However, it quickly approaches a similar steady state value for Ar recycling efficiency >0.9. OEDGE modeling shows that the final equilibrium Ar contamination efficiency is significantly lower for the more closed lower divertor than that for the upper divertor.

Characteristics of the Secondary Divertor on DIII-D

NASA Astrophysics Data System (ADS)

Watkins, J. G.; Lasnier, C. J.; Leonard, A. W.; Evans, T. E.; Pitts, R.; Stangeby, P. C.; Boedo, J. A.; Moyer, R. A.; Rudakov, D. L.

2009-11-01

In order to address a concern that the ITER secondary divertor strike plates may be insufficiently robust to handle the incident pulses of particles and energy from ELMs, we performed dedicated studies of the secondary divertor plasma and scrape-off layer (SOL). Detailed measurements of the ELM energy and particle deposition footprint on the secondary divertor target plates were made with a fast IR camera and Langmuir probes and SOL profile and transport measurements were made with reciprocating probes. The secondary divertor and SOL conditions depended on changes in the magnetic balance and the core plasma density. Larger density resulted in smaller ELMs and the magnetic balance affected how many ELM particles coupled to the secondary SOL and divertor. Particularly striking are the images from a new fast IR camera that resolve ELM heat pulses and show spiral patterns with multiple peaks during ELMs in the secondary divertor.

Thermodynamic phase transitions for Pomeau-Manneville maps

NASA Astrophysics Data System (ADS)

Venegeroles, Roberto

2012-08-01

We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a distributional limit theorem to provide both a powerful tool for calculating thermodynamic potentials as also an understanding of the dynamic characteristics at each instability phase. In particular, topological pressure and Rényi entropy are calculated exactly for such systems. Finally, we show the connection of the distributional limit theorem with non-Gaussian fluctuations of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad. Sci. USA10.1073/pnas.85.13.4591 85, 4591 (1988)].

Divertor-leg instability for finite beta and radially-tilted divertor plate

NASA Astrophysics Data System (ADS)

Cohen, R. H.; Ryutov, D. D.

2004-11-01

Plasma in the divertor leg may experience a fast instability caused by sheath boundary conditions (BC). Perturbations cannot penetrate beyond the X point because of very strong shearing in its vicinity. Accordingly, this instability could increase cross-field transport in the divertor leg, and thereby reduce the heat load on the divertor plate, without having any appreciable negative effect on core plasma confinement. A way of describing the role of shearing in terms of the surface resistivity attributed to a ``control plane'' below the X point has recently been suggested (Contr. Plasma Phys., v. 44, p. 168, 2004). We use this BC, plus sheath BC at the divertor plate. We include effects of finite beta and of the radial tilt of the divertor plate. We optimize the radial tilt in order to maximize radial transport in divertor legs. We discuss experimental signatures of the instability: i) phase velocity and wave-numbers of the most unstable modes; ii) correlations between fluctuations of various parameters; and iii) the differences between fluctuations in the common and private flux regions.

A super-cusp divertor configuration for tokamaks

DOE PAGES

Ryutov, D. D.

2015-08-26

Our study demonstrates a remarkable flexibility of advanced divertor configurations created with the remote poloidal field coils. The emphasis here is on the configurations with three poloidal field nulls in the divertor area. We are seeking the structures where all three nulls lie on the same separatrix, thereby creating two zones of a very strong flux expansion, as envisaged in the concept of Takase’s cusp divertor. It turns out that the set of remote coils can produce a cusp divertor, with additional advantages of: (i) a large stand-off distance between the divertor and the coils and (ii) a thorough controlmore » that these coils exert over the fine features of the configuration. In reference to these additional favourable properties acquired by the cusp divertor, the resulting configuration could be called ‘a super-cusp’. General geometrical features of the three-null configurations produced by remote coils are described. Furthermore, issues on the way to practical applications include the need for a more sophisticated control system and possible constraints related to excessively high currents in the divertor coils.« less

Implementation of a long leg X-point target divertor in the ARC fusion pilot plant

NASA Astrophysics Data System (ADS)

Kuang, A. Q.; Cao, N. M.; Creely, A. J.; Dennett, C. A.; Hecla, J.; Hoffman, H.; Major, M.; Ruiz Ruiz, J.; Tinguely, R. A.; Tolman, E. A.; Brunner, D.; Labombard, B.; Sorbom, B. N.; Whyte, D. G.; Grover, P.; Laughman, C.

2017-10-01

A long leg X-point target divertor geometry in a double null geometry has been implemented in the ARC pilot plant design, exploiting ARC's demountable toroidal field (TF) coils and FLiBe immersion blanket, which allow superconducting poloidal field coils to be located inside the TF coils, adequately shielded from neutrons. This new design maintains the original TF coil size, core plasma shape, and attains a tritium breedin ratio 1.08. The long leg divertor geometry provides significant advantages. Neutron transport computations indicate a factor of 10 reduction in divertor material neutron damage rate compared to the first wall, easing requirements for high heat flux components. Simulations have shown that long legged divertors are able to maintain a passively stable detachment front that stays in the divertor leg over a wide power window, in principle, responding immediately to fast changes in power exhaust. The ARC design exploits this new paradigm for divertor heat flux control: fewer concerns about coping with fast transients and a focus on neutron-tolerant diagnostics to measure and adjust detachment front locations in the outer divertor legs over long timescales.

On heat loading, novel divertors, and fusion reactors

NASA Astrophysics Data System (ADS)

Kotschenreuther, M.; Valanju, P. M.; Mahajan, S. M.; Wiley, J. C.

2007-07-01

The limited thermal power handling capacity of the standard divertors (used in current as well as projected tokamaks) is likely to force extremely high (˜90%) radiation fractions frad in tokamak fusion reactors that have heating powers considerably larger than ITER [D. J. Campbell, Phys. Plasmas 8, 2041 (2001)]. Such enormous values of necessary frad could have serious and debilitating consequences on the core confinement, stability, and dependability for a fusion power reactor, especially in reactors with Internal Transport Barriers. A new class of divertors, called X-divertors (XD), which considerably enhance the divertor thermal capacity through a flaring of the field lines only near the divertor plates, may be necessary and sufficient to overcome these problems and lead to a dependable fusion power reactor with acceptable economics. X-divertors will lower the bar on the necessary confinement to bring it in the range of the present experimental results. Its ability to reduce the radiative burden imparts the X-divertor with a key advantage. Lower radiation demands allow sharply peaked density profiles that enhance the bootstrap fraction creating the possibility for a highly increased beta for the same beta normal discharges. The X-divertor emerges as a beta-enhancer capable of raising it by up to roughly a factor of 2.

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

NASA Astrophysics Data System (ADS)

von Kleist, Max; Schütte, Christof; Zhang, Wei

2018-02-01

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

Ideas of Flat and Curved Space in History of Physics

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2006-04-01

Since ``everything which is not prohibited is compulsory'' (assigned to Gell-Mann) we can postulate infinite flat Cartesian N-dimensional (N: any integer) space-time (ST) as embedding for any curved ST. Ergodicity raises quest of whether total number of inflationary and/or Everett bubbles (mini-verses) is finite, countably infinite (aleph-zero) or uncountably infinite (aleph-one). Are these bubbles form Gaussian distribution or form some non-random subsetting? Perhaps, communication between mini-verses (idea of D.Deutsch) can be facilitated by a kind of minimax non-local dynamics akin to Fermat principle? (Minimax Principle in Bubble Cosmology). Even such classical effects as magnetism and polarization have some non-local features. Can we go below the Planck length to perhaps Compton wavelength of our ``Hubble's bubble'' (h/Mc = 10 to minus 95 m, if M = 10 to 54 kg)? When talking about time loops and ergodicity (eternal return paradigm) is there some hysterisis in the way quantum states are accessed in ``forward'' or ``reverse'' direction? (reverse direction implies backward causality of J.Wheeler and/or Aristotelian final causation).

Ergodicity of two hard balls in integrable polygons

NASA Astrophysics Data System (ADS)

Bálint, Péter; Troubetzkoy, Serge

2004-11-01

We prove the hyperbolicity, ergodicity and thus the Bernoulli property of two hard balls in one of the following four polygons: the square, the equilateral triangle, the 45°-45°-90° triangle or the 30°-60°-90° triangle.

Divertor impurity monitor for the International Thermonuclear Experimental Reactor

NASA Astrophysics Data System (ADS)

Sugie, T.; Ogawa, H.; Nishitani, T.; Kasai, S.; Katsunuma, J.; Maruo, M.; Ebisawa, K.; Ando, T.; Kita, Y.

1999-01-01

The divertor impurity monitoring system of the International Thermonuclear Experimental Reactor has been designed. The main functions of this system are to identify impurity species and to measure the two-dimensional distributions of the particle influxes in the divertor plasmas. The wavelength range is 200-1000 nm. The viewing fans are realized by molybdenum mirrors located in the divertor cassette. With additional viewing fans seeing through the gap between the divertor cassettes, the region approximately from the divertor leg to the x point will be observed. The light from the divertor region passes through the quartz windows on the divertor port plug and the cryostat, and goes through the dog-leg optics in the biological shield. Three different type of spectrometers: (i) survey spectrometers for impurity species monitoring, (ii) filter spectrometers for the particle influx measurement with the spatial resolution of 10 mm and the time resolution of 1 ms, and (iii) high dispersion spectrometers for high resolution wavelength measurements are designed. These spectrometers are installed just behind the biological shield (for λ<450 nm) to prevent the transmission loss in fiber and in the diagnostic room (for λ⩾450 nm) from the point of view of accessibility and flexibility. The optics have been optimized by a ray trace analysis. As a result, 10-15 mm spatial resolution will be achieved in all regions of the divertor.

Response to "Comment on `Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake' " [Phys. Plasmas 21, 054701 (2014)

NASA Astrophysics Data System (ADS)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh

2014-05-01

Relying on coil positions relative to the plasma, the "Comment on `Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake' " [Phys. Plasmas 21, 054701 (2014)], emphasizes a criterion for divertor characterization that was critiqued to be ill posed [M. Kotschenreuther et al., Phys. Plasmas 20, 102507 (2013)]. We find that no substantive physical differences flow from this criteria. However, using these criteria, the successful NSTX experiment by Ryutov et al. [Phys. Plasmas 21, 054701 (2014)] has the coil configuration of an X-divertor (XD), rather than a snowflake (SF). On completing the divertor index (DI) versus distance graph for this NSTX shot (which had an inexplicably missing region), we find that the DI is like an XD for most of the outboard wetted divertor plate. Further, the "proximity condition," used to define an SF [M. Kotschenreuther et al., Phys. Plasmas 20, 102507 (2013)], does not have a substantive physics basis to override metrics based on flux expansion and line length. Finally, if the criteria of the comment are important, then the results of NSTX-like experiments could have questionable applicability to reactors.

Comparison of 2D simulations of detached divertor plasmas with divertor Thomson measurements in the DIII-D tokamak

DOE PAGES

Rognlien, Thomas D.; McLean, Adam G.; Fenstermacher, Max E.; ...

2017-01-27

A modeling study is reported using new 2D data from DIII-D tokamak divertor plasmas and improved 2D transport model that includes large cross-field drifts for the numerically difficult H-mode regime. The data set, which spans a range of plasmas densities for both forward and reverse toroidal magnetic field (B t) over a range of plasma densities, is provided by divertor Thomson scattering (DTS). Measurements utilizing X-point sweeping give corresponding 2D profiles of electron temperature (T e) and density (n e) across both divertor legs for individual discharges. The calculations show the same features of in/out plasma asymmetries as measured inmore » the experiment, with the normal B t direction (ion ∇B drift toward the X-point) having higher n e and lower T e in the inner divertor leg than outer. Corresponding emission data for total radiated power shows a strong inner-divertor/outer-divertor asymmetry that is reproduced by the simulations. Furthermore, these 2D UEDGE transport simulations are enabled for steep-gradient H-mode conditions by newly implemented algorithms to control isolated grid-scale irregularities.« less

Two-way DF relaying assisted D2D communication: ergodic rate and power allocation

NASA Astrophysics Data System (ADS)

Ni, Yiyang; Wang, Yuxi; Jin, Shi; Wong, Kai-Kit; Zhu, Hongbo

2017-12-01

In this paper, we investigate the ergodic rate for a device-to-device (D2D) communication system aided by a two-way decode-and-forward (DF) relay node. We first derive closed-form expressions for the ergodic rate of the D2D link under asymmetric and symmetric cases, respectively. We subsequently discuss two special scenarios including weak interference case and high signal-to-noise ratio case. Then we derive the tight approximations for each of the considered scenarios. Assuming that each transmitter only has access to its own statistical channel state information (CSI), we further derive closed-form power allocation strategy to improve the system performance according to the analytical results of the ergodic rate. Furthermore, some insights are provided for the power allocation strategy based on the analytical results. The strategies are easy to compute and require to know only the channel statistics. Numerical results show the accuracy of the analysis results under various conditions and test the availability of the power allocation strategy.

How a Small Quantum Bath Can Thermalize Long Localized Chains

NASA Astrophysics Data System (ADS)

Luitz, David J.; Huveneers, François; De Roeck, Wojciech

2017-10-01

We investigate the stability of the many-body localized phase for a system in contact with a single ergodic grain modeling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consisting of only three qubits can delocalize a localized chain as soon as the localization length exceeds a critical value separating localized and extended regimes of the whole system. We present a simple theory, consistent with De Roeck and Huveneers's arguments in [Phys. Rev. B 95, 155129 (2017), 10.1103/PhysRevB.95.155129] that assumes a system to be locally ergodic unless the local relaxation time determined by Fermi's golden rule is larger than the inverse level spacing. This theory predicts a critical value for the localization length that is perfectly consistent with our numerical calculations. We analyze in detail the behavior of local operators inside and outside the ergodic grain and find excellent agreement of numerics and theory.

Alternative divertor target concepts for next step fusion devices

NASA Astrophysics Data System (ADS)

Mazul, I. V.

2016-12-01

The operational conditions of a divertor target in the next steps of fusion devices are more severe in comparison with ITER. The current divertor designs and technologies have a limited application concerning these conditions, and so new design concepts/technologies are required. The main reasons which practically prevent the use of the traditional motionless solid divertor target are analyzed. We describe several alternative divertor target concepts in this paper. The comparative analysis of these concepts (including the advantages and the drawbacks) is made and the prospects for their practical implementation are prioritized. The concept of the swept divertor target with a liquid metal interlayer between the moving armour and motionless heat-sink is presented in more detail. The critical issues of this design are listed and outlined, and the possible experiments are presented.

Dynamics of Granular Materials

NASA Technical Reports Server (NTRS)

Behringer, Robert P.

1996-01-01

Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, l/f noise, and fractional Brownian motion provide examples. Work beginning at Duke will focus on gravity driven convection, mixing and gravitational collapse. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collections of grains and the dynamics of a collections of molecules. In particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. In the absence of a steady energy input, granular materials undergo a rapid collapse which is strongly influenced by the presence of gravity. Fluctuations on laboratory scales in such quantities as the stress can be very large-as much as an order of magnitude greater than the mean.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

DOE FES FY2017 Joint Research Target Fourth Quarter Milestone Report for theNational Spherical Torus Experiment Upgrade.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soukhanovskii, V. A.

2017-09-13

A successful high-performance plasma operation with a radiative divertor has been demonstrated on many tokamak devices, however, significant uncertainty remains in accurately modeling detachment thresholds, and in how detachment depends on divertor geometry. Whereas it was originally planned to perform dedicated divertor experiments on the National Spherical Tokamak Upgrade to address critical detachment and divertor geometry questions for this milestone, the experiments were deferred due to technical difficulties. Instead, existing NSTX divertor data was summarized and re-analyzed where applicable, and additional simulations were performed.

Divertor Heat Flux Reduction and Detachment in the National Spherical Torus eXperiment.

NASA Astrophysics Data System (ADS)

Soukhanovskii, Vsevolod

2007-11-01

Steady-state handling of the heat flux is a critical divertor issue for both the International Thermonuclear Experimental Reactor and spherical torus (ST) devices. Because of an inherently compact divertor, it was thought that ST-based devices might not be able to fully utilize radiative and dissipative divertor techniques based on induced power and momentum loss. However, initial experiments conducted in the National Spherical Torus Experiment in an open geometry horizontal carbon plate divertor using 0.8 MA 2-6 MW NBI-heated lower single null H-mode plasmas at the lower end of elongations κ=1.8-2.4 and triangularities δ=0.45-0.75 demonstrated that high divertor peak heat fluxes, up to 6-10 MW/ m^2, could be reduced by 50-75% using a high-recycling radiative divertor regime with D2 injection. Furthermore, similar reduction was obtained with a partially detached divertor (PDD) at high D2 injection rates, however, it was accompanied by an X-point MARFE that quickly led to confinement degradation. Another approach takes advantage of the ST relation between strong shaping and high performance, and utilizes the poloidal magnetic flux expansion in the divertor region. Up to 60 % reduction in divertor peak heat flux was achieved at similar levels of scrape-off layer power by varying plasma shaping and thereby increasing the outer strike point (OSP) poloidal flux expansion from 4-6 to 18-22. In recent experiments conducted in highly-shaped 1.0-1.2 MA 6 MW NBI heated H-mode plasmas with divertor D2 injection at rates up to 10^22 s-1, a PDD regime with OSP peak heat flux 0.5-1.5 MW/m^2 was obtained without noticeable confinement degradation. Calculations based on a two point scrape-off layer model with parameterized power and momentum losses show that the short parallel connection length at the OSP sets the upper limit on the radiative exhaust channel, and both the impurity radiation and large momentum sink achievable only at high divertor neutral pressures are required for detachment.

Protein electron transfer: is biology (thermo)dynamic?

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.

2015-12-01

Simple physical mechanisms are behind the flow of energy in all forms of life. Energy comes to living systems through electrons occupying high-energy states, either from food (respiratory chains) or from light (photosynthesis). This energy is transformed into the cross-membrane proton-motive force that eventually drives all biochemistry of the cell. Life’s ability to transfer electrons over large distances with nearly zero loss of free energy is puzzling and has not been accomplished in synthetic systems. The focus of this review is on how this energetic efficiency is realized. General physical mechanisms and interactions that allow proteins to fold into compact water-soluble structures are also responsible for a rugged landscape of energy states and a broad distribution of relaxation times. Specific to a protein as a fluctuating thermal bath is the protein-water interface, which is heterogeneous both dynamically and structurally. The spectrum of interfacial fluctuations is a consequence of protein’s elastic flexibility combined with a high density of surface charges polarizing water dipoles into surface nanodomains. Electrostatics is critical to the protein function and the relevant questions are: (i) What is the spectrum of interfacial electrostatic fluctuations? (ii) Does the interfacial biological water produce electrostatic signatures specific to proteins? (iii) How is protein-mediated chemistry affected by electrostatics? These questions connect the fluctuation spectrum to the dynamical control of chemical reactivity, i.e. the dependence of the activation free energy of the reaction on the dynamics of the bath. Ergodicity is often broken in protein-driven reactions and thermodynamic free energies become irrelevant. Continuous ergodicity breaking in a dense spectrum of relaxation times requires using dynamically restricted ensembles to calculate statistical averages. When applied to the calculation of the rates, this formalism leads to the nonergodic activated kinetics, which extends the transition-state theory to dynamically dispersive media. Releasing the grip of thermodynamics in kinetic calculations through nonergodicity provides the mechanism for an efficient optimization between reaction rates and the spectrum of relaxation times of the protein-water thermal bath. Bath dynamics, it appears, play as important role as the free energy in optimizing biology’s performance.

Nonequilibrium viscosity of glass

NASA Astrophysics Data System (ADS)

Mauro, John C.; Allan, Douglas C.; Potuzak, Marcel

2009-09-01

Since glass is a nonequilibrium material, its properties depend on both composition and thermal history. While most prior studies have focused on equilibrium liquid viscosity, an accurate description of nonequilibrium viscosity is essential for understanding the low temperature dynamics of glass. Departure from equilibrium occurs as a glass-forming system is cooled through the glass transition range. The glass transition involves a continuous breakdown of ergodicity as the system gradually becomes trapped in a subset of the available configurational phase space. At very low temperatures a glass is perfectly nonergodic (or “isostructural”), and the viscosity is described well by an Arrhenius form. However, the behavior of viscosity during the glass transition range itself is not yet understood. In this paper, we address the problem of glass viscosity using the enthalpy landscape model of Mauro and Loucks [Phys. Rev. B 76, 174202 (2007)] for selenium, an elemental glass former. To study a wide range of thermal histories, we compute nonequilibrium viscosity with cooling rates from 10-12 to 1012K/s . Based on these detailed landscape calculations, we propose a simplified phenomenological model capturing the essential physics of glass viscosity. The phenomenological model incorporates an ergodicity parameter that accounts for the continuous breakdown of ergodicity at the glass transition. We show a direct relationship between the nonequilibrium viscosity parameters and the fragility of the supercooled liquid. The nonequilibrium viscosity model is validated against experimental measurements of Corning EAGLE XG™ glass. The measurements are performed using a specially designed beam-bending apparatus capable of accurate nonequilibrium viscosity measurements up to 1016Pas . Using a common set of parameters, the phenomenological model provides an accurate description of EAGLE XG™ viscosity over the full range of measured temperatures and fictive temperatures.

Control of particle and power exhaust in pellet fuelled ITER DT scenarios employing integrated models

NASA Astrophysics Data System (ADS)

Wiesen, S.; Köchl, F.; Belo, P.; Kotov, V.; Loarte, A.; Parail, V.; Corrigan, G.; Garzotti, L.; Harting, D.

2017-07-01

The integrated model JINTRAC is employed to assess the dynamic density evolution of the ITER baseline scenario when fuelled by discrete pellets. The consequences on the core confinement properties, α-particle heating due to fusion and the effect on the ITER divertor operation, taking into account the material limitations on the target heat loads, are discussed within the integrated model. Using the model one can observe that stable but cyclical operational regimes can be achieved for a pellet-fuelled ITER ELMy H-mode scenario with Q  =  10 maintaining partially detached conditions in the divertor. It is shown that the level of divertor detachment is inversely correlated with the core plasma density due to α-particle heating, and thus depends on the density evolution cycle imposed by pellet ablations. The power crossing the separatrix to be dissipated depends on the enhancement of the transport in the pedestal region being linked with the pressure gradient evolution after pellet injection. The fuelling efficacy of the deposited pellet material is strongly dependent on the E  ×  B plasmoid drift. It is concluded that integrated models like JINTRAC, if validated and supported by realistic physics constraints, may help to establish suitable control schemes of particle and power exhaust in burning ITER DT-plasma scenarios.

Advanced Plasma Shape Control to Enable High-Performance Divertor Operation on NSTX-U

NASA Astrophysics Data System (ADS)

Vail, Patrick; Kolemen, Egemen; Boyer, Mark; Welander, Anders

2017-10-01

This work presents the development of an advanced framework for control of the global plasma shape and its application to a variety of shape control challenges on NSTX-U. Operations in high-performance plasma scenarios will require highly-accurate and robust control of the plasma poloidal shape to accomplish such tasks as obtaining the strong-shaping required for the avoidance of MHD instabilities and mitigating heat flux through regulation of the divertor magnetic geometry. The new control system employs a high-fidelity model of the toroidal current dynamics in NSTX-U poloidal field coils and conducting structures as well as a first-principles driven calculation of the axisymmetric plasma response. The model-based nature of the control system enables real-time optimization of controller parameters in response to time-varying plasma conditions and control objectives. The new control scheme is shown to enable stable and on-demand plasma operations in complicated magnetic geometries such as the snowflake divertor. A recently-developed code that simulates the nonlinear evolution of the plasma equilibrium is used to demonstrate the capabilities of the designed shape controllers. Plans for future real-time implementations on NSTX-U and elsewhere are also presented. Supported by the US DOE under DE-AC02-09CH11466.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vahala, G.; Tracy, E.

During the past year, the authors have concentrated on (1) divertor physics, (2) thermo-lattice Boltzmann (TLBE) approach to turbulence, and (3) phase space techniques in gyro-resonance problems in collaboration with Dieter Sigmar (MIT), Sergei Krasheninnikov (MIT), Linda Vahala (ODU), Joseph Morrison (AS and M/NASA-Langley), Pavol Pavlo and Josef Preinhaelter (institute of Plasma Physics, Czech Academy of Sciences) and Allan Kaufman (LBL/U.C.Berkeley). Using a 2-equation compressible closure model with a 2D mean flow, the authors are investigating the effects of 3D neutral turbulence on reducing the heat load to the divertor plate by various toroidal cavity geometries. These studies are beingmore » extended to examine 3D mean flows. Thermal Lattice Boltzmann (TLBE) methods are being investigated to handle 3D turbulent flows in nontrivial geometries. It is planned to couple the TLBE collisional regime to the weakly collisional regime and so be able to tackle divertor physics. In the application of phase space techniques to minority-ion RF heating, resonance heating is treated as a multi-stage process. A generalization of the Case-van Kampen analysis is presented for multi-dimensional non-uniform plasmas. Effects such as particle trapping and the ray propagation dynamics in tokamak geometry can now be handled using Weyl calculus.« less

Divertor target shape optimization in realistic edge plasma geometry

NASA Astrophysics Data System (ADS)

Dekeyser, W.; Reiter, D.; Baelmans, M.

2014-07-01

Tokamak divertor design for next-step fusion reactors heavily relies on numerical simulations of the plasma edge. Currently, the design process is mainly done in a forward approach, where the designer is strongly guided by his experience and physical intuition in proposing divertor shapes, which are then thoroughly assessed by numerical computations. On the other hand, automated design methods based on optimization have proven very successful in the related field of aerodynamic design. By recasting design objectives and constraints into the framework of a mathematical optimization problem, efficient forward-adjoint based algorithms can be used to automatically compute the divertor shape which performs the best with respect to the selected edge plasma model and design criteria. In the past years, we have extended these methods to automated divertor target shape design, using somewhat simplified edge plasma models and geometries. In this paper, we build on and extend previous work to apply these shape optimization methods for the first time in more realistic, single null edge plasma and divertor geometry, as commonly used in current divertor design studies. In a case study with JET-like parameters, we show that the so-called one-shot method is very effective is solving divertor target design problems. Furthermore, by detailed shape sensitivity analysis we demonstrate that the development of the method already at the present state provides physically plausible trends, allowing to achieve a divertor design with an almost perfectly uniform power load for our particular choice of edge plasma model and design criteria.

Tokamak power exhaust with the snowflake divertor: Present results and outstanding issues

DOE PAGES

Soukhanovskii, V. A.; Xu, X.

2015-09-15

Here, a snowflake divertor magnetic configuration (Ryutov in Phys Plasmas 14(6):064502, 2007) with the second-order poloidal field null offers a number of possible advantages for tokamak plasma heat and particle exhaust in comparison with the standard poloidal divertor with the first-order null. Results from snowflake divertor experiments are briefly reviewed and future directions for research in this area are outlined.

Interpretations of the impact of cross-field drifts on divertor flows in DIII-D with UEDGE

DOE PAGES

Jaervinen, Aaro E.; Allen, Steve L.; Groth, Mathias; ...

2017-01-27

Simulations using the multi-fluid code UEDGE indicates that, in low confinement (Lmode) plasmas in DIII-D, recycling driven flows dominate poloidal particle flows in the divertor, whereas E×B drift flows dominate the radial particle flows. In contrast, in high confinement (H-mode) conditions E×B drift flows dominate both poloidal and radial particle flows in the divertor. UEDGE indicates that the toroidal C 2+ flow velocities in the divertor plasma are entrained within 30% to the background deuterium flow in both Land H-mode plasmas in the plasma region where the CIII 465 nm emission is measured. Therefore, UEDGE indicates that the Carbon Dopplermore » Coherence Imaging System (CIS), measuring the toroidal velocity of the C 2+ ions, can provide insight to the deuterium flows in the divertor. Parallel-to-B velocity dominates the toroidal divertor flow; direct drift impact being less than 1%. Toroidal divertor flow is predicted to reverse when the magnetic field is reversed. This is explained by the parallel-B flow towards the nearest divertor plate corresponding to opposite toroidal directions in opposite toroidal field configurations. Due to strong poloidal E×B flows in H-mode, net poloidal particle transport can be in opposite direction than the poloidal component of the parallel-B plasma flow.« less

Rheological observation of glassy dynamics of dilute polymer solutions near the coil-stretch transition in elongational flows.

PubMed

Sridhar, T; Nguyen, D A; Prabhakar, R; Prakash, J Ravi

2007-04-20

It has long been conjectured that the macroscopic dynamics of dilute polymer solutions may exhibit a glasslike slowdown caused by ergodicity breaking, in the vicinity of the coil-stretch transition in elongational flows. We report experimental observations using a filament stretching rheometer that confirm the existence of such glassy states. It is observed that different time-dependent elongational strain-rate profiles lead to a pronounced history dependence and aging effects within a narrow range of strain rates. The results have a direct bearing on the analysis and design of processes employing dilute polymer solutions, such as ink-jet printing, surface coating, and turbulent-drag reduction.

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

2014-01-01

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

Testing the role of molecular physics in dissipative divertor operations through helium plasmas at DIII-D

DOE PAGES

Canik, John M.; Briesemeister, Alexis R.; McLean, Adam G.; ...

2017-05-10

Recent experiments in DIII-D helium plasmas are examined to resolve the role of atomic and molecular physics in major discrepancies between experiment and modeling of dissipative divertor operation. Helium operation removes the complicated molecular processes of deuterium plasmas that are a prime candidate for the inability of standard fluid models to reproduce dissipative divertor operation, primarily the consistent under-prediction of radiated power. Modeling of these experiments shows that the full divertor radiation can be accounted for, but only if measures are taken to ensure that the model reproduces the measured divertor density. Relying on upstream measurements instead results in amore » lower divertor density and radiation than is measured, indicating a need for improved modeling of the connection between the diverter and the upstream scrape-off layer. Furthermore, these results show that fluid models are able to quantitatively describe the divertor-region plasma, including radiative losses, and indicate that efforts to improve the fidelity of the molecular deuterium models are likely to help resolve the discrepancy in radiation for deuterium plasmas.« less

Exploration of magnetic perturbation effects on advanced divertor configurations in NSTX-U

DOE Data Explorer

Frerichs, H. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Waters, I. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Schmitz, O. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Canal, G. P. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Evans, T. E. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Feng, Y. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Soukhanovskii, V. A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

2016-06-01

The control of divertor heat loads - both steady state and transient - remains a key challenge for the successful operation of ITER and FNSF. Magnetic perturbations provide a promising technique to control ELMs (transients), but understanding their detailed impact is difficult due to their symmetry breaking nature. One approach for reducing steady state heat loads are so called 'advanced divertors' which aim at optimizing the magnetic field configuration: the snowflake and the (super-)X-divertor. It is likely that both concepts - magnetic perturbations and advanced divertors - will have to work together, and we explore their interaction based on the NSTX-U setup. An overview of different divertor configurations under the impact of magnetic perturbations is presented, and the resulting impact on plasma edge transport is investigated with the EMC3-EIRENE code. Variations in size of the magnetic footprint of the perturbed separatrix are found, which is related to the level of flux expansion on the divertor target. Non-axisymmetric peaking of the heat flux related to the perturbed separatrix is found at the outer strike point, but only in locations where flux expansion is not too large.

Evaluation of heat and particle controllability on the JT-60SA divertor

NASA Astrophysics Data System (ADS)

Kawashima, H.; Hoshino, K.; Shimizu, K.; Takizuka, T.; Ide, S.; Sakurai, S.; Asakura, N.

2011-08-01

The JT-60SA divertor design has been established on the basis of engineering requirements and physics analysis. Heat and particle fluxes under the full input power of 41 MW can give severe heat loads on the divertor targets, while the allowable heat load is limited below 15 MW/m2. Dependence of the heat flux mitigation on a D2 gas-puff is evaluated by SONIC simulations for high density (ne_ave ˜ 1 × 1020 m-3) high current plasmas. It is found that the peak heat load 10 MW/m2 with dense (ned > 4 × 1020 m-3) and cold (Ted, Tid ⩽ 1 eV) divertor plasmas are obtained at a moderate gas-puff of Γpuff = 15 × 1021 s-1. Divertor plasmas are controlled from attached to detached condition using the divertor pump with pumping-speed below 100 m3/s. In full non-inductive current drive plasmas with low density (ne_ave ˜ 5 × 1019 m-3), the reduction of divertor heat load is achieved with the Ar injection.

Optimized tokamak power exhaust with double radiative feedback in ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Kallenbach, A.; Bernert, M.; Eich, T.; Fuchs, J. C.; Giannone, L.; Herrmann, A.; Schweinzer, J.; Treutterer, W.; the ASDEX Upgrade Team

2012-12-01

A double radiative feedback technique has been developed on the ASDEX Upgrade tokamak for optimization of power exhaust with a standard vertical target divertor. The main chamber radiation is measured in real time by a subset of three foil bolometer channels and controlled by argon injection in the outer midplane. The target heat flux is in addition controlled by nitrogen injection in the divertor private flux region using either a thermoelectric sensor or the scaled divertor radiation obtained by a bolometer channel in the outer divertor. No negative interference of the two radiation controllers has been observed so far. The combination of main chamber and divertor radiative cooling extends the operational space of a standard divertor configuration towards high values of P/R. Pheat/R = 14 MW m-1 has been achieved so far with nitrogen seeding alone as well as with combined N + Ar injection, with the time-averaged divertor peak heat flux below 5 MW m-2. Good plasma performance can be maintained under these conditions, namely H98(y,2) = 1 and βN = 3.

Crowding Induces Complex Ergodic Diffusion and Dynamic Elongation of Large DNA Molecules

PubMed Central

Chapman, Cole D.; Gorczyca, Stephanie; Robertson-Anderson, Rae M.

2015-01-01

Despite the ubiquity of molecular crowding in living cells, the effects of crowding on the dynamics of genome-sized DNA are poorly understood. Here, we track single, fluorescent-labeled large DNA molecules (11, 115 kbp) diffusing in dextran solutions that mimic intracellular crowding conditions (0–40%), and determine the effects of crowding on both DNA mobility and conformation. Both DNAs exhibit ergodic Brownian motion and comparable mobility reduction in all conditions; however, crowder size (10 vs. 500 kDa) plays a critical role in the underlying diffusive mechanisms and dependence on crowder concentration. Surprisingly, in 10-kDa dextran, crowder influence saturates at ∼20% with an ∼5× drop in DNA diffusion, in stark contrast to exponentially retarded mobility, coupled to weak anomalous subdiffusion, with increasing concentration of 500-kDa dextran. Both DNAs elongate into lower-entropy states (compared to random coil conformations) when crowded, with elongation states that are gamma distributed and fluctuate in time. However, the broadness of the distribution of states and the time-dependence and length scale of elongation length fluctuations depend on both DNA and crowder size with concentration having surprisingly little impact. Results collectively show that mobility reduction and coil elongation of large crowded DNAs are due to a complex interplay between entropic effects and crowder mobility. Although elongation and initial mobility retardation are driven by depletion interactions, subdiffusive dynamics, and the drastic exponential slowing of DNA, up to ∼300×, arise from the reduced mobility of larger crowders. Our results elucidate the highly important and widely debated effects of cellular crowding on genome-sized DNA. PMID:25762333

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

PubMed Central

Khammash, Mustafa

2014-01-01

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191

Increased heat dissipation with the X-divertor geometry facilitating detachment onset at lower density in DIII-D

NASA Astrophysics Data System (ADS)

Covele, B.; Kotschenreuther, M.; Mahajan, S.; Valanju, P.; Leonard, A.; Watkins, J.; Makowski, M.; Fenstermacher, M.; Si, H.

2017-08-01

The X-divertor geometry on DIII-D has demonstrated reduced particle and heat fluxes to the target, facilitating detachment onset at 10-20% lower upstream density and higher H-mode pedestal pressure than a standard divertor. SOLPS modeling suggests that this effect cannot be explained by an increase in total connection length alone, but rather by the addition of connection length specifically in the power-dissipating volume near the target, via poloidal flux expansion and flaring. However, poloidal flaring must work synergistically with divertor closure to most effectively reduce the detachment density threshold. The model also points to carbon radiation as the primary driver of power dissipation in divertors on the DIII-D floor, which is consistent with experimental observations. Sustainable divertor detachment at lower density has beneficial consequences for energy confinement and current drive efficiency for core operation, while simultaneously satisfying the exhaust requirements of the plasma-facing components.

Reactor application of an improved bundle divertor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, T.F.; Ruck, G.W.; Lee, A.Y.

1978-11-01

A Bundle Divertor was chosen as the impurity control and plasma exhaust system for the beam driven Demonstration Tokamak Hybrid Reactor - DTHR. In the context of a preconceptual design study of the reactor and associated facility a bundle divertor concept was developed and integrated into the reactor system. The overall system was found feasible and scalable for reactors with intermediate torodial field strengths on axis. The important design characteristics are: the overall average current density of the divertor coils is 0.73 kA for each tesla of toroidal field on axis; the divertor windings are made from super-conducting cables supportedmore » by steel structures and are designed to be maintainable; the particle collection assembly and auxiliary cryosorption vacuum pump are dual systems designed such that they can be reactivated alterntively to allow for continuous reactor operation; and the power requirement for energizing and operating the divertor is about 5 MW.« less

Evaluating Stellarator Divertor Designs with EMC3

NASA Astrophysics Data System (ADS)

Bader, Aaron; Anderson, D. T.; Feng, Y.; Hegna, C. C.; Talmadge, J. N.

2013-10-01

In this paper various improvements of stellarator divertor design are explored. Next step stellarator devices require innovative divertor solutions to handle heat flux loads and impurity control. One avenue is to enhance magnetic flux expansion near strike points, somewhat akin to the X-Divertor concept in Tokamaks. The effect of judiciously placed external coils on flux deposition is calculated for configurations based on the HSX stellarator. In addition, we attempt to optimize divertor plate location to facilitate the external coil placement. Alternate areas of focus involve altering edge island size to elucidate the driving physics in the edge. The 3-D nature of stellarators complicates design and necessitates analysis of new divertor structures with appropriate simulation tools. We evaluate the various configurations with the coupled codes EMC3-EIRENE, allowing us to benchmark configurations based on target heat flux, impurity behavior, radiated power, and transitions to high recycling and detached regimes. Work supported by DOE-SC0006103.

Upgrade of Langmuir probe diagnostic in ITER-like tungsten mono-block divertor on experimental advanced superconducting tokamak.

PubMed

Xu, J C; Wang, L; Xu, G S; Luo, G N; Yao, D M; Li, Q; Cao, L; Chen, L; Zhang, W; Liu, S C; Wang, H Q; Jia, M N; Feng, W; Deng, G Z; Hu, L Q; Wan, B N; Li, J; Sun, Y W; Guo, H Y

2016-08-01

In order to withstand rapid increase in particle and power impact onto the divertor and demonstrate the feasibility of the ITER design under long pulse operation, the upper divertor of the EAST tokamak has been upgraded to actively water-cooled, ITER-like tungsten mono-block structure since the 2014 campaign, which is the first attempt for ITER on the tokamak devices. Therefore, a new divertor Langmuir probe diagnostic system (DivLP) was designed and successfully upgraded on the tungsten divertor to obtain the plasma parameters in the divertor region such as electron temperature, electron density, particle and heat fluxes. More specifically, two identical triple probe arrays have been installed at two ports of different toroidal positions (112.5-deg separated toroidally), which can provide fundamental data to study the toroidal asymmetry of divertor power deposition and related 3-dimension (3D) physics, as induced by resonant magnetic perturbations, lower hybrid wave, and so on. The shape of graphite tip and fixed structure of the probe are designed according to the structure of the upper tungsten divertor. The ceramic support, small graphite tip, and proper connector installed make it possible to be successfully installed in the very narrow interval between the cassette body and tungsten mono-block, i.e., 13.5 mm. It was demonstrated during the 2014 and 2015 commissioning campaigns that the newly upgraded divertor Langmuir probe diagnostic system is successful. Representative experimental data are given and discussed for the DivLP measurements, then proving its availability and reliability.

Experimental study of heating scheme effect on the inner divertor power footprint widths in EAST lower single null discharges

NASA Astrophysics Data System (ADS)

Deng, G. Z.; Xu, J. C.; Liu, X.; Liu, X. J.; Liu, J. B.; Zhang, H.; Liu, S. C.; Chen, L.; Yan, N.; Feng, W.; Liu, H.; Xia, T. Y.; Zhang, B.; Shao, L. M.; Ming, T. F.; Xu, G. S.; Guo, H. Y.; Xu, X. Q.; Gao, X.; Wang, L.

2018-04-01

A comprehensive work of the effects of plasma current and heating schemes on divertor power footprint widths is carried out in the experimental advanced superconducting tokamak (EAST). The divertor power footprint widths, i.e., the scrape-off layer heat flux decay length λ q and the heat spreading S, are crucial physical and engineering parameters for fusion reactors. Strong inverse scaling of λ q and S with plasma current have been demonstrated for both neutral beam (NB) and lower hybrid wave (LHW) heated L-mode and H-mode plasmas at the inner divertor target. For plasmas heated by the combination of the two kinds of auxiliary heating schemes (NB and LHW), the divertor power widths tend to be larger in plasmas with higher ratio of LHW power. Comparison between experimental heat flux profiles at outer mid-plane (OMP) and divertor target for NB heated and LHW heated L-mode plasmas reveals that the magnetic topology changes induced by LHW may be the main reason to the wider divertor power widths in LHW heated discharges. The effect of heating schemes on divertor peak heat flux has also been investigated, and it is found that LHW heated discharges tend to have a lower divertor peak heat flux compared with NB heated discharges under similar input power. All these findings seem to suggest that plasmas with LHW auxiliary heating scheme are better heat exhaust scenarios for fusion reactors and should be the priorities for the design of next-step fusion reactors like China Fusion Engineering Test Reactor.

Upgrade of Langmuir probe diagnostic in ITER-like tungsten mono-block divertor on experimental advanced superconducting tokamak

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, J. C.; Jia, M. N.; Feng, W.

2016-08-15

In order to withstand rapid increase in particle and power impact onto the divertor and demonstrate the feasibility of the ITER design under long pulse operation, the upper divertor of the EAST tokamak has been upgraded to actively water-cooled, ITER-like tungsten mono-block structure since the 2014 campaign, which is the first attempt for ITER on the tokamak devices. Therefore, a new divertor Langmuir probe diagnostic system (DivLP) was designed and successfully upgraded on the tungsten divertor to obtain the plasma parameters in the divertor region such as electron temperature, electron density, particle and heat fluxes. More specifically, two identical triplemore » probe arrays have been installed at two ports of different toroidal positions (112.5-deg separated toroidally), which can provide fundamental data to study the toroidal asymmetry of divertor power deposition and related 3-dimension (3D) physics, as induced by resonant magnetic perturbations, lower hybrid wave, and so on. The shape of graphite tip and fixed structure of the probe are designed according to the structure of the upper tungsten divertor. The ceramic support, small graphite tip, and proper connector installed make it possible to be successfully installed in the very narrow interval between the cassette body and tungsten mono-block, i.e., 13.5 mm. It was demonstrated during the 2014 and 2015 commissioning campaigns that the newly upgraded divertor Langmuir probe diagnostic system is successful. Representative experimental data are given and discussed for the DivLP measurements, then proving its availability and reliability.« less

Nanoscale mapping of heterogeneity of the polarization reversal in lead-free relaxor–ferroelectric ceramic composites

DOE PAGES

Gobeljic, D.; Shvartsman, V. V.; Belianinov, A.; ...

2016-01-05

Relaxor/ferroelectric ceramic/ceramic composites have shown to be promising in generating large electromechanical strain at moderate electric fields. However, the mechanisms of polarization and strain coupling between grains of different nature in the composites remain unclear. To rationalize the coupling mechanisms we performed advanced piezoresponse force microscopy (PFM) studies of 0.92BNT-0.06BT-0.02KNN/0.93BNT-0.07BT (ergodic/non-ergodic relaxor) composites. PFM is able to distinguish grains of different phases by characteristic domain patterns. Polarization switching has been probed locally, on a sub-grain scale. k-Means clustering analysis applied to arrays of local hysteresis loops reveals variations of polarization switching characteristics between the ergodic and non-ergodic relaxor grains. Here,more » we report a different set of switching parameters for grains in the composites as opposed to the pure phase samples. These results confirm ceramic/ceramic composites to be a viable approach to tailor the piezoelectric properties and optimize the macroscopic electromechanical characteristics.« less

Simulations of carbon sputtering in fusion reactor divertor plates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marian, J; Zepeda-Ruiz, L A; Gilmer, G H

2005-10-03

The interaction of edge plasma with material surfaces raises key issues for the viability of the International Thermonuclear Reactor (ITER) and future fusion reactors, including heat-flux limits, net material erosion, and impurity production. After exposure of the graphite divertor plate to the plasma in a fusion device, an amorphous C/H layer forms. This layer contains 20-30 atomic percent D/T bonded to C. Subsequent D/T impingement on this layer produces a variety of hydrocarbons that are sputtered back into the sheath region. We present molecular dynamics (MD) simulations of D/T impacts on amorphous carbon layer as a function of ion energymore » and orientation, using the AIREBO potential. In particular, energies are varied between 10 and 150 eV to transition from chemical to physical sputtering. These results are used to quantify yield, hydrocarbon composition and eventual plasma contamination.« less

Derivation of the dipole map

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2004-09-01

In our method of maps [Punjabi et al., Phy. Rev. Lett. 69, 3322 (1992), and Punjabi et al., J. Plasma Phys. 52, 91 (1994)], symplectic maps are used to calculate the trajectories of magnetic field lines in divertor tokamaks. Effects of the magnetic perturbations are calculated using the low MN map [Ali et al., Phys. Plasmas 11, 1908 (2004)] and the dipole map [Punjabi et al., Phys. Plasmas 10, 3992 (2003)]. The dipole map is used to calculate the effects of externally located current carrying coils on the trajectories of the field lines, the stochastic layer, the magnetic footprint, and the heat load distribution on the collector plates in divertor tokamaks [Punjabi et al., Phys. Plasmas 10, 3992 (2003)]. Symplectic maps are general, efficient, and preserve and respect the Hamiltonian nature of the dynamics. In this brief communication, a rigorous mathematical derivation of the dipole map is given.

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

Real-time control of divertor detachment in H-mode with impurity seeding using Langmuir probe feedback in JET-ITER-like wall

NASA Astrophysics Data System (ADS)

Guillemaut, C.; Lennholm, M.; Harrison, J.; Carvalho, I.; Valcarcel, D.; Felton, R.; Griph, S.; Hogben, C.; Lucock, R.; Matthews, G. F.; Perez Von Thun, C.; Pitts, R. A.; Wiesen, S.; contributors, JET

2017-04-01

Burning plasmas with 500 MW of fusion power on ITER will rely on partially detached divertor operation to keep target heat loads at manageable levels. Such divertor regimes will be maintained by a real-time control system using the seeding of radiative impurities like nitrogen (N), neon or argon as actuator and one or more diagnostic signals as sensors. Recently, real-time control of divertor detachment has been successfully achieved in Type I ELMy H-mode JET-ITER-like wall discharges by using saturation current (I sat) measurements from divertor Langmuir probes as feedback signals to control the level of N seeding. The degree of divertor detachment is calculated in real-time by comparing the outer target peak I sat measurements to the peak I sat value at the roll-over in order to control the opening of the N injection valve. Real-time control of detachment has been achieved in both fixed and swept strike point experiments. The system has been progressively improved and can now automatically drive the divertor conditions from attached through high recycling and roll-over down to a user-defined level of detachment. Such a demonstration is a successful proof of principle in the context of future operation on ITER which will be extensively equipped with divertor target probes.

Giant room-temperature electrostrictive coefficients in lead-free relaxor ferroelectric ceramics by compositional tuning

NASA Astrophysics Data System (ADS)

Ullah, Aman; Gul, Hafiza Bushra; Ullah, Amir; Sheeraz, Muhammad; Bae, Jong-Seong; Jo, Wook; Ahn, Chang Won; Kim, Ill Won; Kim, Tae Heon

2018-01-01

A thermotropic phase boundary between non-ergodic and ergodic relaxor phases is tuned in lead-free Bi1/2Na1/2TiO3-based ceramics through a structural transition driven by compositional modification (usually named as "morphotropic approach"). The substitution of Bi(Ni1/2Ti1/2)O3 for Bi1/2(Na0.78K0.22)1/2TiO3 induces a transition from tetragonal to "metrically" cubic phase and thereby, the ergodic relaxor ferroelectric phase becomes predominant at room temperature. A shift of the transition temperature (denoted as TF-R) in the non-ergodic-to-ergodic phase transition is corroborated via temperature-dependent dielectric permittivity and loss measurements. By monitoring the chemical composition dependence of polarization-electric field and strain-electric field hysteresis loops, it is possible to track the critical concentration of Bi(Ni1/2Ti1/2)O3 where the (1 - x)Bi0.5(Na0.78K0.22)0.5TiO3-xBi(Ni0.5Ti0.5)O3 ceramic undergoes the phase transition around room temperature. At the Bi(Ni0.5Ti0.5)O3 content of x = 0.050, the highest room-temperature electrostrictive coefficient of 0.030 m4/C2 is achieved with no hysteretic characteristic, which can foster the realization of actual electrostrictive devices with high operational efficiency at room temperature.

Impact of nonzero boresight pointing error on ergodic capacity of MIMO FSO communication systems.

PubMed

Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Beatriz; Castillo-Vázquez, Carmen

2016-02-22

A thorough investigation of the impact of nonzero boresight pointing errors on the ergodic capacity of multiple-input/multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) reception under different turbulence models, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.) is addressed in this paper. Novel closed-form asymptotic expressions at high signal-to-noise ratio (SNR) for the ergodic capacity of MIMO FSO systems are derived when different geometric arrangements of the receive apertures at the receiver are considered in order to reduce the effect of nonzero inherent boresight displacement, which is inevitably present when more than one receive aperture is considered. As a result, the asymptotic ergodic capacity of MIMO FSO systems is evaluated over log-normal (LN), gamma-gamma (GG) and exponentiated Weibull (EW) atmospheric turbulence in order to study different turbulence conditions, different sizes of receive apertures as well as different aperture averaging conditions. It is concluded that the use of single-input/multiple-output (SIMO) and MIMO techniques can significantly increase the ergodic capacity respect to the direct path link when the inherent boresight displacement takes small values, i.e. when the spacing among receive apertures is not too big. The effect of nonzero additional boresight errors, which is due to the thermal expansion of the building, is evaluated in multiple-input/single-output (MISO) and single-input/single-output (SISO) FSO systems. Simulation results are further included to confirm the analytical results.

Impurity seeding for tokamak power exhaust: from present devices via ITER to DEMO

NASA Astrophysics Data System (ADS)

Kallenbach, A.; Bernert, M.; Dux, R.; Casali, L.; Eich, T.; Giannone, L.; Herrmann, A.; McDermott, R.; Mlynek, A.; Müller, H. W.; Reimold, F.; Schweinzer, J.; Sertoli, M.; Tardini, G.; Treutterer, W.; Viezzer, E.; Wenninger, R.; Wischmeier, M.; the ASDEX Upgrade Team

2013-12-01

A future fusion reactor is expected to have all-metal plasma facing materials (PFMs) to ensure low erosion rates, low tritium retention and stability against high neutron fluences. As a consequence, intrinsic radiation losses in the plasma edge and divertor are low in comparison to devices with carbon PFMs. To avoid localized overheating in the divertor, intrinsic low-Z and medium-Z impurities have to be inserted into the plasma to convert a major part of the power flux into radiation and to facilitate partial divertor detachment. For burning plasma conditions in ITER, which operates not far above the L-H threshold power, a high divertor radiation level will be mandatory to avoid thermal overload of divertor components. Moreover, in a prototype reactor, DEMO, a high main plasma radiation level will be required in addition for dissipation of the much higher alpha heating power. For divertor plasma conditions in present day tokamaks and in ITER, nitrogen appears most suitable regarding its radiative characteristics. If elevated main chamber radiation is desired as well, argon is the best candidate for the simultaneous enhancement of core and divertor radiation, provided sufficient divertor compression can be obtained. The parameter Psep/R, the power flux through the separatrix normalized by the major radius, is suggested as a suitable scaling (for a given electron density) for the extrapolation of present day divertor conditions to larger devices. The scaling for main chamber radiation from small to large devices has a higher, more favourable dependence of about Prad,main/R2. Krypton provides the smallest fuel dilution for DEMO conditions, but has a more centrally peaked radiation profile compared to argon. For investigation of the different effects of main chamber and divertor radiation and for optimization of their distribution, a double radiative feedback system has been implemented in ASDEX Upgrade (AUG). About half the ITER/DEMO values of Psep/R have been achieved so far, and close to DEMO values of Prad,main/R2, albeit at lower Psep/R. Further increase of this parameter may be achieved by increasing the neutral pressure or improving the divertor geometry.

Weakly Nonergodic Dynamics in the Gross-Pitaevskii Lattice

NASA Astrophysics Data System (ADS)

Mithun, Thudiyangal; Kati, Yagmur; Danieli, Carlo; Flach, Sergej

2018-05-01

The microcanonical Gross-Pitaevskii (also known as the semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm densities. The grand canonical Gibbs distribution fails to describe a part of the density space, due to the boundedness of its kinetic energy spectrum. We define Poincaré equilibrium manifolds and compute the statistics of microcanonical excursion times off them. The tails of the distribution functions quantify the proximity of the many-body dynamics to a weakly nonergodic phase, which occurs when the average excursion time is infinite. We find that a crossover to weakly nonergodic dynamics takes place inside the non-Gibbs phase, being unnoticed by the largest Lyapunov exponent. In the ergodic part of the non-Gibbs phase, the Gibbs distribution should be replaced by an unknown modified one. We relate our findings to the corresponding integrable limit, close to which the actions are interacting through a short range coupling network.

Acoustic dynamics of supercooled indomethacin probed by Brillouin light scattering.

PubMed

De Panfilis, S; Pogna, E A A; Virga, A; Scopigno, T

2014-07-21

Acoustics dynamics of the molecular glass-former indomethacin (IMC) have been investigated by Brillouin light scattering (BLS) at GHz frequencies. Elastic response of the system has been tracked from the melting temperature down to the glass transition through the supercooled liquid. Both the structural arrest and the vibrational dynamics are described by modeling the experimentally determined dynamic structure factor within the framework of the Langevin equation, through a simplified choice of memory function which allows one to determine sound velocity and the acoustic attenuation coefficient as a function of temperature. The density fluctuation spectra in the glassy phase, as probed by BLS, are compared with time-domain results from photoacoustics experiments. The arising scenario is discussed in the context of current literature reporting inelastic X-ray scattering and BLS in platelet geometry. The link between the probed elastic properties and the non-ergodicity factor of the glass phase is finally scrutinized.

Invariant measures in brain dynamics

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł

2006-10-01

This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a “folding” property on the space of ensembles.

Intermittent Fermi-Pasta-Ulam Dynamics at Equilibrium

NASA Astrophysics Data System (ADS)

Campbell, David; Danieli, Carlo; Flach, Sergej

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body syste. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. We show that previously obtained scaling laws for equipartition times are modified at low energy density due to an unexpected slowing down of the relaxation. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. The long excursions arise from sticky dynamics close to regular orbits in the phase space. Our method is generalizable to large classes of many-body systems. The authors acknowledge financial support from IBS (Project Code IBS-R024-D1).

Electric-field-temperature phase diagram of Mn-doped Bi{sub 0.5}(Na{sub 0.9}K{sub 0.1}){sub 0.5}TiO{sub 3} ceramics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ehara, Yoshitaka, E-mail: Ehara@ceramics.tu-darmstadt.de; Novak, Nikola; Yasui, Shintaro

2015-12-28

An electric field–temperature (E-T) phase diagram for a lead-free 0.5 mol. % Mn-doped Bi(Na{sub 0.1}K{sub 0.9})TiO{sub 3} ceramics was investigated. The x-ray diffraction, dielectric and polarization measurements revealed relaxor behavior and were used to characterize the stability regions of the non-ergodic relaxor, ergodic relaxor and electric field induced ferroelectric states. As indicated by the polarization–current density profiles, transformation between two electric fields, induced ferroelectric states with opposite polarization direction arise via a two-step process through an intermediate relaxor state. Interplay between the ferroelectric state conversion and intermediate relaxor state is governed by the dynamics of polarization relaxation. The presented E-T phase diagrammore » revealed the effects of the applied electric field and temperature on stability regions. This is of special interest since the Bi{sub 0.5}(Na{sub 0.1}K{sub 0.9}){sub 0.5}TiO{sub 3} ceramics were proposed as a potential piezoceramic material.« less

Ergodicity of the Stochastic Nosé-Hoover Heat Bath

NASA Astrophysics Data System (ADS)

Wei Chung Lo,; Baowen Li,

2010-07-01

We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

The influence of Filaments in the Private Flux Region on Divertor Power and Particle Deposition

NASA Astrophysics Data System (ADS)

Harrison, James

2014-10-01

Recent advances in imaging of the MAST divertor have revealed, for the first time, evidence for filaments in the private flux region (PFR). Detailed analysis of the image data shows 3 distinct types of fluctuations occurring within the divertor volume: highly sheared filaments in the SOL originating from the outer midplane, high frequency (>50 kHz) filaments near the separatrix of the outer divertor leg and filaments in the private flux region originating from inner divertor leg. With the need to extrapolate divertor performance from existing machines to future devices, these observations can contribute to our quantitative understanding of transport in the PFR. In particular, they suggest that transport in the PFR is, at least in part, driven by turbulence, which may not be well captured by the Eich/Wagner description of the divertor footprint, expressed in terms of exponential decay in space above the X-point and Gaussian spreading below the X-point. The PFR filaments are observed to move largely parallel with the flux surfaces in a way equivalent to a toroidal angular velocity of order 2 ×104 rad/s in H-mode, and slower by a factor of order 2 in L-mode. During their transit parallel to the flux surfaces across the PFR, the filaments eject plasma in bursts, away from the separatrix, deeper into the private flux region. Correlation analysis suggests that they are generated by processes local to the inner divertor leg, as there is a weak correlation between fluctuations in the SOL and PFR above what is expected from line integration effects. Scaling of filament properties with machine operating parameters, such as plasma current, density and auxiliary heating power will be presented, together with a comparison with data from divertor Langmuir probes and IR thermography to estimate the role PFR filaments play in determining the width of the divertor footprint.

An innovative small angle slot divertor concept for long pulse advanced tokamaks

NASA Astrophysics Data System (ADS)

Guo, Houyang

2017-10-01

A new Small Angle Slot (SAS) divertor is being developed in DIII-D to address the challenge of efficient divertor heat dispersal at the relatively low plasma density required for non-inductive current drive in future advanced tokamaks. SAS features a small incident angle near the plasma strike point on the divertor target plate with a progressively opening slot. SOLPS (B2-Eirene) edge code analysis finds that SAS can achieve strong plasma cooling when the strike point is placed near the small angle target plate in the slot, leading to low electron temperature Te across the entire divertor target. This is enabled by strong coupling between a gas tight slot and directed neutral recycling by the small angle target to enhance neutral buildup near the target. SOLPS analysis reveals a strong correlation between Te and D2 density at the target for various divertor configurations including the flat target, slanted target, and lower single null divertor. The strong correlation suggests that achievement of low Te may reduce essentially to identifying the divertor baffle geometry that achieves the highest target gas density at a given upstream condition. The SAS divertor concept has recently been tested in DIII-D for a range of plasma configurations and conditions with precise control of slot strike point location. In confirmation of SOLPS predictions, a sharp transition is observed when the strike point is moved to the critical outer corner of SAS. A set of Langmuir probes imbedded in SAS show that the Te radial profile, which is peaked at the strike point when it is located away from the SAS corner, becomes low across the target when the strike point is located near the corner. With further increase in density, deep-slot detachment occurs with Te 1 eV, measured by the unique DIII-D divertor Thomson Scattering diagnostic. Work supported by US DOE under DE-FC02-04ER54698.

Exploration of magnetic perturbation effects on advanced divertor configurations in NSTX-U

DOE PAGES

Frerichs, H.; Schmitz, O.; Waters, I.; ...

2016-06-01

The control of divertor heat loads - both steady state and transient - remains a key challenge for the successful operation of ITER and FNSF. Magnetic perturbations provide a promising technique to control ELMs (transients), but understanding their detailed impact is difficult due to their symmetry breaking nature. One approach for reducing steady state heat loads are so called 'advanced divertors' which aim at optimizing the magnetic field configuration: the snowflake and the (super-)X-divertor. It is likely that both concepts - magnetic perturbations and advanced divertors - will have to work together, and we explore their inter- action based onmore » the NSTX-U setup. An overview of different divertor con gurations under the impact of magnetic perturbations is presented, and the resulting impact on plasma edge transport is investigated with the EMC3-EIRENE code. Variations in size of the magnetic footprint of the perturbed separatrix are found, which is related to the level of flux expansion on the divertor target. Non-axisymmetric peaking of the heat flux related to the perturbed separatrix is found at the outer strike point, but only in locations where flux expansion is not too large.« less

Examining Innovative Divertor and Main Chamber Options for a National Divertor Test Tokamak

NASA Astrophysics Data System (ADS)

Labombard, B.; Umansky, M.; Brunner, D.; Kuang, A. Q.; Marmar, E.; Wallace, G.; Whyte, D.; Wukitch, S.

2016-10-01

The US fusion community has identified a compelling need for a National Divertor Test Tokamak. The 2015 Community Planning Workshop on PMI called for a national working group to develop options. Important elements of a NDTT, adopted from the ADX concept, include the ability to explore long-leg divertor `solutions for power exhaust and particle control' (Priority Research Direction B) and to employ inside-launch RF actuators combined with double-null topologies as `plasma solution for main chamber wall components, including tools for controllable sustained operation' (PRD-C). Here we examine new information on these ideas. The projected performance of super-X and X-point target long-leg divertors is looking very promising; a stable fully-detached divertor condition handling an order-of-magnitude increase in power handling over conventional divertors may be possible. New experiments on Alcator C-Mod are addressing issues of high-field side versus low-field side heat flux sharing in double-null topologies and the screening of impurities that might originate from RF actuators placed in the high-field side - both with favorable results. Supported by USDoE Awards DE-FC02-99ER54512 and DE-AC52-07NA27344.

Turbulent Simulations of Divertor Detachment Based On BOUT + + Framework

NASA Astrophysics Data System (ADS)

Chen, Bin; Xu, Xueqiao; Xia, Tianyang; Ye, Minyou

2015-11-01

China Fusion Engineering Testing Reactor is under conceptual design, acting as a bridge between ITER and DEMO. The detached divertor operation offers great promise for a reduction of heat flux onto divertor target plates for acceptable erosion. Therefore, a density scan is performed via an increase of D2 gas puffing rates in the range of 0 . 0 ~ 5 . 0 ×1023s-1 by using the B2-Eirene/SOLPS 5.0 code package to study the heat flux control and impurity screening property. As the density increases, it shows a gradually change of the divertor operation status, from low-recycling regime to high-recycling regime and finally to detachment. Significant radiation loss inside the confined plasma in the divertor region during detachment leads to strong parallel density and temperature gradients. Based on the SOLPS simulations, BOUT + + simulations will be presented to investigate the stability and turbulent transport under divertor plasma detachment, particularly the strong parallel gradient driven instabilities and enhanced plasma turbulence to spread heat flux over larger surface areas. The correlation between outer mid-plane and divertor turbulence and the related transport will be analyzed. Prepared by LLNL under Contract DE-AC52-07NA27344. LLNL-ABS-675075.

Favorable effects of turbulent plasma mixing on the performance of innovative tokamak divertors

NASA Astrophysics Data System (ADS)

Ryutov, D. D.; Cohen, R. H.; Rognlien, T. D.; Umansky, M. V.

2013-10-01

The problem of reducing the heat load on plasma-facing components is one of the most demanding issues for MFE devices. The general approach to the solution of this problem is the use of a specially configured poloidal magnetic field, so called magnetic divertors. In recent years, novel divertors possessing the 2-nd and 3-rd order nulls of the poloidal field (PF) have been proposed. They are called a ``snowflake'' (SF) and a ``cloverleaf'' (CL) divertor, respectively, due to characteristic shape of the magnetic separatrix. Among several beneficial features of such divertors is an effect of strong turbulent plasma mixing that is intrinsic to the zone of weak PF near the null-point. The turbulence spreads the heat flux between multiple divertor exhaust channels and increases the heat flux width within each channel. Among physical processes affecting the onset of convection the curvature-driven mode of axisymmetric rolls is most prominent. The effect is quite significant for the SF and is even stronger for the CL divertor. Projections to future ITER-scale facilities are discussed. Work performed for U.S. DoE by LLNL under Contract DE-AC52-07NA27344.

Design of ITER divertor VUV spectrometer and prototype test at KSTAR tokamak

NASA Astrophysics Data System (ADS)

Seon, Changrae; Hong, Joohwan; Song, Inwoo; Jang, Juhyeok; Lee, Hyeonyong; An, Younghwa; Kim, Bosung; Jeon, Taemin; Park, Jaesun; Choe, Wonho; Lee, Hyeongon; Pak, Sunil; Cheon, MunSeong; Choi, Jihyeon; Kim, Hyeonseok; Biel, Wolfgang; Bernascolle, Philippe; Barnsley, Robin; O'Mullane, Martin

2017-12-01

Design and development of the ITER divertor VUV spectrometer have been performed from the year 1998, and it is planned to be installed in the year 2027. Currently, the design of the ITER divertor VUV spectrometer is in the phase of detail design. It is optimized for monitoring of chord-integrated VUV signals from divertor plasmas, chosen to contain representative lines emission from the tungsten as the divertor material, and other impurities. Impurity emission from overall divertor plasmas is collimated through the relay optics onto the entrance slit of a VUV spectrometer with working wavelength range of 14.6-32 nm. To validate the design of the ITER divertor VUV spectrometer, two sets of VUV spectrometers have been developed and tested at KSTAR tokamak. One set of spectrometer without the field mirror employs a survey spectrometer with the wavelength ranging from 14.6 nm to 32 nm, and it provides the same optical specification as the spectrometer part of the ITER divertor VUV spectrometer system. The other spectrometer with the wavelength range of 5-25 nm consists of a commercial spectrometer with a concave grating, and the relay mirrors with the same geometry as the relay mirrors of the ITER divertor VUV spectrometer. From test of these prototypes, alignment method using backward laser illumination could be verified. To validate the feasibility of tungsten emission measurement, furthermore, the tungsten powder was injected in KSTAR plasmas, and the preliminary result could be obtained successfully with regard to the evaluation of photon throughput. Contribution to the Topical Issue "Atomic and Molecular Data and their Applications", edited by Gordon W.F. Drake, Jung-Sik Yoon, Daiji Kato, Grzegorz Karwasz.

Development of a Method for Local Electron Temperature and Density Measurements in the Divertor of the JET Tokamak

NASA Technical Reports Server (NTRS)

Jupen, C.; Meigs, A.; Bhatia, A. K.; Brezinsek, S.; OMullane, M.

2004-01-01

Plasma volume recombination in the divertor, a process in which charged particles recombine to neutral atoms, contributes to plasma detachment and hence cooling at the divertor target region. Detachment has been observed at JET and other tokamaks and is known to occur at low electron temperatures (T(sub e)<1 eV) and at high electron density (n(sub e)>10(exp 20)/m(exp 3)). The ability to measure such low temperatures is therefore of interest for modelling the divertor. In present work we report development of a new spectroscopic technique for investigation of local electron density (n(sub e)) and temperature (T,) in the outer divertor at JET.

Divertor electron temperature and impurity diffusion measurements with a spectrally resolved imaging radiometer.

PubMed

Clayton, D J; Jaworski, M A; Kumar, D; Stutman, D; Finkenthal, M; Tritz, K

2012-10-01

A divertor imaging radiometer (DIR) diagnostic is being studied to measure spatially and spectrally resolved radiated power P(rad)(λ) in the tokamak divertor. A dual transmission grating design, with extreme ultraviolet (~20-200 Å) and vacuum ultraviolet (~200-2000 Å) gratings placed side-by-side, can produce coarse spectral resolution over a broad wavelength range covering emission from impurities over a wide temperature range. The DIR can thus be used to evaluate the separate P(rad) contributions from different ion species and charge states. Additionally, synthetic spectra from divertor simulations can be fit to P(rad)(λ) measurements, providing a powerful code validation tool that can also be used to estimate electron divertor temperature and impurity transport.

Competitive agents in a market: Statistical physics of the minority game

NASA Astrophysics Data System (ADS)

Sherrington, David

2007-10-01

A brief review is presented of the minority game, a simple frustrated many-body system stimulated by considerations of a market of competitive speculative agents. Its cooperative behaviour exhibits phase transitions and both ergodic and non-ergodic regimes. It provides novel challenges to statistical physics, reminiscent of those of mean-field spin glasses.

Entropy, Ergodicity, and Stem Cell Multipotency

NASA Astrophysics Data System (ADS)

Ridden, Sonya J.; Chang, Hannah H.; Zygalakis, Konstantinos C.; MacArthur, Ben D.

2015-11-01

Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference.

Dynamics of a stochastic cell-to-cell HIV-1 model with distributed delay

NASA Astrophysics Data System (ADS)

Ji, Chunyan; Liu, Qun; Jiang, Daqing

2018-02-01

In this paper, we consider a stochastic cell-to-cell HIV-1 model with distributed delay. Firstly, we show that there is a global positive solution of this model before exploring its long-time behavior. Then sufficient conditions for extinction of the disease are established. Moreover, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Finally, we provide some numerical examples to illustrate theoretical results.

Electron pressure balance in the SOL through the transition to detachment

DOE PAGES

McLean, A. G.; Leonard, A. W.; Makowski, M. A.; ...

2015-02-07

Upgrades to core and divertor Thomson scattering (DTS) diagnostics at DIII-D have provided measurements of electron pressure profiles in the lower divertor from attached- to fully-detached divertor plasma conditions. Detailed, multistep sequences of discharges with increasing line-averaged density were run at several levels of P inj. Strike point sweeping allowed 2D divertor characterization using DTS optimized to measure T e down to 0.5 eV. The ionization front at the onset of detachment is found to move upwards in a controlled manner consistent with the indication that scrape-off layer parallel power flux is converted from conducted to convective heat transport. Measurementsmore » of n e, T e and p e in the divertor versus Lparallel demonstrate a rapid transition from Te ≥ 15 eV to ≤3 eV occurring both at the outer strike point and upstream of the X-point. Furthermore, these observations provide a strong benchmark for ongoing modeling of divertor detachment for existing and future tokamak devices.« less

Increased heat dissipation with the X-divertor geometry facilitating detachment onset at lower density in DIII-D

DOE PAGES

Covele, Brent; Kotschenreuther, M.; Mahajan, S.; ...

2017-06-23

The X-Divertor geometry on DIII-D has demonstrated reduced particle and heat fluxes to the target, facilitating detachment onset at ~20% lower upstream density and higher H-mode pedestal pressure than a standard divertor. SOLPS modeling suggests that this effect cannot be explained by an increase in total connection length alone, but rather by the addition of connection length specifically in the power-dissipating volume near the target, via poloidal flux expansion and flaring. But, poloidal flaring must work synergistically with divertor closure to most effectively reduce the detachment density threshold. Furthermore, the model also points to carbon radiation as the primary drivermore » of power dissipation in divertors on the DIII-D floor, which is consistent with experimental observations. Sustainable divertor detachment at lower density has beneficial consequences for energy confinement and current drive efficiency in the core for advanced tokamak (AT) operation, while simultaneously satisfying the exhaust requirements of the plasma-facing components.« less

Electron pressure balance in the SOL through the transition to detachment

NASA Astrophysics Data System (ADS)

McLean, A. G.; Leonard, A. W.; Makowski, M. A.; Groth, M.; Allen, S. L.; Boedo, J. A.; Bray, B. D.; Briesemeister, A. R.; Carlstrom, T. N.; Eldon, D.; Fenstermacher, M. E.; Hill, D. N.; Lasnier, C. J.; Liu, C.; Osborne, T. H.; Petrie, T. W.; Soukhanovskii, V. A.; Stangeby, P. C.; Tsui, C.; Unterberg, E. A.; Watkins, J. G.

2015-08-01

Upgrades to core and divertor Thomson scattering (DTS) diagnostics at DIII-D have provided measurements of electron pressure profiles in the lower divertor from attached- to fully-detached divertor plasma conditions. Detailed, multistep sequences of discharges with increasing line-averaged density were run at several levels of Pinj. Strike point sweeping allowed 2D divertor characterization using DTS optimized to measure Te down to 0.5 eV. The ionization front at the onset of detachment is found to move upwards in a controlled manner consistent with the indication that scrape-off layer parallel power flux is converted from conducted to convective heat transport. Measurements of ne, Te and pe in the divertor versus Lparallel demonstrate a rapid transition from Te ⩾ 15 eV to ⩽3 eV occurring both at the outer strike point and upstream of the X-point. These observations provide a strong benchmark for ongoing modeling of divertor detachment for existing and future tokamak devices.

Increased heat dissipation with the X-divertor geometry facilitating detachment onset at lower density in DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Covele, Brent; Kotschenreuther, M.; Mahajan, S.

The X-Divertor geometry on DIII-D has demonstrated reduced particle and heat fluxes to the target, facilitating detachment onset at ~20% lower upstream density and higher H-mode pedestal pressure than a standard divertor. SOLPS modeling suggests that this effect cannot be explained by an increase in total connection length alone, but rather by the addition of connection length specifically in the power-dissipating volume near the target, via poloidal flux expansion and flaring. But, poloidal flaring must work synergistically with divertor closure to most effectively reduce the detachment density threshold. Furthermore, the model also points to carbon radiation as the primary drivermore » of power dissipation in divertors on the DIII-D floor, which is consistent with experimental observations. Sustainable divertor detachment at lower density has beneficial consequences for energy confinement and current drive efficiency in the core for advanced tokamak (AT) operation, while simultaneously satisfying the exhaust requirements of the plasma-facing components.« less

Impurity ion flow and temperature measured in a detached divertor with externally applied non-axisymmetric fields on DIII-D

DOE PAGES

Briesemeister, A. R.; Isler, R. C.; Allen, S. L.; ...

2014-11-15

In this study, externally applied non-axisymmetric magnetic fields are shown to have little effect on the impurity ion flow velocity and temperature as measured by the multichord divertor spectrometer in the DIII-D divertor for both attached and detached conditions. These experiments were performed in H-mode plasmas with the grad-B drift toward the target plates, with and without n = 3 resonant magnetic perturbations (RMPs). The flow velocity in the divertor is shown to change by as much as 30% when deuterium gas puffing is used to create detachment of the divertor plasma. No measurable changes in the C III flowmore » were observed in response to the RMP fields for the conditions used in this work. Images of the C III emission are used along with divertor Thomson scattering to show that the local electron and C III temperatures are equilibrated for the conditions shown.« less

Analyses of microstructure, composition and retention of hydrogen isotopes in divertor tiles of JET with the ITER-like wall

NASA Astrophysics Data System (ADS)

Masuzaki, S.; Tokitani, M.; Otsuka, T.; Oya, Y.; Hatano, Y.; Miyamoto, M.; Sakamoto, R.; Ashikawa, N.; Sakurada, S.; Uemura, Y.; Azuma, K.; Yumizuru, K.; Oyaizu, M.; Suzuki, T.; Kurotaki, H.; Hamaguchi, D.; Isobe, K.; Asakura, N.; Widdowson, A.; Heinola, K.; Jachmich, S.; Rubel, M.; contributors, JET

2017-12-01

Results of the comprehensive surface analyses of divertor tiles and dusts retrieved from JET after the first ITER-like wall campaign (2011-2012) are presented. The samples cored from the divertor tiles were analyzed. Numerous nano-size bubble-like structures were observed in the deposition layer on the apron of the inner divertor tile, and a beryllium dust with the same structures were found in the matter collected from the inner divertor after the campaign. This suggests that the nano-size bubble-like structures can make the deposition layer to become brittle and may lead to cracking followed by dust generation. X-ray photoelectron spectroscopy analyses of chemical states of species in the deposition layers identified the formation of beryllium-tungsten intermetallic compounds on an inner vertical tile. Different tritium retention profiles along the divertor tiles were observed at the top surfaces and at deeper regions of the tiles by using the imaging plate technique.

Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems

NASA Astrophysics Data System (ADS)

Everest, B.; Marcuzzi, M.; Garrahan, J. P.; Lesanovsky, I.

2016-11-01

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization.

PubMed

De Luca, Andrea; Rosso, Alberto

2015-08-21

Dynamic nuclear polarization (DNP) is to date the most effective technique to increase the nuclear polarization opening disruptive perspectives for medical applications. In a DNP setting, the interacting spin system is quasi-isolated and brought out of equilibrium by microwave irradiation. Here we show that the resulting stationary state strongly depends on the ergodicity properties of the spin many-body eigenstates. In particular, the dipolar interactions compete with the disorder induced by local magnetic fields resulting in two distinct dynamical phases: while for weak interaction, only a small enhancement of polarization is observed, for strong interactions the spins collectively equilibrate to an extremely low effective temperature that boosts DNP efficiency. We argue that these two phases are intimately related to the problem of thermalization in closed quantum systems where a many-body localization transition can occur varying the strength of the interactions.

X-Divertor Geometries for Deeper Detachment Without Degrading the DIII-D H-Mode

NASA Astrophysics Data System (ADS)

Covele, Brent; Kotschenreuther, M. T.; Valanju, P. M.; Mahajan, S. M.; Leonard, A. W.; Hyatt, A. W.; McLean, A. G.; Thomas, D. M.; Guo, H. Y.; Watkins, J. G.; Makowski, M. A.; Hill, D. N.

2015-11-01

Recent DIII-D experiments comparing the standard divertor (SD) and X-Divertor (XD) geometries show heat and particle flux reduction at the divertor target plate. The XD features large poloidal flux expansion, increased connection length, and poloidal field line flaring, quantified by the Divertor Index. Both SD and XD were pushed deep into detachment with increased gas puffing, until core energy confinement and pedestal pressure were substantially reduced. As expected, outboard target heat fluxes are significantly reduced in the XD compared to the SD under similar upstream plasma conditions, even at low Greenwald fraction. The high-triangularity (floor) XD cases show larger reduction in temperature, heat, and particle flux relative to the SD in all cases, while low-triangularity (shelf) XD cases show more modest reductions over the SD. Consequently, heat flux reduction and divertor detachment may be achieved in the XD with less gas puffing and higher pedestal pressures. Further causative analysis, as well as detailed modeling with SOLPS, is underway. These initial experiments suggest the XD as a promising candidate to achieve divertor heat flux control compatible with robust H-mode operation. Work supported by US DOE under DE-FC02-04ER54698, DE-AC52-07NA27344, DE-FG02-04ER54754, and DE-FG02-04ER54742.

Critical need for MFE: the Alcator DX advanced divertor test facility

NASA Astrophysics Data System (ADS)

Vieira, R.; Labombard, B.; Marmar, E.; Irby, J.; Wolf, S.; Bonoli, P.; Fiore, C.; Granetz, R.; Greenwald, M.; Hutchinson, I.; Hubbard, A.; Hughes, J.; Lin, Y.; Lipschultz, B.; Parker, R.; Porkolab, M.; Reinke, M.; Rice, J.; Shiraiwa, S.; Terry, J.; Theiler, C.; Wallace, G.; White, A.; Whyte, D.; Wukitch, S.

2013-10-01

Three critical challenges must be met before a steady-state, power-producing fusion reactor can be realized: how to (1) safely handle extreme plasma exhaust power, (2) completely suppress material erosion at divertor targets and (3) do this while maintaining a burning plasma core. Advanced divertors such as ``Super X'' and ``X-point target'' may allow a fully detached, low temperature plasma to be produced in the divertor while maintaining a hot boundary layer around a clean plasma core - a potential game-changer for magnetic fusion. No facility currently exists to test these ideas at the required parallel heat flux densities. Alcator DX will be a national facility, employing the high magnetic field technology of Alcator combined with high-power ICRH and LHCD to test advanced divertor concepts at FNSF/DEMO power exhaust densities and plasma pressures. Its extended vacuum vessel contains divertor cassettes with poloidal field coils for conventional, snowflake, super-X and X-point target geometries. Divertor and core plasma performance will be explored in regimes inaccessible in conventional devices. Reactor relevant ICRF and LH drivers will be developed, utilizing high-field side launch platforms for low PMI. Alcator DX will inform the conceptual development and accelerate the readiness-for-deployment of next-step fusion facilities.

The dependence of divertor power sharing on magnetic flux balance in near double-null configurations on Alcator C-Mod

NASA Astrophysics Data System (ADS)

Brunner, D.; Kuang, A. Q.; LaBombard, B.; Terry, J. L.

2018-07-01

Management of power exhaust will be a crucial task for tokamak fusion reactors. Reactor concepts are often proposed with double-null divertors, i.e. having two magnetic separatrices in an up-down symmetric configuration. This arrangement is potentially advantageous since the majority of the tokamak exhaust power tends to flow to the outer pair of divertor legs at large major radius, where the geometry is favorable for spreading the heat over a large surface area and there is more room for advanced divertor configurations. Despite the importance, there have been relatively few studies of divertor power sharing in near double null configurations and no studies at the poloidal magnetic fields and scrape-off layer power widths anticipated for a reactor. Motivated by this need we have undertaken a systematic study on Alcator C-Mod, examining the effect of magnetic flux balance on the power sharing among the four divertor legs in near double-null plasmas. Ohmic L-modes at three values of plasma current and ICRF-heated enhanced D-alpha (EDA) H-modes and I-modes at a single value of plasma current are explored, producing poloidal magnetic fields of 0.42, 0.62 and 0.85 Tesla. For Ohmic L-modes and ICRF-heated EDA H-modes, we find that the point of equal power sharing between upper and lower divertors occurs remarkably close to a balanced double null. Power sharing amongst the outer (upper versus lower) and inner (upper versus lower) pairs of divertors can be described in terms of a logistic function of magnetic flux balance, consistent with heat flux mapping along magnetic field lines to the outer midplane. Power sharing between inner and outer legs is found to follow a Gaussian-like function of magnetic flux balance with non-zero power to the inner divertors at double null. The overall behavior of H-modes operated near double null and for I-modes operating to within one heat flux e-folding of double null are found similar to Ohmic L-modes, with a significant reduction of power on the inner divertor legs. The results are encapsulated in terms of empirically-informed analytic functions of magnetic flux balance. When combined with magnetic equilibrium control system specifications, these relationships can be used to specify the power flux handling requirements for each of the four divertor target plates.

Basic physical processes and reduced models for plasma detachment

NASA Astrophysics Data System (ADS)

Stangeby, P. C.

2018-04-01

The divertor of a tokamak reactor will have to satisfy a number of critical constraints, the first of which is that the divertor targets not fail due to excessive heating or sputter-erosion. This paramount constraint of target survival defines the operating window for the principal plasma properties at the divertor target, the density n t and temperature, T t. In particular T et < 10 eV is shown to be required. Code and experimental studies show that the pressure–momentum loss by the plasma that occurs along flux tubes in the edge, between the divertor entrance and target, (i) correlates strongly with T et, and (ii) begins to increase as T et falls below 10 eV, becoming very strong by 1 eV. The transition between the high-recycling regime and the detached divertor regime has therefore been defined here to occur when T et < 10 eV. Simple analytic models are developed (i) to relate (T t, n t) to the controlling conditions ‘upstream’ e.g. at the divertor entrance, and (ii) in turn to relate (T t, n t) to other important divertor quantities including (a) the required level of radiative cooling in the divertor, and (b) the ion flux to the target in the presence of volumetric loss of particles, momentum and power in the divertor. The 2 Point Model, 2PM, is a widely used analytic model for relating (T t, n t) to the controlling upstream conditions. The 2PM is derived here for various levels of complexity regarding the effects included. Analytic models of divertor detachment provide valuable insight and useful approximations, but more complete modeling requires the use of edge codes such as EDGE2D, SOLPS, SONIC, UEDGE, etc. Edge codes have grown to become quite sophisticated and now constitute, in effect, ‘code-experiments’ that—just as for actual experiments—can benefit from interpretation in terms of simple conceptual frameworks. 2 Point Model Formatting, 2PMF, of edge code output can provide such a conceptual framework. Methods of applying 2PMF are illustrated here with some examples.

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

NASA Astrophysics Data System (ADS)

Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Ergodic actions of SμU(2) on C∗-algebras from II1 subfactors

NASA Astrophysics Data System (ADS)

Pinzari, Claudia; Roberts, John E.

2010-03-01

To a proper inclusion N⊂M of II factors of finite Jones index [M:N], we associate an ergodic C∗-action of the quantum group SμU(2) (or more generally of certain groups Ao(F)). The higher relative commutant N'∩M can be identified with the spectral space of the rth tensor power u of the defining representation of the quantum group. The index and the deformation parameter are related by -1≤μ<0 and [M:N]=|μ+μ-1|. This ergodic action may be thought of as a virtual subgroup of SμU(2) in the sense of Mackey arising from the tensor category generated by the N-bimodule NMN. μ is negative as NMN is a real bimodule.

Design, R&D and commissioning of EAST tungsten divertor

NASA Astrophysics Data System (ADS)

Yao, D. M.; Luo, G. N.; Zhou, Z. B.; Cao, L.; Li, Q.; Wang, W. J.; Li, L.; Qin, S. G.; Shi, Y. L.; Liu, G. H.; Li, J. G.

2016-02-01

After commissioning in 2005, the EAST superconducting tokamak had been operated with its water cooled divertors for eight campaigns up to 2012, employing graphite as plasma facing material. With increase in heating power over 20 MW in recent years, the heat flux going to the divertors rises rapidly over 10 MW m-2 for steady state operation. To accommodate the rapid increasing heat load in EAST, the bolting graphite tile divertor must be upgraded. An ITER-like tungsten (W) divertor has been designed and developed; and firstly used for the upper divertor of EAST. The EAST upper W divertor is modular structure with 80 modules in total. Eighty sets of W/Cu plasma-facing components (PFC) with each set consisting of an outer vertical target (OVT), an inner vertical target (IVT) and a DOME, are attached to 80 stainless steel cassette bodies (CB) by pins. The monoblock W/Cu-PFCs have been developed for the strike points of both OVT and IVT, and the flat type W/Cu-PFCs for the DOME and the baffle parts of both OVT and IVT, employing so-called hot isostatic pressing (HIP) technology for tungsten to CuCrZr heat sink bonding, and electron beam welding for CuCrZr to CuCrZr and CuCrZr to other material bonding. Both monoblock and flat type PFC mockups passed high heat flux (HHF) testing by means of electron beam facilities. The 80 divertor modules were installed in EAST in 2014 and results of the first commissioning are presented in this paper.

Developing and validating advanced divertor solutions on DIII-D for next-step fusion devices

NASA Astrophysics Data System (ADS)

Guo, H. Y.; Hill, D. N.; Leonard, A. W.; Allen, S. L.; Stangeby, P. C.; Thomas, D.; Unterberg, E. A.; Abrams, T.; Boedo, J.; Briesemeister, A. R.; Buchenauer, D.; Bykov, I.; Canik, J. M.; Chrobak, C.; Covele, B.; Ding, R.; Doerner, R.; Donovan, D.; Du, H.; Elder, D.; Eldon, D.; Lasa, A.; Groth, M.; Guterl, J.; Jarvinen, A.; Hinson, E.; Kolemen, E.; Lasnier, C. J.; Lore, J.; Makowski, M. A.; McLean, A.; Meyer, B.; Moser, A. L.; Nygren, R.; Owen, L.; Petrie, T. W.; Porter, G. D.; Rognlien, T. D.; Rudakov, D.; Sang, C. F.; Samuell, C.; Si, H.; Schmitz, O.; Sontag, A.; Soukhanovskii, V.; Wampler, W.; Wang, H.; Watkins, J. G.

2016-12-01

A major challenge facing the design and operation of next-step high-power steady-state fusion devices is to develop a viable divertor solution with order-of-magnitude increases in power handling capability relative to present experience, while having acceptable divertor target plate erosion and being compatible with maintaining good core plasma confinement. A new initiative has been launched on DIII-D to develop the scientific basis for design, installation, and operation of an advanced divertor to evaluate boundary plasma solutions applicable to next step fusion experiments beyond ITER. Developing the scientific basis for fusion reactor divertor solutions must necessarily follow three lines of research, which we plan to pursue in DIII-D: (1) Advance scientific understanding and predictive capability through development and comparison between state-of-the art computational models and enhanced measurements using targeted parametric scans; (2) Develop and validate key divertor design concepts and codes through innovative variations in physical structure and magnetic geometry; (3) Assess candidate materials, determining the implications for core plasma operation and control, and develop mitigation techniques for any deleterious effects, incorporating development of plasma-material interaction models. These efforts will lead to design, installation, and evaluation of an advanced divertor for DIII-D to enable highly dissipative divertor operation at core density (n e/n GW), neutral fueling and impurity influx most compatible with high performance plasma scenarios and reactor relevant plasma facing components (PFCs). This paper highlights the current progress and near-term strategies of boundary/PMI research on DIII-D.

Developing and validating advanced divertor solutions on DIII-D for next-step fusion devices

DOE PAGES

Guo, H. Y.; Hill, D. N.; Leonard, A. W.; ...

2016-09-14

A major challenge facing the design and operation of next-step high-power steady-state fusion devices is to develop a viable divertor solution with order-of-magnitude increases in power handling capability relative to present experience, while having acceptable divertor target plate erosion and being compatible with maintaining good core plasma confinement. A new initiative has been launched on DIII-D to develop the scientific basis for design, installation, and operation of an advanced divertor to evaluate boundary plasma solutions applicable to next step fusion experiments beyond ITER. Developing the scientific basis for fusion reactor divertor solutions must necessarily follow three lines of research, whichmore » we plan to pursue in DIII-D: (1) Advance scientific understanding and predictive capability through development and comparison between state-of-the art computational models and enhanced measurements using targeted parametric scans; (2) Develop and validate key divertor design concepts and codes through innovative variations in physical structure and magnetic geometry; (3) Assess candidate materials, determining the implications for core plasma operation and control, and develop mitigation techniques for any deleterious effects, incorporating development of plasma-material interaction models. These efforts will lead to design, installation, and evaluation of an advanced divertor for DIII-D to enable highly dissipative divertor operation at core density (n e/n GW), neutral fueling and impurity influx most compatible with high performance plasma scenarios and reactor relevant plasma facing components (PFCs). In conclusion, this paper highlights the current progress and near-term strategies of boundary/PMI research on DIII-D.« less

Why many polymers are so fragile: A new perspective

DOE PAGES

Dalle-Ferrier, C.; Kisliuk, A.; Hong, L.; ...

2016-10-21

Many polymers exhibit much steeper temperature dependence of their structural relaxation time (higher fragility) than liquids of small molecules, and the mechanism of this unusually high fragility in polymers remains a puzzle. To reveal additional hints for understanding the underlying mechanism, we analyzed correlation of many properties of polymers to their fragility on example of model polymer polystyrene with various molecular weights (MWs). Here, we demonstrate that these correlations work for short chains (oligomers), but fail progressively with increase in MW. Our surprising discovery is that the steepness of the temperature dependence (fragility) of the viscosity that is determined bymore » chain relaxation follows the correlations at all molecular weights. These results suggest that the molecular level relaxation still follows the behavior usual for small molecules even in polymers, and its fragility (chain fragility) falls in the range usual for molecular liquids. It is the segmental relaxation that has this unusually high fragility. We also speculate that many polymers cannot reach an ergodic state on the time scale of segmental dynamics due to chain connectivity and rigidity. This leads to sharper decrease in accessible configurational entropy upon cooling and results in steeper temperature dependence of segmental relaxation. Our proposed scenario provides a new important insight into the specifics of polymer dynamics: the role of ergodicity time and length scale. At the end, we suggest that a similar scenario can be applicable also to other molecular systems with slow intra-molecular degrees of freedom and to chemically complex systems where the time scale of chemical fluctuations can be longer than the time scale of structural relaxation.« less

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles.

PubMed

Wheeler, Richard John

2015-11-05

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point "snapshot" of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes--cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)--as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. © 2015 Wheeler. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Why many polymers are so fragile: A new perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dalle-Ferrier, C.; Kisliuk, A.; Hong, L.

Many polymers exhibit much steeper temperature dependence of their structural relaxation time (higher fragility) than liquids of small molecules, and the mechanism of this unusually high fragility in polymers remains a puzzle. To reveal additional hints for understanding the underlying mechanism, we analyzed correlation of many properties of polymers to their fragility on example of model polymer polystyrene with various molecular weights (MWs). Here, we demonstrate that these correlations work for short chains (oligomers), but fail progressively with increase in MW. Our surprising discovery is that the steepness of the temperature dependence (fragility) of the viscosity that is determined bymore » chain relaxation follows the correlations at all molecular weights. These results suggest that the molecular level relaxation still follows the behavior usual for small molecules even in polymers, and its fragility (chain fragility) falls in the range usual for molecular liquids. It is the segmental relaxation that has this unusually high fragility. We also speculate that many polymers cannot reach an ergodic state on the time scale of segmental dynamics due to chain connectivity and rigidity. This leads to sharper decrease in accessible configurational entropy upon cooling and results in steeper temperature dependence of segmental relaxation. Our proposed scenario provides a new important insight into the specifics of polymer dynamics: the role of ergodicity time and length scale. At the end, we suggest that a similar scenario can be applicable also to other molecular systems with slow intra-molecular degrees of freedom and to chemically complex systems where the time scale of chemical fluctuations can be longer than the time scale of structural relaxation.« less

Optimization of a bundle divertor for FED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hively, L.M.; Rothe, K.E.; Minkoff, M.

1982-01-01

Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations.

Impurity-induced divertor plasma oscillations

DOE PAGES

Smirnov, R. D.; Kukushkin, A. S.; Krasheninnikov, S. I.; ...

2016-01-07

Two different oscillatory plasma regimes induced by seeding the plasma with high- and low-Z impurities are found for ITER-like divertor plasmas, using computer modeling with the DUSTT/UEDGE and SOLPS4.3 plasma-impurity transport codes. The oscillations are characterized by significant variations of the impurity-radiated power and of the peak heat load on the divertor targets. Qualitative analysis of the divertor plasma oscillations reveals different mechanisms driving the oscillations in the cases of high- and low-Z impurity seeding. The oscillations caused by the high-Z impurities are excited near the X-point by an impurity-related instability of the radiation-condensation type, accompanied by parallel impurity ionmore » transport affected by the thermal and plasma friction forces. The driving mechanism of the oscillations induced by the low-Z impurities is related to the cross-field transport of the impurity atoms, causing alteration between the high and low plasma temperature regimes in the plasma recycling region near the divertor targets. As a result, the implications of the impurity-induced plasma oscillations for divertor operation in the next generation tokamaks are also discussed.« less

The effects of particle recycling on the divertor plasma: A particle-in-cell with Monte Carlo collision simulation

NASA Astrophysics Data System (ADS)

Chang, Mingyu; Sang, Chaofeng; Sun, Zhenyue; Hu, Wanpeng; Wang, Dezhen

2018-05-01

A Particle-In-Cell (PIC) with Monte Carlo Collision (MCC) model is applied to study the effects of particle recycling on divertor plasma in the present work. The simulation domain is the scrape-off layer of the tokamak in one-dimension along the magnetic field line. At the divertor plate, the reflected deuterium atoms (D) and thermally released deuterium molecules (D2) are considered. The collisions between the plasma particles (e and D+) and recycled neutral particles (D and D2) are described by the MCC method. It is found that the recycled neutral particles have a great impact on divertor plasma. The effects of different collisions on the plasma are simulated and discussed. Moreover, the impacts of target materials on the plasma are simulated by comparing the divertor with Carbon (C) and Tungsten (W) targets. The simulation results show that the energy and momentum losses of the C target are larger than those of the W target in the divertor region even without considering the impurity particles, whereas the W target has a more remarkable influence on the core plasma.

Modelling of Divertor Detachment in MAST Upgrade

NASA Astrophysics Data System (ADS)

Moulton, David; Carr, Matthew; Harrison, James; Meakins, Alex

2017-10-01

MAST Upgrade will have extensive capabilities to explore the benefits of alternative divertor configurations such as the conventional, Super-X, x divertor, snowflake and variants in a single device with closed divertors. Initial experiments will concentrate on exploring the Super-X and conventional configurations, in terms of power and particle loads to divertor surfaces, access to detachment and its control. Simulations have been carried out with the SOLPS5.0 code validated against MAST experiments. The simulations predict that the Super-X configuration has significant advantages over the conventional, such as lower detachment threshold (2-3x lower in terms of upstream density and 4x higher in terms of PSOL). Synthetic spectroscopy diagnostics from these simulations have been created using the Raysect ray tracing code to produce synthetic filtered camera images, spectra and foil bolometer data. Forward modelling of the current set of divertor diagnostics will be presented, together with a discussion of future diagnostics and analysis to improve estimates of the plasma conditions. Work supported by the RCUK Energy Programme [Grant Number EP/P012450/1] and EURATOM.

Thermal Fatigue Study on the Divertor Plate Materials

NASA Astrophysics Data System (ADS)

Wu, Ji-hong; Zhang, Fu; Xu, Zeng-yu; Yan, Jian-cheng

2002-10-01

Thermal fatigue property of the divertor plate is one of the key issues that governs the lifetime of the divertor plate. Taking tungsten as surface material, a small-mock-up divertor plate was made by hot isostatic press welding (HIP). A thermal cycling experiment for divertor mock-up was carried out in the vacuum, where a high-heat-flux electronic gun was used as the thermal source. A cyclic heat flux of 9 MW/m2 was loaded onto the mock-up, a heating duration of 20 s was selected, the cooling water flow rate was 80 ml/s. After 1000 cycles, the surface and the W/Cu joint of the mock-up did not show any damage. The SEM was used to analyze the microstructure of the welding joint, where no cracks were found also.

Modelling of 13CH4 injection and local carbon deposition at the outer divertor of ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Aho-Mantila, L.; Airila, M. I.; Wischmeier, M.; Krieger, K.; Pugno, R.; Coster, D. P.; Chankin, A. V.; Neu, R.; Rohde, V.

2009-12-01

Numerical modelling of 13CH4 injection into the outer divertor plasma of the full tungsten, vertical target of ASDEX Upgrade is presented. The SOLPS5.0 code package is used to calculate a realistic scrape-off layer plasma background corresponding to L-mode discharges in the attached divertor plasma regime. The ERO code is then used for detailed modelling of the hydrocarbon break-up, re-deposition and re-erosion processes. The deposition patterns observed at two different poloidal locations are shown to strongly reflect the cross-field gradients in divertor plasma density and temperature, as well as the local plasma collisionality. Experimental results with forward and reversed BT, accompanied by numerical modelling, also point towards a significant poloidal hydrocarbon E×B drift in the divertor region.

Conceptual design of a divertor Thomson scattering diagnostic for NSTX-U

DOE Office of Scientific and Technical Information (OSTI.GOV)

McLean, A. G., E-mail: mclean@fusion.gat.com; Soukhanovskii, V. A.; Allen, S. L.

2014-11-15

A conceptual design for a divertor Thomson scattering (DTS) diagnostic has been developed for the NSTX-U device to operate in parallel with the existing multipoint Thomson scattering system. Higher projected peak heat flux in NSTX-U will necessitate application of advanced magnetics geometries and divertor detachment. Interpretation and modeling of these divertor scenarios will depend heavily on local measurement of electron temperature, T{sub e}, and density, n{sub e}, which DTS provides in a passive manner. The DTS design for NSTX-U adopts major elements from the successful DIII-D DTS system including 7-channel polychromators measuring T{sub e} to 0.5 eV. If implemented onmore » NSTX-U, the divertor TS system would provide an invaluable diagnostic for the boundary program to characterize the edge plasma.« less

Tritium analysis of divertor tiles used in JET ITER-like wall campaigns by means of β-ray induced x-ray spectrometry

NASA Astrophysics Data System (ADS)

Hatano, Y.; Yumizuru, K.; Koivuranta, S.; Likonen, J.; Hara, M.; Matsuyama, M.; Masuzaki, S.; Tokitani, M.; Asakura, N.; Isobe, K.; Hayashi, T.; Baron-Wiechec, A.; Widdowson, A.; contributors, JET

2017-12-01

Energy spectra of β-ray induced x-rays from divertor tiles used in ITER-like wall campaigns of the Joint European Torus were measured to examine tritium (T) penetration into tungsten (W) layers. The penetration depth of T evaluated from the intensity ratio of W(Lα) x-rays to W(Mα) x-rays showed clear correlation with poloidal position; the penetration depth at the upper divertor region reached several micrometers, while that at the lower divertor region was less than 500 nm. The deep penetration at the upper part was ascribed to the implantation of high energy T produced by DD fusion reactions. The poloidal distribution of total x-ray intensity indicated higher T retention in the inboard side than the outboard side of the divertor region.

Effect of 3D magnetic perturbations on divertor conditions and detachment in tokamak and stellarator

DOE PAGES

Ahn, J. -W.; Briesemester, A. R.; Kobayashi, M.; ...

2017-06-22

Enhanced perpendicular heat and momentum transport induces parallel pressure loss leading to divertor detachment, which can be produced by the increase of density in 2D tokamaks. However, in the 3D configurations such as tokamaks with 3D fields and stellarators, the fraction of perpendicular transport can be higher even in a lower density regime, which could lead to the early transition to detachment without passing through the high-recycling regime. 3D fields applied to the limiter tokamak plasmas produce edge stochastic layers close to the last closed flux surface (LCFS), which can allow for enhanced perpendicular transport and indeed the absence ofmore » high recycling regime and early detachment have been observed in TEXTOR and Tore Supra. However, in the X-point divertor tokamaks with the applied 3D fields, the parallel transport is still dominant and the detachment facilitation has not been observed yet. Rather, 3D fields affected detachment adversely under certain conditions, either by preventing detachment onset as seen in DIII-D or by re-attaching the existing detached plasma as shown in NSTX. The possible way for strong 3D effects to induce access to the early detachment in divertor tokamaks appears to be via significant perpendicular loss of parallel momentum by frictional force for the counter-streaming flows between neighboring flow channels in the divertor. In principle, the adjacent lobes in the 3D divertor tokamak may generate the counter-streaming flow channels. However, an EMC3-EIRENE simulation for ITER H-mode plasmas demonstrated that screened RMP leads to significantly reduced counter-flows near the divertor target, therefore the momentum loss effect leading to detachment facilitation is expected to be small. This is consistent with the observation in LHD, which showed screening (amplification) of RMP fields in the attachment (stable detachment) case. In conclusion, work for optimal parameter window for best divertor operation scenario is needed particularly for the 3D divertor tokamak configuration.« less

Effect of 3D magnetic perturbations on divertor conditions and detachment in tokamak and stellarator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahn, J. -W.; Briesemester, A. R.; Kobayashi, M.

Enhanced perpendicular heat and momentum transport induces parallel pressure loss leading to divertor detachment, which can be produced by the increase of density in 2D tokamaks. However, in the 3D configurations such as tokamaks with 3D fields and stellarators, the fraction of perpendicular transport can be higher even in a lower density regime, which could lead to the early transition to detachment without passing through the high-recycling regime. 3D fields applied to the limiter tokamak plasmas produce edge stochastic layers close to the last closed flux surface (LCFS), which can allow for enhanced perpendicular transport and indeed the absence ofmore » high recycling regime and early detachment have been observed in TEXTOR and Tore Supra. However, in the X-point divertor tokamaks with the applied 3D fields, the parallel transport is still dominant and the detachment facilitation has not been observed yet. Rather, 3D fields affected detachment adversely under certain conditions, either by preventing detachment onset as seen in DIII-D or by re-attaching the existing detached plasma as shown in NSTX. The possible way for strong 3D effects to induce access to the early detachment in divertor tokamaks appears to be via significant perpendicular loss of parallel momentum by frictional force for the counter-streaming flows between neighboring flow channels in the divertor. In principle, the adjacent lobes in the 3D divertor tokamak may generate the counter-streaming flow channels. However, an EMC3-EIRENE simulation for ITER H-mode plasmas demonstrated that screened RMP leads to significantly reduced counter-flows near the divertor target, therefore the momentum loss effect leading to detachment facilitation is expected to be small. This is consistent with the observation in LHD, which showed screening (amplification) of RMP fields in the attachment (stable detachment) case. In conclusion, work for optimal parameter window for best divertor operation scenario is needed particularly for the 3D divertor tokamak configuration.« less

DTT: a divertor tokamak test facility for the study of the power exhaust issues in view of DEMO

NASA Astrophysics Data System (ADS)

Albanese, R.; WPDTT2 Team; DTT Project Proposal Contributors, the

2017-01-01

In parallel with the programme to optimize the operation with a conventional divertor based on detached conditions to be tested on the ITER device, a project has been launched to investigate alternative power exhaust solutions for DEMO, aimed at the definition and the design of a divertor tokamak test facility (DTT). The DTT project proposal refers to a set of parameters selected so as to have edge conditions as close as possible to DEMO, while remaining compatible with DEMO bulk plasma performance in terms of dimensionless parameters and given constraints. The paper illustrates the DTT project proposal, referring to a 6 MA plasma with a major radius of 2.15 m, an aspect ratio of about 3, an elongation of 1.6-1.8, and a toroidal field of 6 T. This selection will guarantee sufficient flexibility to test a wide set of divertor concepts and techniques to cope with large heat loads, including conventional tungsten divertors; liquid metal divertors; both conventional and advanced magnetic configurations (including single null, snow flake, quasi snow flake, X divertor, double null); internal coils for strike point sweeping and control of the width of the scrape-off layer in the divertor region; and radiation control. The Poloidal Field system is planned to provide a total flux swing of more than 35 Vs, compatible with a pulse length of more than 100 s. This is compatible with the mission of studying the power exhaust problem and is obtained using superconducting coils. Particular attention is dedicated to diagnostics and control issues, especially those relevant for plasma control in the divertor region, designed to be as compatible as possible with a DEMO-like environment. The construction is expected to last about seven years, and the selection of an Italian site would be compatible with a budget of 500 M€.

Singularities and non-hyperbolic manifolds do not coincide

NASA Astrophysics Data System (ADS)

Simányi, Nándor

2013-06-01

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai ergodic hypothesis.

X-Divertors on ITER - with no hardware changes

NASA Astrophysics Data System (ADS)

Valanju, Prashant; Covele, Brent; Kotschenreuther, Mike; Mahajan, Swadesh; Kessel, Charles

2014-10-01

Using CORSICA, we have discovered that X-Divertor (XD) equilibria are possible on ITER - without any extra PF coils inside the TF coils, and with no changes to ITER's poloidal field (PF) coil set, divertor cassette, strike points, or first wall. Starting from the Standard Divertor (SD), a sequence of XD configurations (with increasing flux expansions at the divertor plate) can be made by reprogramming ITER PF coil currents while keeping them all under their design limits (Lackner and Zohm have shown this to be impossible for Snowflakes). The strike point is held fixed, so no changes in the divertor or pumping hardware will be needed. The main plasma shape is kept very close to the SD case, so no hardware changes to the main chamber will be needed. Time-dependent ITER-XD operational scenarios are being checked using TSC. This opens the possibility that many XDs could be tested and used to assist in high-power operation on ITER. Because of the toroidally segmented ITER divertor plates, strongly detached operation may be critical for making use of the largest XD flux expansion possible. The flux flaring in XDs is expected to increase the stability of detachment, so that H-mode confinement is not affected. Detachment stability is being examined with SOLPS. This work supported by US DOE Grants DE-FG02-04ER54742 and DE-FG02-04ER54754 and by TACC at UT Austin.

Impact of the plasma geometry on divertor power exhaust: experimental evidence from TCV and simulations with SolEdge2D and TOKAM3X

NASA Astrophysics Data System (ADS)

Gallo, A.; Fedorczak, N.; Elmore, S.; Maurizio, R.; Reimerdes, H.; Theiler, C.; Tsui, C. K.; Boedo, J. A.; Faitsch, M.; Bufferand, H.; Ciraolo, G.; Galassi, D.; Ghendrih, P.; Valentinuzzi, M.; Tamain, P.; the EUROfusion MST1 Team; the TCV Team

2018-01-01

A deep understanding of plasma transport at the edge of magnetically confined fusion plasmas is needed for the handling and control of heat loads on the machine first wall. Experimental observations collected on a number of tokamaks over the last three decades taught us that heat flux profiles at the divertor targets of X-point configurations can be parametrized by using two scale lengths for the scrape-off layer (SOL) transport, separately characterizing the main SOL ({λ }q) and the divertor SOL (S q ). In this work we challenge the current interpretation of these two scale lengths as well as their dependence on plasma parameters by studying the effect of divertor geometry modifications on heat exhaust in the Tokamak à Configuration Variable. In particular, a significant broadening of the heat flux profiles at the outer divertor target is diagnosed while increasing the length of the outer divertor leg in lower single null, Ohmic, L-mode discharges. Efforts to reproduce this experimental finding with both diffusive (SolEdge2D-EIRENE) and turbulent (TOKAM3X) modelling tools confirm the validity of a diffusive approach for simulating heat flux profiles in more traditional, short leg, configurations while highlighting the need of a turbulent description for modified, long leg, ones in which strongly asymmetric divertor perpendicular transport develops.

Flow reversal, convection, and modeling in the DIII-D divertor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boedo, J.A.; Porter, G.D.; Schaffer, M.J.

1998-12-01

Measurements of the parallel Mach number of background plasma in the DIII-D tokamak divertor [M. A. Mahdavi {ital et al.} in {ital Proceedings, 16th International Conference}, Montreal, 1996 (International Atomic Energy Agency, Vienna, 1997) Vol. I, p. 397] were performed using a fast scanning Mach probe. The parallel particle flow shows evidence of complex behavior such as reverse flow, i.e., flow away from the target plate, stagnant flow, and large scale convection. For detached discharges, measurements confirm predictions of convective flow towards the divertor target plate at near sound speed over large regions in the divertor. The resulting convected heatmore » flux is a dominant heat transport mechanism in the divertor. For attached discharges with high recycling, particle flow reversal in a thin region at or near the outer separatrix, thereby confirming the existence of a mechanism by which impurities can be transported away from the divertor target plates. Modeling results from the two-dimensional fluid code UEDGE [G. D. Porter and the DIII-D Team, {open_quotes}Divertor characterization experiments and modelling in DIII-D,{close_quotes} in {ital Proceedings of the 23rd European Conference on Controlled Fusion and Plasma Physics}, 24{endash}28 June 1996, Kiev, Ukraine (European Physical Society, Petit-Lancy, Switzerland, 1996), Vol. 20C, Part II, p. 699] can reproduce the main features of the experimental observations. {copyright} {ital 1998 American Institute of Physics.}« less

Gyrokinetic simulation of edge blobs and divertor heat-load footprint

NASA Astrophysics Data System (ADS)

Chang, C. S.; Ku, S.; Hager, R.; Churchill, M.; D'Azevedo, E.; Worley, P.

2015-11-01

Gyrokinetic study of divertor heat-load width Lq has been performed using the edge gyrokinetic code XGC1. Both neoclassical and electrostatic turbulence physics are self-consistently included in the simulation with fully nonlinear Fokker-Planck collision operation and neutral recycling. Gyrokinetic ions and drift kinetic electrons constitute the plasma in realistic magnetic separatrix geometry. The electron density fluctuations from nonlinear turbulence form blobs, as similarly seen in the experiments. DIII-D and NSTX geometries have been used to represent today's conventional and tight aspect ratio tokamaks. XGC1 shows that the ion neoclassical orbit dynamics dominates over the blob physics in setting Lq in the sample DIII-D and NSTX plasmas, re-discovering the experimentally observed 1/Ip type scaling. Magnitude of Lq is in the right ballpark, too, in comparison with experimental data. However, in an ITER standard plasma, XGC1 shows that the negligible neoclassical orbit excursion effect makes the blob dynamics to dominate Lq. Differently from Lq 1mm (when mapped back to outboard midplane) as was predicted by simple-minded extrapolation from the present-day data, XGC1 shows that Lq in ITER is about 1 cm that is somewhat smaller than the average blob size. Supported by US DOE and the INCITE program.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ono, M.; Jaworski, M. A.; Kaita, R.

Steady-state fusion reactor operation presents major divertor technology challenges, including high divertor heat flux both steady-state and transients. In addition to those issues, there are unresolved issues of long term dust accumulation and associated tritium inventory and safety issues. It has been suggested that radiative liquid lithium divertor concepts with a modest lithium-loop could provide a possible solution for these outstanding fusion reactor technology issues while potentially improving the reactor plasma performance. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peak heat flux while maintaining essentially Li-freemore » core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid lithium divertor (RLLD) concept and its variant, the active liquid lithium divertor concept (ARLLD), taking advantage of the enhanced Li radiation in relatively poorly confined divertor plasmas. It was estimated that only a few moles/sec of lithium injection would be needed to significantly reduce the divertor heat flux in a tokamak fusion power plant. By operating at lower temperatures ≤ 500°C than the first wall ~ 600 – 700°C, the LL-covered divertor chamber wall surfaces can serve as an effective particle pump, as impurities generally migrate toward lower temperature LL divertor surfaces. To maintain the LL purity, a closed LL loop system with a modest circulating capacity of ~ 1 liter/second (l/sec) is envisioned to sustain the steady-state operation of a 1 GW-electric class fusion power plant. By running the Li loop continuously, it can carry the dust particles and impurities generated in the vacuum vessel to outside where the dust / impurities are removed by relatively simple filter and cold/hot trap systems. Using a cold trap system, it can recover in tritium (T) in real time from LL at a rate of ~ 0.5 g / sec needed to sustain the fusion reaction while minimizing the T inventory issue. With an expected T fraction of ≤ 0.7 %, an acceptable level of T inventory can be achieved. In NSTX-U, preparations are now underway to elucidate the physics of Li plasma interactions with a number of Li application tools and Li radiation spectroscopic instruments. The NSTX-U Li evaporator which provides Li coating over the lower divertor plate, can offer important information on the RLLD concept, and the Li granule injector will test some of the key physics issue on the ARLLD concept. A LL-loop is also being prepared off line for prototyping future use on NSTX-U.« less

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

NASA Astrophysics Data System (ADS)

Hu, Xiaohu; Hong, Liang; Dean Smith, Micholas; Neusius, Thomas; Cheng, Xiaolin; Smith, Jeremy C.

2016-02-01

Internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behaviour with effective relaxation times existing over many decades in time, from ps up to ~102 s (refs ,,,). Here, using molecular dynamics simulations, we show that, on timescales from 10-12 to 10-5 s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behaviour persists up to timescales approaching the in vivo lifespan of individual protein molecules.

Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.

PubMed

Heyl, Markus; Vojta, Matthias

2014-10-31

One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Covele, Brent; Kotschenreuther, M.; Mahajan, S.

The X-Divertor geometry on DIII-D has demonstrated reduced particle and heat fluxes to the target, facilitating detachment onset at ~20% lower upstream density and higher H-mode pedestal pressure than a standard divertor. SOLPS modeling suggests that this effect cannot be explained by an increase in total connection length alone, but rather by the addition of connection length specifically in the power-dissipating volume near the target, via poloidal flux expansion and flaring. But, poloidal flaring must work synergistically with divertor closure to most effectively reduce the detachment density threshold. Furthermore, the model also points to carbon radiation as the primary drivermore » of power dissipation in divertors on the DIII-D floor, which is consistent with experimental observations. Sustainable divertor detachment at lower density has beneficial consequences for energy confinement and current drive efficiency in the core for advanced tokamak (AT) operation, while simultaneously satisfying the exhaust requirements of the plasma-facing components.« less

Status of National Spherical Torus Experiment Liquid Lithium Divertor

NASA Astrophysics Data System (ADS)

Kugel, H. W.; Viola, M.; Ellis, R.; Bell, M.; Gerhardt, S.; Kaita, R.; Kallman, J.; Majeski, R.; Mansfield, D.; Roquemore, A. L.; Schneider, H.; Timberlake, J.; Zakharov, L.; Nygren, R. E.; Allain, J. P.; Maingi, R.; Soukhanovskii, V.

2009-11-01

Recent NSTX high power divertor experiments have shown significant and recurring benefits of solid lithium coatings on plasma facing components to the performance of divertor plasmas in both L- and H- mode confinement regimes heated by high-power neutral beams. The next step in this work is the 2009 installation of a Liquid Lithium Divertor (LLD). The 20 cm wide LLD located on the lower outer divertor, consists of four, 80 degree sections; each section is separated by a row of graphite diagnostic tiles. The temperature controlled LLD structure consists of a 0.01cm layer of vacuum flame-sprayed, 50 percent porous molybdenum, on top of 0.02 cm, 316-SS brazed to a 1.9 cm Cu base. The physics design of the LLD encompasses the desired plasma requirements, the experimental capabilities and conditions, power handling, radial location, pumping capability, operating temperature, lithium filling, MHD forces, and diagnostics for control and characterization.

Measurement and modeling of surface temperature dynamics of the NSTX liquid lithium divertor

NASA Astrophysics Data System (ADS)

McLean, A. G.; Gan, K. F.; Ahn, J.-W.; Gray, T. K.; Maingi, R.; Abrams, T.; Jaworski, M. A.; Kaita, R.; Kugel, H. W.; Nygren, R. E.; Skinner, C. H.; Soukhanovskii, V. A.

2013-07-01

Dual-band infrared (IR) measurements of the National Spherical Torus eXperiment (NSTX) Liquid Lithium Divertor (LLD) are reported that demonstrate liquid Li is more effective at removing plasma heat flux than Li-conditioned graphite. Extended dwell of the outer strike point (OSP) on the LLD caused an incrementally larger area to be heated above the Li melting point through the discharge leading to enhanced D retention and plasma confinement. Measurement of Tsurface near the OSP demonstrates a significant reduction of the LLD surface temperature compared to that of Li-coated graphite at the same major radius. Modeling of these data with a 2-D simulation of the LLD structure in the DFLUX code suggests that the structure of the LLD was successful at handling up to q⊥,peak = 5 MW/m2 inter-ELM and up to 10 MW/m2 during ELMs from its plasma-facing surface as intended, and provide an innovative method for inferring the Li layer thickness.

Ergodicity Breaking in Geometric Brownian Motion

NASA Astrophysics Data System (ADS)

Peters, O.; Klein, W.

2013-03-01

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.

Observations on the Proper Orthogonal Decomposition

NASA Technical Reports Server (NTRS)

Berkooz, Gal

1992-01-01

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER

DOE PAGES

Chang, Choong Seock; Ku, Seung -Hoe; Loarte, Alberto; ...

2017-07-11

Here, the XGC1 edge gyrokinetic code is used to study the width of the heat-flux to divertor plates in attached plasma condition. The flux-driven simulation is performed until an approximate power balance is achieved between the heat-flux across the steep pedestal pressure gradient and the heat-flux on the divertor plates.

Innovative divertor concept development on DIII-D and EAST

DOE PAGES

Guo, H. Y.; Allen, S.; Canik, J.; ...

2016-06-02

A critical issue facing the design and operation of next-step high-power steady-state fusion devices is the control of heat fluxes and erosion at the plasma-facing components, in particular, the divertor target plates. A new initiative has been launched on DIII-D to develop and demonstrate innovative boundary plasma-materials interface solutions. The central purposes of this new initiative are to advance scientific understanding in this critical area and develop an advanced divertor concept for application to next-step fusion devices. Finally, DIII-D will leverage strong collaborative efforts on the EAST superconducting tokamak for extending integrated high performance advanced divertor solutions to true steady-state.

Real-time radiative divertor feedback control development for the NSTX-U tokamak using a vacuum ultraviolet spectrometer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soukhanovskii, V. A., E-mail: vlad@llnl.gov; Kaita, R.; Stratton, B.

2016-11-15

A radiative divertor technique is planned for the NSTX-U tokamak to prevent excessive erosion and thermal damage of divertor plasma-facing components in H-mode plasma discharges with auxiliary heating up to 12 MW. In the radiative (partially detached) divertor, extrinsically seeded deuterium or impurity gases are used to increase plasma volumetric power and momentum losses. A real-time feedback control of the gas seeding rate is planned for discharges of up to 5 s duration. The outer divertor leg plasma electron temperature T{sub e} estimated spectroscopically in real time will be used as a control parameter. A vacuum ultraviolet spectrometer McPherson Modelmore » 251 with a fast charged-coupled device detector is developed for temperature monitoring between 5 and 30 eV, based on the Δn = 0, 1 line intensity ratios of carbon, nitrogen, or neon ion lines in the spectral range 300–1600 Å. A collisional-radiative model-based line intensity ratio will be used for relative calibration. A real-time T{sub e}-dependent signal within a characteristic divertor detachment equilibration time of ∼10–15 ms is expected.« less

Real-time radiative divertor feedback control development for the NSTX-U tokamak using a vacuum ultraviolet spectrometer

DOE PAGES

Soukhanovskii, V. A.; Kaita, R.; Stratton, B.

2016-08-04

Here, a radiative divertor technique is planned for the NSTX-U tokamak to prevent excessive erosion and thermal damage of divertor plasma-facing components in H-mode plasma discharges with auxiliary heating up to 12 MW. In the radiative (partially detached) divertor, extrinsically seeded deuterium or impurity gases are used to increase plasma volumetric power and momentum losses. A real-time feedback control of the gas seeding rate is planned for discharges of up to 5 s duration. The outer divertor leg plasma electron temperature T e estimated spectroscopically in real time will be used as a control parameter. A vacuum ultraviolet spectrometer McPhersonmore » Model 251 with a fast charged-coupled device detector is developed for temperature monitoring between 5 and 30 eV, based on the Δn = 0, 1 line intensity ratios of carbon, nitrogen, or neon ion lines in the spectral range 300–1600 Å. A collisional-radiative model-based line intensity ratio will be used for relative calibration. A real-time T e-dependent signal within a characteristic divertor detachment equilibration time of ~10–15 ms is expected.« less

Tungsten migration in Alcator C-Mod: sputtering and melting

NASA Astrophysics Data System (ADS)

Wright, G. M.; Barnard, H.; Lipschultz, B.; Whyte, D. G.

2010-11-01

A row of bulk tungsten (W) tiles were installed near the typical outer strike-point location in the Alcator C-Mod divertor in 2007. In the 2009/2010 campaign, one of the W tiles mechanically failed resulting in significant W melting at that location. Post-campaign PIXE surface analysis has been used to observe tungsten (W) deposition and migration patterns in the divertor for the typical operations (sputtering only) and operation with melted components. For sputtering conditions, W deposition of up to 20 nm equivalent thickness is observed at various divertor surfaces indicating prompt re-deposition at the outer divertor, neutral and ion transport through the private-flux region and ion transport in the scrape off layer. For melting conditions, W deposition of up to 400 nm equivalent thickness is observed at some locations at the outer divertor. However, the toroidal distribution of W on the outer divertor is strongly non-uniform. There is no W deposition measured on the inner wall limiter. These results indicate that impurity migration is affected by the erosion mechanism and source, with the migration from melting being less predictable and uniform than from the sputtering case. Supported by USDoE award DE-SC00-02060.

Scrape off layer modelling studies for SST-I

NASA Astrophysics Data System (ADS)

Warrier, M.; Jaishankar, S.; Deshpande, S.; Coster, D.; Schneider, R.; Chaturvedi, S.; Srinivasan, R.; Braams, B. J.; SST Team

SOL modelling results for SST-1 (SST Team, Proceedings of the 16th IEEE/NPSS Symposium on Fusion Engineering, Champaign, IL, vol. II, 1995, p. 481) show a sheath limited flow regime. This is due to the low edge densities required by lower hybrid current drive (LHCD), coupled with high power input per unit volume. Coupled plasma-neutral transport studies using B2-Eirene [R. Schneider et al., J. Nucl. Mater. 196-198 (1992) 810] show significantly high charge exchange losses and radiated power from the core. It also shows that the heat flux to the inner divertor is higher than that to the outer divertor due to thinner inner SOL widths. The Monte-Carlo neutral transport code DEGAS [D. Heifitz et al., J. Comput. Phys. 46 (1982) 309] was used to optimise the baffle plate geometry and it was seen that a configuration where the baffle plate shields the main plasma from the divertor strike point results in reduced backflow of neutrals. The divertor erosion code DIVER (M. Warrier et al., SST Divertor Modelling Report, 1996-1997) was used to predict a steady state operating temperature for the SST divertor plate lying in the range 750-1000°C for which the erosion will be minimum.

Results from core-edge experiments in high Power, high performance plasmas on DIII-D

DOE PAGES

Petrie, T. W.; Fenstermacher, M. E.; Holcomb, C. T.; ...

2016-12-24

Here, significant challenges to reducing divertor heat flux in highly powered near-double null divertor (DND) hybrid plasmas, while still maintaining both high performance metrics and low enough density for application of RF heating, are identified. For these DNDs on DIII-D, the scaling of the peak heat flux at the outer target (q ⊥ P) ∝ [P SOL x I P] 0.92 for P SOL = 8-19 MW and I P = 1.0–1.4 MA, and is consistent with standard ITPA scaling for single-null H-mode plasmas. Two divertor heat flux reduction methods were tested. First, applying the puff-and-pump radiating divertor to DIII-Dmore » plasmas may be problematical at high power and H98 (≥ 1.5) due to improvement in confinement time with deuterium gas puffing which can lead to unacceptably high core density under certain conditions. Second, q ⊥ P for these high performance DNDs was reduced by ≈35% when an open divertor is closed on the common flux side of the outer divertor target (“semi-slot”) but also that heating near the slot opening is a significant source for impurity contamination of the core.« less

Electric field divertor plasma pump

DOEpatents

Schaffer, Michael J.

1994-01-01

An electric field plasma pump includes a toroidal ring bias electrode (56) positioned near the divertor strike point of a poloidal divertor of a tokamak (20), or similar plasma-confining apparatus. For optimum plasma pumping, the separatrix (40) of the poloidal divertor contacts the ring electrode (56), which then also acts as a divertor plate. A plenum (54) or other duct near the electrode (56) includes an entrance aperture open to receive electrically-driven plasma. The electrode (56) is insulated laterally with insulators (63,64), one of which (64) is positioned opposite the electrode at the entrance aperture. An electric field E is established between the ring electrode (56) and a vacuum vessel wall (22), with the polarity of the bias applied to the electrode being relative to the vessel wall selected such that the resultant electric field E interacts with the magnetic field B already existing in the tokamak to create an E.times.B/B.sup.2 drift velocity that drives plasma into the entrance aperture. The pumped plasma flow into the entrance aperture is insensitive to variations, intentional or otherwise, of the pump and divertor geometry. Pressure buildups in the plenum or duct connected to the entrance aperture in excess of 10 mtorr are achievable.

Electric field divertor plasma pump

DOEpatents

Schaffer, M.J.

1994-10-04

An electric field plasma pump includes a toroidal ring bias electrode positioned near the divertor strike point of a poloidal divertor of a tokamak, or similar plasma-confining apparatus. For optimum plasma pumping, the separatrix of the poloidal divertor contacts the ring electrode, which then also acts as a divertor plate. A plenum or other duct near the electrode includes an entrance aperture open to receive electrically-driven plasma. The electrode is insulated laterally with insulators, one of which is positioned opposite the electrode at the entrance aperture. An electric field E is established between the ring electrode and a vacuum vessel wall, with the polarity of the bias applied to the electrode being relative to the vessel wall selected such that the resultant electric field E interacts with the magnetic field B already existing in the tokamak to create an E [times] B/B[sup 2] drift velocity that drives plasma into the entrance aperture. The pumped plasma flow into the entrance aperture is insensitive to variations, intentional or otherwise, of the pump and divertor geometry. Pressure buildups in the plenum or duct connected to the entrance aperture in excess of 10 mtorr are achievable. 11 figs.

ELM elimination with lithium aerosol injection in upper-single null discharges using the tungsten divertor in EAST

NASA Astrophysics Data System (ADS)

Sun, Z.; Maingi, R.; Hu, J.; Lunsford, R.; Diallo, A.; Tritz, K.; Osborne, T.; Canik, J.; Zuo, G.; Wang, L.; Xu, G.; Gong, X.; EAST Team Team

2017-10-01

A reproducible, fully non-inductive H-mode regime devoid of large ELMs has been achieved by continuous Li injection in EAST into the upper `ITER-like' tungsten divertor, extending previous results on the graphite divertor. These discharges did not suffer from density or impurity accumulation, and maintained constant core radiated power. The new results extend the energy confinement multiplier H98(y,2) 1.2, as compared to H98(y,2) 0.75 previously on the graphite divertor. The observed ELM elimination is correlated with a decrease in particle recycling, as expected from the strong Li coating before the experiment, and real-time Li aerosol injection. In addition, core W concentration was reduced during the Li injection. ELM elimination is likely related to the reduced recycling and density /temperature profile changes. A low-n electromagnetic coherent mode (MCM) at 40kHz became stronger in amplitude and also more coherent. The MCM shows strong magnetic fluctuations as measured by fast Mirnov coils, but weak density fluctuations. As compared to the graphite divertor, Li injection into the tungsten divertor eliminated ELMs at twice the previous auxiliary heating power, and reduced pedestal collisionality.

Plasma-wall interactions in ITER

NASA Astrophysics Data System (ADS)

Parker, R.; Janeschitz, G.; Pacher, H. D.; Post, D.; Chiocchio, S.; Federici, G.; Ladd, P.; Iter Joint Central Team; Home Teams

1997-02-01

This paper reviews the status of the design of the divertor and first-wall/shield, the main in-vessel components for ITER. Under nominal ignited conditions, 300 MW of alpha power will be produced and must be removed from the divertor and first-wall. Additional power from auxiliary sources up to the level of 100 MW must also be removed in the case of driven burns. In the ignited case, about 100 MW will be radiated to the first wall as bremsstrahlung. Allowing the remaining power to be conducted to the divertor target plates would result in excessive heat fluxes. The power handling strategy is to radiate an additional 100-150 MW in the SOL and the divertor channel via a combination of radiation from hydrogen, and intrinsic and seeded impurities. Vertical targets have been adopted for the baseline divertor configuration. This geometry promotes partial detachment, as found in present experiments and in the results of modelling runs for ITER conditions, and power densities on the target plates can be ≤ 5 MW/ m2. Such regimes promote relatively high pressure (> 1 Pa) in the divertor and even with a low helium enrichment factor of 0.2, the required pumping speed to pump helium is ≤ 50 m3/ s. An important physics question is the quality of core confinement in these attractive divertor regimes. In addition to power and particle handling issues, the effects of disruptions play a major role in the design and performance of in-vessel components. Both centered disruptions and VDE's produce stresses in the first-wall/shield modules, backplate and the divertor wings and cassettes that are near or even somewhat in excess of allowables for normal operation. Also plasma-wall contact from disruptions, including at the divertor target, together with material properties are major factors determining component lifetime. Considering the potential for impurity contamination and minimizing tritium inventory as well as thermomechanical performance, the present material selection calls for carbon divertor targets near the strike point, tungsten on the rest of the target and on the baffle where the charge-exchange flux could be high, and beryllium elsewhere. All three materials and relevant joining techniques are being developed in the R&D program and the final selection for the first assembly will be made at the end of the EDA.

Studies of power exhaust and divertor design for a 1.5 GW-level fusion power DEMO

NASA Astrophysics Data System (ADS)

Asakura, N.; Hoshino, K.; Suzuki, S.; Tokunaga, S.; Someya, Y.; Utoh, H.; Kudo, H.; Sakamoto, Y.; Hiwatari, R.; Tobita, K.; Shimizu, K.; Ezato, K.; Seki, Y.; Ohno, N.; Ueda, Y.; Joint Special TeamDEMO Design

2017-12-01

Power exhaust to the divertor and the conceptual design have been investigated for a steady-state DEMO in Japan with 1.5 GW-level fusion power and the major radius of 8.5 m, where the plasma parameters were revised appropriate for the impurity seeding scenario. A system code survey for the Ar impurity seeding suggested the volume-averaged density, impurity concentration and exhaust power from the main plasma of {{P}sep ~ }   =  205-285 MW. The divertor plasma simulation (SONIC) was performed in the divertor leg length of 1.6 m with the fixed exhaust power to the edge of {{P}out}   =  250 MW and the total radiation fraction at the edge, SOL and divertor ({{P}rad}/{{P}out}   =  0.8), as a first step to investigate appropriate design of the divertor size and geometry. At the outer target, partial detachment was produced near the strike-point, and the peak heat load ({{q}target} ) at the attached region was reduced to ~5 MW m-2 with appropriate fuel and impurity puff rates. At the inner divertor target, full detachment of ion flux was produced and the peak {{q}target} was less than 10 MW m-2 mostly due to the surface-recombination. These results showed a power exhaust scenario and the divertor design concept. An integrated design of the water-cooling heat sink for the long leg divertor was proposed. Cu-ally (CuCrZr) cooling pipe was applicable as the heat sink to handle the high heat flux near the strike-point, where displacements per atom rate was estimated to be 0.5-1.5 per year by neutronics calculation. An arrangement of the coolant rooting for Cu-alloy and Reduced Activation Ferritic Martensitic (RAFM) steel (F82H) pipes in a divertor cassette was investigated, and the heat transport analysis of the W-monoblock and Cu-alloy pipe under the peak {{q}target} of 10 MWm-2 and nuclear heating was performed. The maximum temperatures on the W-surface and Cu-alloy pipe were 1021 and 331 °C. Heat flux of 16 MW m-2 was distributed in the major part of the coolant pipe. These results were acceptable for the plasma facing and structural materials.

Dynamical manifestations of quantum chaos

NASA Astrophysics Data System (ADS)

Torres Herrera, Eduardo Jonathan; Santos, Lea

2017-04-01

A main feature of a chaotic quantum system is a rigid spectrum, where the levels do not cross. Dynamical quantities, such as the von Neumann entanglement entropy, Shannon information entropy, and out-of-time correlators can differentiate the ergodic from the nonergodic phase in disordered interacting systems, but not level repulsion from level crossing in the delocalized phase of disordered and clean models. This is in contrast with the long-time evolution of the survival probability of the initial state. The onset of correlated energy levels is manifested by a drop, referred to as correlation hole, below the asymptotic value of the survival probability. The correlation hole is an unambiguous indicator of the presence of level repulsion. EJTH is grateful to VIEP, BUAP for financial support through the VIEP projects program.

Dynamical complexity of short and noisy time series. Compression-Complexity vs. Shannon entropy

NASA Astrophysics Data System (ADS)

Nagaraj, Nithin; Balasubramanian, Karthi

2017-07-01

Shannon entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two such Compression-Complexity Measures namely Lempel-Ziv complexity (LZ) and Effort-To-Compress (ETC) on short time series from chaotic dynamical systems in the presence of noise. Both LZ and ETC outperform Shannon entropy (H) in accurately characterizing the dynamical complexity of such systems. For very short binary sequences (which arise in neuroscience applications), ETC has higher number of distinct complexity values than LZ and H, thus enabling a finer resolution. For two-state ergodic Markov chains, we empirically show that ETC converges to a steady state value faster than LZ. Compression-Complexity measures are promising for applications which involve short and noisy time series.

Detecting many-body-localization lengths with cold atoms

NASA Astrophysics Data System (ADS)

Guo, Xuefei; Li, Xiaopeng

2018-03-01

Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.

Combining pressure and temperature control in dynamics on energy landscapes

NASA Astrophysics Data System (ADS)

Hoffmann, Karl Heinz; Christian Schön, J.

2017-05-01

Complex systems from science, technology or mathematics usually appear to be very different in their specific dynamical evolution. However, the concept of an energy landscape with its basins corresponding to locally ergodic regions separated by energy barriers provides a unifying approach to the description of complex systems dynamics. In such systems one is often confronted with the task to control the dynamics such that a certain basin is reached with the highest possible probability. Typically one aims for the global minimum, e.g. when dealing with global optimization problems, but frequently other local minima such as the metastable compounds in materials science are of primary interest. Here we show how this task can be solved by applying control theory using magnesium fluoride as an example system, where different modifications of MgF2 are considered as targets. In particular, we generalize previous work restricted to temperature controls only and present controls which simultaneously adjust temperature and pressure in an optimal fashion.

A Fast Visible Camera Divertor-Imaging Diagnostic on DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roquemore, A; Maingi, R; Lasnier, C

2007-06-19

In recent campaigns, the Photron Ultima SE fast framing camera has proven to be a powerful diagnostic when applied to imaging divertor phenomena on the National Spherical Torus Experiment (NSTX). Active areas of NSTX divertor research addressed with the fast camera include identification of types of EDGE Localized Modes (ELMs)[1], dust migration, impurity behavior and a number of phenomena related to turbulence. To compare such edge and divertor phenomena in low and high aspect ratio plasmas, a multi-institutional collaboration was developed for fast visible imaging on NSTX and DIII-D. More specifically, the collaboration was proposed to compare the NSTX smallmore » type V ELM regime [2] and the residual ELMs observed during Type I ELM suppression with external magnetic perturbations on DIII-D[3]. As part of the collaboration effort, the Photron camera was installed recently on DIII-D with a tangential view similar to the view implemented on NSTX, enabling a direct comparison between the two machines. The rapid implementation was facilitated by utilization of the existing optics that coupled the visible spectral output from the divertor vacuum ultraviolet UVTV system, which has a view similar to the view developed for the divertor tangential TV camera [4]. A remote controlled filter wheel was implemented, as was the radiation shield required for the DIII-D installation. The installation and initial operation of the camera are described in this paper, and the first images from the DIII-D divertor are presented.« less

Dephasing Catastrophe in 4-ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase.

PubMed

Liao, Yunxiang; Foster, Matthew S

2018-06-08

In two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d=4-ε dimensions, and find a nontrivial fixed point corresponding to a temperature T^{*}∼ε>0 where the dephasing time diverges. Assuming that this fixed point survives to ε=2, we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d>1 spatial dimensions.

Dephasing Catastrophe in 4 -ɛ Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase

NASA Astrophysics Data System (ADS)

Liao, Yunxiang; Foster, Matthew S.

2018-06-01

In two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d =4 -ɛ dimensions, and find a nontrivial fixed point corresponding to a temperature T*˜ɛ >0 where the dephasing time diverges. Assuming that this fixed point survives to ɛ =2 , we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d >1 spatial dimensions.

Ergodic model for the expansion of spherical nanoplasmas.

PubMed

Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O

2007-06-01

Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

Passive runaway electron suppression in tokamak disruptions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, H. M.; Helander, P.; Boozer, A. H.

2013-07-15

Runaway electrons created in disruptions pose a serious problem for tokamaks with large current. It would be desirable to have a runaway electron suppression method which is passive, i.e., a method that does not rely on an uncertain disruption prediction system. One option is to let the large electric field inherent in the disruption drive helical currents in the wall. This would create ergodic regions in the plasma and increase the runaway losses. Whether these regions appear at a suitable time and place to affect the formation of the runaway beam depends on disruption parameters, such as electron temperature andmore » density. We find that it is difficult to ergodize the central plasma before a beam of runaway current has formed. However, the ergodic outer region will make the Ohmic current profile contract, which can lead to instabilities that yield large runaway electron losses.« less

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

NASA Technical Reports Server (NTRS)

Meyer, C. D., Jr.

1979-01-01

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

Liquid lithium applications for solving challenging fusion reactor issues and NSTX-U contributions

DOE PAGES

Ono, M.; Jaworski, M. A.; Kaita, R.; ...

2016-08-05

Steady-state fusion reactor operation presents major divertor technology challenges, including high divertor heat flux both steady-state and transients. In addition to those issues, there are unresolved issues of long term dust accumulation and associated tritium inventory and safety issues. It has been suggested that radiative liquid lithium divertor concepts with a modest lithium-loop could provide a possible solution for these outstanding fusion reactor technology issues while potentially improving the reactor plasma performance. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peak heat flux while maintaining essentially Li-freemore » core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid lithium divertor (RLLD) concept and its variant, the active liquid lithium divertor concept (ARLLD), taking advantage of the enhanced Li radiation in relatively poorly confined divertor plasmas. It was estimated that only a few moles/sec of lithium injection would be needed to significantly reduce the divertor heat flux in a tokamak fusion power plant. By operating at lower temperatures ≤ 500°C than the first wall ~ 600 – 700°C, the LL-covered divertor chamber wall surfaces can serve as an effective particle pump, as impurities generally migrate toward lower temperature LL divertor surfaces. To maintain the LL purity, a closed LL loop system with a modest circulating capacity of ~ 1 liter/second (l/sec) is envisioned to sustain the steady-state operation of a 1 GW-electric class fusion power plant. By running the Li loop continuously, it can carry the dust particles and impurities generated in the vacuum vessel to outside where the dust / impurities are removed by relatively simple filter and cold/hot trap systems. Using a cold trap system, it can recover in tritium (T) in real time from LL at a rate of ~ 0.5 g / sec needed to sustain the fusion reaction while minimizing the T inventory issue. With an expected T fraction of ≤ 0.7 %, an acceptable level of T inventory can be achieved. In NSTX-U, preparations are now underway to elucidate the physics of Li plasma interactions with a number of Li application tools and Li radiation spectroscopic instruments. The NSTX-U Li evaporator which provides Li coating over the lower divertor plate, can offer important information on the RLLD concept, and the Li granule injector will test some of the key physics issue on the ARLLD concept. A LL-loop is also being prepared off line for prototyping future use on NSTX-U.« less

The snowflake divertor

DOE PAGES

Ryutov, D. D.; Soukhanovskii, V. A.

2015-11-17

The snowflake magnetic configuration is characterized by the presence of two closely spaced poloidal field nulls that create a characteristic hexagonal (reminiscent of a snowflake) separatrix structure. The magnetic field properties and the plasma behaviour in the snowflake are determined by the simultaneous action of both nulls, this generating a lot of interesting physics, as well as providing a chance for improving divertor performance. One of the most interesting effects of the snowflake geometry is the heat flux sharing between multiple divertor channels. The authors summarise experimental results obtained with the snowflake configuration on several tokamaks. Wherever possible, relation tomore » the existing theoretical models is described. Divertor concepts utilizing the properties of a snowflake configuration are briefly discussed.« less

Divertor target for magnetic containment device

DOEpatents

Luzzi, Jr., Theodore E.

1982-01-01

In a plasma containment device of a type having superconducting field coils for magnetically shaping the plasma into approximately the form of a torus, an improved divertor target for removing impurities from a "scrape off" region of the plasma comprises an array of water cooled swirl tubes onto which the scrape off flux is impinged. Impurities reflected from the divertor target are removed from the target region by a conventional vacuum getter system. The swirl tubes are oriented and spaced apart within the divertor region relative to the incident angle of the scrape off flux to cause only one side of each tube to be exposed to the flux to increase the burnout rating of the target. The divertor target plane is oriented relative to the plane of the path of the scrape off flux such that the maximum heat flux onto a swirl tube is less than the tube design flux. The containment device is used to contain the plasma of a tokamak fusion reactor and is applicable to other long pulse plasma containment systems.

ELM elimination with Li powder injection in EAST discharges using the tungsten upper divertor

DOE PAGES

Maingi, R.; Hu, J. S.; Sun, Z.; ...

2018-01-05

Here, we report the first successful use of lithium (Li) to eliminate edge-localized modes (ELMs) with tungsten divertor plasma-facing components in the EAST device. Li powder injected into the scrape-off layer of the tungsten upper divertor successfully eliminated ELMs for 3–5 s in EAST. The ELM elimination became progressively more effective in consecutive discharges at constant lithium delivery rates, and the divertor D α baseline emission was reduced, both signatures of improved wall conditioning. A modest decrease in stored energy and normalized energy confinement was also observed, but the confinement relative to H98 remained well above 1, extending the previousmore » ELM elimination results via Li injection into the lower carbon divertor in EAST. These results can be compared with recent observations with lithium pellets in ASDEX-Upgrade that failed to mitigate ELMs, highlighting one comparative advantage of continuous powder injection for real-time ELM elimination.« less

Minimum magnetic curvature for resilient divertors using Compact Toroidal Hybrid geometry

NASA Astrophysics Data System (ADS)

Bader, A.; Hegna, C. C.; Cianciosa, M.; Hartwell, G. J.

2018-05-01

The properties of resilient divertors are explored using equilibria derived from Compact Toroidal Hybrid (CTH) geometries. Resilience is defined here as the robustness of the strike point patterns as the plasma geometry and/or plasma profiles are changed. The addition of plasma current in the CTH configurations significantly alters the shape of the last closed flux surface and the rotational transform profile, however, it does not alter the strike point pattern on the target plates, and hence has resilient divertor features. The limits of when a configuration transforms to a resilient configuration is then explored. New CTH-like configurations are generated that vary from a perfectly circular cross section to configurations with increasing amounts of toroidal shaping. It is found that even small amounts of toroidal shaping lead to strike point localization that is similar to the standard CTH configuration. These results show that only a small degree of three-dimensional shaping is necessary to produce a resilient divertor, implying that any highly shaped optimized stellarator will possess the resilient divertor property.

Development of heat sink concept for near-term fusion power plant divertor

NASA Astrophysics Data System (ADS)

Rimza, Sandeep; Khirwadkar, Samir; Velusamy, Karupanna

2017-04-01

Development of an efficient divertor concept is an important task to meet in the scenario of the future fusion power plant. The divertor, which is a vital part of the reactor has to discharge the considerable fraction of the total fusion thermal power (∼15%). Therefore, it has to survive very high thermal fluxes (∼10 MW/m2). In the present paper, an efficient divertor heat exchanger cooled by helium is proposed for the fusion tokamak. The Plasma facing surface of divertor made-up of several modules to overcome the stresses caused by high heat flux. The thermal hydraulic performance of one such module is numerically investigated in the present work. The result shows that the proposed design is capable of handling target heat flux values of 10 MW/m2. The computational model has been validated against high-heat flux experiments and a satisfactory agreement is noticed between the present simulation and the reported results.

ELM elimination with Li powder injection in EAST discharges using the tungsten upper divertor

NASA Astrophysics Data System (ADS)

Maingi, R.; Hu, J. S.; Sun, Z.; Tritz, K.; Zuo, G. Z.; Xu, W.; Huang, M.; Meng, X. C.; Canik, J. M.; Diallo, A.; Lunsford, R.; Mansfield, D. K.; Osborne, T. H.; Gong, X. Z.; Wang, Y. F.; Li, Y. Y.; EAST Team

2018-02-01

We report the first successful use of lithium (Li) to eliminate edge-localized modes (ELMs) with tungsten divertor plasma-facing components in the EAST device. Li powder injected into the scrape-off layer of the tungsten upper divertor successfully eliminated ELMs for 3-5 s in EAST. The ELM elimination became progressively more effective in consecutive discharges at constant lithium delivery rates, and the divertor D α baseline emission was reduced, both signatures of improved wall conditioning. A modest decrease in stored energy and normalized energy confinement was also observed, but the confinement relative to H98 remained well above 1, extending the previous ELM elimination results via Li injection into the lower carbon divertor in EAST (Hu et al 2015 Phys. Rev. Lett. 114 055001). These results can be compared with recent observations with lithium pellets in ASDEX-Upgrade that failed to mitigate ELMs (Lang et al 2017 Nucl. Fusion 57 016030), highlighting one comparative advantage of continuous powder injection for real-time ELM elimination.

ELM elimination with Li powder injection in EAST discharges using the tungsten upper divertor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maingi, R.; Hu, J. S.; Sun, Z.

Here, we report the first successful use of lithium (Li) to eliminate edge-localized modes (ELMs) with tungsten divertor plasma-facing components in the EAST device. Li powder injected into the scrape-off layer of the tungsten upper divertor successfully eliminated ELMs for 3–5 s in EAST. The ELM elimination became progressively more effective in consecutive discharges at constant lithium delivery rates, and the divertor D α baseline emission was reduced, both signatures of improved wall conditioning. A modest decrease in stored energy and normalized energy confinement was also observed, but the confinement relative to H98 remained well above 1, extending the previousmore » ELM elimination results via Li injection into the lower carbon divertor in EAST. These results can be compared with recent observations with lithium pellets in ASDEX-Upgrade that failed to mitigate ELMs, highlighting one comparative advantage of continuous powder injection for real-time ELM elimination.« less

Double-null divertor configuration discharge and disruptive heat flux simulation using TSC on EAST

NASA Astrophysics Data System (ADS)

Bo, SHI; Jinhong, YANG; Cheng, YANG; Desheng, CHENG; Hui, WANG; Hui, ZHANG; Haifei, DENG; Junli, QI; Xianzu, GONG; Weihua, WANG

2018-07-01

The tokamak simulation code (TSC) is employed to simulate the complete evolution of a disruptive discharge in the experimental advanced superconducting tokamak. The multiplication factor of the anomalous transport coefficient was adjusted to model the major disruptive discharge with double-null divertor configuration based on shot 61 916. The real-time feed-back control system for the plasma displacement was employed. Modeling results of the evolution of the poloidal field coil currents, the plasma current, the major radius, the plasma configuration all show agreement with experimental measurements. Results from the simulation show that during disruption, heat flux about 8 MW m‑2 flows to the upper divertor target plate and about 6 MW m‑2 flows to the lower divertor target plate. Computations predict that different amounts of heat fluxes on the divertor target plate could result by adjusting the multiplication factor of the anomalous transport coefficient. This shows that TSC has high flexibility and predictability.

Experience on divertor fuel retention after two ITER-Like Wall campaigns

NASA Astrophysics Data System (ADS)

Heinola, K.; Widdowson, A.; Likonen, J.; Ahlgren, T.; Alves, E.; Ayres, C. F.; Baron-Wiechec, A.; Barradas, N.; Brezinsek, S.; Catarino, N.; Coad, P.; Guillemaut, C.; Jepu, I.; Krat, S.; Lahtinen, A.; Matthews, G. F.; Mayer, M.; Contributors, JET

2017-12-01

The JET ITER-Like Wall experiment, with its all-metal plasma-facing components, provides a unique environment for plasma and plasma-wall interaction studies. These studies are of great importance in understanding the underlying phenomena taking place during the operation of a future fusion reactor. Present work summarizes and reports the plasma fuel retention in the divertor resulting from the two first experimental campaigns with the ITER-Like Wall. The deposition pattern in the divertor after the second campaign shows same trend as was observed after the first campaign: highest deposition of 10-15 μm was found on the top part of the inner divertor. Due to the change in plasma magnetic configurations from the first to the second campaign, and the resulted strike point locations, an increase of deposition was observed on the base of the divertor. The deuterium retention was found to be affected by the hydrogen plasma experiments done at the end of second experimental campaign.

Simple Map with Low MN Perturbation for a Single-Null Divertor Tokamak with Constant Width of Stochastic Layer

NASA Astrophysics Data System (ADS)

Verma, Arun; Smith, Terry; Punjabi, Alkesh; Boozer, Allen

1996-11-01

In this work, we investigate the effects of low MN perturbations in a single-null divertor tokamak with stochastic scrape-off layer. The unperturbed magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). We choose the combinations of the map parameter k, and the strength of the low MN perturbation such that the width of stochastic layer remains unchanged. We give detailed results on the effects of low MN perturbation on the magnetic topology of the stochastic layer and on the footprint of field lines on the divertor plate given the constraint of constant width of the stochastic layer. The low MN perturbations occur naturally and therefore their effects are of considerable importance in tokamak divertor physics. This work is supported by US DOE OFES. Use of CRAY at HU and at NERSC is gratefully acknowledged.

Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models

PubMed Central

Grün, Sonja; Helias, Moritz

2017-01-01

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition. PMID:28968396

Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models.

PubMed

Rostami, Vahid; Porta Mana, PierGianLuca; Grün, Sonja; Helias, Moritz

2017-10-01

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.

On Heat Loading, Novel Divertors, and Fusion Reactors

NASA Astrophysics Data System (ADS)

Kotschenreuther, Mike

2006-10-01

A new magnetic divertor geometry has been proposed to solve reactor heat exhaust problems, which are far more severe for a reactor than for ITER. Using reactor-compatible coils to generate an extra X-point downstream from the main X-point, the new X-divertor (XD) is shown to greatly expand magnetic flux at the divertor plates. As a result, the heat is distributed over a larger area and the line length is greatly increased. The heat-flux limitations of a standard divertor (SD) force a high core radiation fraction (fRad) in most reactor designs that necessarily have a several times higher ratio of heating power to radius (P/R) than ITER. It is argued that such high values of fRad will probably have serious deleterious consequences on the core confinement and stability of a burning plasma. Operation with internal transport barriers (ITBs) does not appear to overcome this problem. By reducing the core fRad within an acceptable range, the X-divertor is shown to substantially lower the core confinement requirement for a fusion reactor. As a bonus, the XD also enables the use of liquid metals by reducing the MHD drag. A possible series of experiments for an efficient and attractive path to practical fusion power is suggested.

Plasma power recycling at the divertor surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Xian -Zhu; Guo, Zehua

With a divertor made of solid materials like carbon and tungsten, plasma ions are expected to be recycled at the divertor surface with a time-averaged particle recycling coefficient very close to unity in steady-state operation. This means that almost every plasma ion (hydrogen and helium) will be returned to the plasma, mostly as neutrals. The power flux deposited by the plasma on the divertor surface, on the other hand, can have varying recycling characteristics depending on the material choice of the divertor; the run-time atomic composition of the surface, which can be modified by material mix due to impurity migrationmore » in the chamber; and the surface morphology change over time. In general, a high-Z–material (such as tungsten) surface tends to reflect light ions and produce stronger power recycling, while a low-Z–material (such as carbon) surface tends to have a larger sticking coefficient for light ions and hence lower power recycling. Here, an explicit constraint on target plasma density and temperature is derived from the truncated bi-Maxwellian sheath model, in relation to the absorbed power load and power recycling coefficient at the divertor surface. Lastly, it is shown that because of the surface recombination energy flux, the attached plasma has a sharper response to power recycling in comparison to a detached plasma.« less

Plasma power recycling at the divertor surface

DOE PAGES

Tang, Xian -Zhu; Guo, Zehua

2016-12-03

With a divertor made of solid materials like carbon and tungsten, plasma ions are expected to be recycled at the divertor surface with a time-averaged particle recycling coefficient very close to unity in steady-state operation. This means that almost every plasma ion (hydrogen and helium) will be returned to the plasma, mostly as neutrals. The power flux deposited by the plasma on the divertor surface, on the other hand, can have varying recycling characteristics depending on the material choice of the divertor; the run-time atomic composition of the surface, which can be modified by material mix due to impurity migrationmore » in the chamber; and the surface morphology change over time. In general, a high-Z–material (such as tungsten) surface tends to reflect light ions and produce stronger power recycling, while a low-Z–material (such as carbon) surface tends to have a larger sticking coefficient for light ions and hence lower power recycling. Here, an explicit constraint on target plasma density and temperature is derived from the truncated bi-Maxwellian sheath model, in relation to the absorbed power load and power recycling coefficient at the divertor surface. Lastly, it is shown that because of the surface recombination energy flux, the attached plasma has a sharper response to power recycling in comparison to a detached plasma.« less

Conceptual design of divertor and first wall for DEMO-FNS

NASA Astrophysics Data System (ADS)

Sergeev, V. Yu.; Kuteev, B. V.; Bykov, A. S.; Gervash, A. A.; Glazunov, D. A.; Goncharov, P. R.; Dnestrovskij, A. Yu.; Khayrutdinov, R. R.; Klishchenko, A. V.; Lukash, V. E.; Mazul, I. V.; Molchanov, P. A.; Petrov, V. S.; Rozhansky, V. A.; Shpanskiy, Yu. S.; Sivak, A. B.; Skokov, V. G.; Spitsyn, A. V.

2015-11-01

Key issues of design of the divertor and the first wall of DEMO-FNS are presented. A double null closed magnetic configuration was chosen with long external legs and V-shaped corners. The divertor employs a cassette design similar to that of ITER. Water-cooled first wall of the tokamak is made of Be tiles and CuCrZr-stainless steel shells. Lithium injection and circulation technologies are foreseen for protection of plasma facing components. Simulations of thermal loads onto the first wall and divertor plates suggest a possibility to distribute heat loads making them less than 10 MW m-2. Evaluations of sputtering and evaporation of plasma-facing materials suggest that lithium may protect the first wall. To prevent Be erosion at the outer divertor plates either the full detached divertor operation or arrangement of the renewal lithium flow on targets should be implemented. Test bed experiments on the Tsefey-M facility with the first wall mockup coated by Ве tiles and cooled by water are presented. The temperature of the surface of tiles reached 280-300 °С at 5 MW m-2 and 600-650 °С at 10.5 MW m-2. The mockup successfully withstood 1000 cycles with the lower thermal loading and 100 cycles with higher thermal loading.

DOE Office of Scientific and Technical Information (OSTI.GOV)

M. Ono, M. Jaworski, R. Kaita, C. N. Skinner, J.P. Allain, R. Maingi, F. Scotti, V.A. Soukhanovskii, and the NSTX-U Team

Developing a reactor compatible divertor and managing the associated plasma material interaction (PMI) has been identified as a high priority research area for magnetic confinement fusion. Accordingly on NSTXU, the PMI research has received a strong emphasis. With ~ 15 MW of auxiliary heating power, NSTX-U will be able to test the PMI physics with the peak divertor plasma facing component (PFC) heat loads of up to 40-60 MW/m2 . To support the PMI research, a comprehensive set of PMI diagnostic tools are being implemented. The snow-flake configuration can produce exceptionally high divertor flux expansion of up to ~ 50.more » Combined with the radiative divertor concept, the snow-flake configuration has reduced the divertor heat flux by an order of magnitude in NSTX. Another area of active PMI investigation is the effect of divertor lithium coating (both in solid and liquid phases). The overall NSTX lithium PFC coating results suggest exciting opportunities for future magnetic confinement research including significant electron energy confinement improvements, Hmode power threshold reduction, the control of Edge Localized Modes (ELMs), and high heat flux handling. To support the NSTX-U/PPPL PMI research, there are also a number of associated PMI facilities implemented at PPPL/Princeton University including the Liquid Lithium R&D facility, Lithium Tokamak Experiment, and Laboratories for Materials Characterization and Surface Chemistry.« less

Conceptual design study for heat exhaust management in the ARC fusion pilot plant

NASA Astrophysics Data System (ADS)

Dennett, C. A.; Cao, N. M.; Creely, A. J.; Hecla, J.; Hoffman, H.; Kuang, A. Q.; Major, M.; Ruiz Ruiz, J.; Tinguely, R. A.; Tolman, E. A.; Brunner, D.; Labombard, B.; Sorbom, B. N.; Whyte, D. G.; Grover, P.; Laughman, C.

2017-10-01

The ARC pilot plant conceptual design study has been extended to explore solutions for managing heat exhaust resulting from 525 MW of fusion power in a compact (R 3.3 m) tokamak. Superconducting poloidal field coils are configured to produce double-null equilibria that support X-point target divertors while maintaining the original core plasma shape and toroidal field coil size. Long outer divertor legs are appended to the original vacuum vessel, providing both large surface areas for surface dissipation of radiative heat and significantly reduced neutron damage for divertor components. A molten salt FLiBe blanket adequately shields all superconductors and functions as a tritium breeder, with advanced neutronics calculations indicating a tritium breeding ratio of 1.08. In addition, FLiBe is used as the active coolant for the entire vessel. A tungsten swirl-tube cooling channel is implemented in the divertor, capable of exhausting 12 MW/m2, heat flux while keeping total FliBe pumping power below 1% of fusion power. Finally, three novel diagnostics are explored: Cherenkov radiation emitted in FLiBe to measure fusion reaction rate, microwave interferometry to measure divertor detachment front location, and IR imaging through the FLiBe blanket to monitor selected divertor ``hotspots.''

Actively convected liquid metal divertor

NASA Astrophysics Data System (ADS)

Shimada, Michiya; Hirooka, Yoshi

2014-12-01

The use of actively convected liquid metals with j × B force is proposed to facilitate heat handling by the divertor, a challenging issue associated with magnetic fusion experiments such as ITER. This issue will be aggravated even more for DEMO and power reactors because the divertor heat load will be significantly higher and yet the use of copper would not be allowed as the heat sink material. Instead, reduced activation ferritic/martensitic steel alloys with heat conductivities substantially lower than that of copper, will be used as the structural materials. The present proposal is to fill the lower part of the vacuum vessel with liquid metals with relatively low melting points and low chemical activities including Ga and Sn. The divertor modules, equipped with electrodes and cooling tubes, are immersed in the liquid metal. The electrode, placed in the middle of the liquid metal, can be biased positively or negatively with respect to the module. The j × B force due to the current between the electrode and the module provides a rotating motion for the liquid metal around the electrodes. The rise in liquid temperature at the separatrix hit point can be maintained at acceptable levels from the operation point of view. As the rotation speed increases, the current in the liquid metal is expected to decrease due to the v × B electromotive force. This rotating motion in the poloidal plane will reduce the divertor heat load significantly. Another important benefit of the convected liquid metal divertor is the fast recovery from unmitigated disruptions. Also, the liquid metal divertor concept eliminates the erosion problem.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahn, J. -W.; Briesemester, A. R.; Kobayashi, M.

Enhanced perpendicular heat and momentum transport induces parallel pressure loss leading to divertor detachment, which can be produced by the increase of density in 2D tokamaks. However, in the 3D configurations such as tokamaks with 3D fields and stellarators, the fraction of perpendicular transport can be higher even in a lower density regime, which could lead to the early transition to detachment without passing through the high-recycling regime. 3D fields applied to the limiter tokamak plasmas produce edge stochastic layers close to the last closed flux surface (LCFS), which can allow for enhanced perpendicular transport and indeed the absence ofmore » high recycling regime and early detachment have been observed in TEXTOR and Tore Supra. However, in the X-point divertor tokamaks with the applied 3D fields, the parallel transport is still dominant and the detachment facilitation has not been observed yet. Rather, 3D fields affected detachment adversely under certain conditions, either by preventing detachment onset as seen in DIII-D or by re-attaching the existing detached plasma as shown in NSTX. The possible way for strong 3D effects to induce access to the early detachment in divertor tokamaks appears to be via significant perpendicular loss of parallel momentum by frictional force for the counter-streaming flows between neighboring flow channels in the divertor. In principle, the adjacent lobes in the 3D divertor tokamak may generate the counter-streaming flow channels. However, an EMC3-EIRENE simulation for ITER H-mode plasmas demonstrated that screened RMP leads to significantly reduced counter-flows near the divertor target, therefore the momentum loss effect leading to detachment facilitation is expected to be small. This is consistent with the observation in LHD, which showed screening (amplification) of RMP fields in the attachment (stable detachment) case. In conclusion, work for optimal parameter window for best divertor operation scenario is needed particularly for the 3D divertor tokamak configuration.« less

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Suppressed gross erosion of high-temperature lithium via rapid deuterium implantation

DOE PAGES

Abrams, T.; Jaworski, M. A.; Chen, M.; ...

2015-12-17

Lithium-coated high-Z substrates are planned for use in the NSTX-U divertor and are a candidate plasma facing component (PFC) for reactors, but it remains necessary to characterize the gross Li erosion rate under high plasma fluxes (>10 23 m -2 s -1), typical for the divertor region. In this work, a realistic model for the compositional evolution of a Li/D layer is developed that incorporates first principles molecular dynamics (MD) simulations of D diffusion in liquid Li. Predictions of Li erosion from a mixed Li/D material are also developed that include formation of lithium deuteride (LiD). The erosion rate ofmore » Li from LiD is predicted to be significantly lower than from pure Li. This prediction is tested in the Magnum-PSI linear plasma device at ion fluxes of 10 23-10 24 m -2 s -1 and Li surface temperatures. ≤800 °C. Li/LiD coatings ranging in thickness from 0.2 to 500 μm are studied. The dynamic D/Li concentrations are inferred via diffusion simulations. The pure Li erosion rate remains greater than Langmuir Law evaporation, as expected. For mixed-material Li/LiD surfaces, the erosion rates are reduced, in good agreement with modelling in almost all cases. Lastly, these results imply that the temperature limit for a Li-coated PFC may be significantly higher than previously imagined.« less

Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics.

PubMed

Galvelis, Raimondas; Sugita, Yuji

2017-06-13

The free energy calculations of complex chemical and biological systems with molecular dynamics (MD) are inefficient due to multiple local minima separated by high-energy barriers. The minima can be escaped using an enhanced sampling method such as metadynamics, which apply bias (i.e., importance sampling) along a set of collective variables (CV), but the maximum number of CVs (or dimensions) is severely limited. We propose a high-dimensional bias potential method (NN2B) based on two machine learning algorithms: the nearest neighbor density estimator (NNDE) and the artificial neural network (ANN) for the bias potential approximation. The bias potential is constructed iteratively from short biased MD simulations accounting for correlation among CVs. Our method is capable of achieving ergodic sampling and calculating free energy of polypeptides with up to 8-dimensional bias potential.

Divertor power and particle fluxes between and during type-I ELMs in the ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Kallenbach, A.; Dux, R.; Eich, T.; Fischer, R.; Giannone, L.; Harhausen, J.; Herrmann, A.; Müller, H. W.; Pautasso, G.; Wischmeier, M.; ASDEX Upgrade Team

2008-08-01

Particle, electric charge and power fluxes for type-I ELMy H-modes are measured in the divertor of the ASDEX Upgrade tokamak by triple Langmuir probes, shunts, infrared (IR) thermography and spectroscopy. The discharges are in the medium to high density range, resulting in predominantly convective edge localized modes (ELMs) with moderate fractional stored energy losses of 2% or below. Time resolved data over ELM cycles are obtained by coherent averaging of typically one hundred similar ELMs, spatial profiles from the flush-mounted Langmuir probes are obtained by strike point sweeps. The application of simple physics models is used to compare different diagnostics and to make consistency checks, e.g. the standard sheath model applied to the Langmuir probes yields power fluxes which are compared with the thermographic measurements. In between ELMs, Langmuir probe and thermography power loads appear consistent in the outer divertor, taking into account additional load due to radiation and charge exchange neutrals measured by thermography. The inner divertor is completely detached and no significant power flow by charged particles is measured. During ELMs, quite similar power flux profiles are found in the outer divertor by thermography and probes, albeit larger uncertainties in Langmuir probe evaluation during ELMs have to be taken into account. In the inner divertor, ELM power fluxes from thermography are a factor 10 larger than those derived from probes using the standard sheath model. This deviation is too large to be caused by deficiencies of probe analysis. The total ELM energy deposition from IR is about a factor 2 higher in the inner divertor compared with the outer divertor. Spectroscopic measurements suggest a quite moderate contribution of radiation to the target power load. Shunt measurements reveal a significant positive charge flow into the inner target during ELMs. The net number of elementary charges correlates well with the total core particle loss obtained from highly resolved density profiles. As a consequence, the discrepancy between probe and IR measurements is attributed to the ion power channel via a high mean impact energy of the ions at the inner target. The dominant contributing mechanism is proposed to be the directed loss of ions from the pedestal region into the inner divertor.

A multichannel visible spectroscopy system for the ITER-like W divertor on EAST.

PubMed

Mao, Hongmin; Ding, Fang; Luo, Guang-Nan; Hu, Zhenhua; Chen, Xiahua; Xu, Feng; Yang, Zhongshi; Chen, Jingbo; Wang, Liang; Ding, Rui; Zhang, Ling; Gao, Wei; Xu, Jichan; Wu, Chengrui

2017-04-01

To facilitate long-pulse high power operation, an ITER-like actively cooled tungsten (W) divertor was installed in Experimental Advanced Superconducting Tokamak (EAST) to replace the original upper graphite divertor in 2014. A dedicated multichannel visible spectroscopic diagnostic system has been accordingly developed for the characterization of the plasma and impurities in the W divertor. An array of 22 lines-of-sight (LOSs) provides a profile measurement of the light emitted from the plasma along upper outer divertor, and the other 17 vertical LOSs view the upper inner divertor, achieving a 13 mm poloidal resolution in both regions. The light emitted from the plasma is collected by a specially designed optical lens assembly and then transferred to a Czerny-Turner spectrometer via 40 m quartz fibers. At the end, the spectra dispersed by the spectrometer are recorded with an Electron-Multiplying Charge Coupled Device (EMCCD). The optical throughput and quantum efficiency of the system are optimized in the wavelength range 350-700 nm. The spectral resolution/coverage can be adjusted from 0.01 nm/3 nm to 0.41 nm/140 nm by switching the grating with suitable groove density. The frame rate depends on the setting of LOS number in EMCCD and can reach nearly 2 kHz for single LOS detection. The light collected by the front optical lens can also be divided and partly transferred to a photomultiplier tube array with specified bandpass filter, which can provide faster sampling rates by up to 200 kHz. The spectroscopic diagnostic is routinely operated in EAST discharges with absolute optical calibrations applied before and after each campaign, monitoring photon fluxes from impurities and H recycling in the upper divertor. This paper presents the technical details of the diagnostic and typical measurements during EAST discharges.

The appearance and propagation of filaments in the private flux region in Mega Amp Spherical Tokamak

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, J. R.; Fishpool, G. M.; Thornton, A. J.

2015-09-15

The transport of particles via intermittent filamentary structures in the private flux region (PFR) of plasmas in the MAST tokamak has been investigated using a fast framing camera recording visible light emission from the volume of the lower divertor, as well as Langmuir probes and IR thermography monitoring particle and power fluxes to plasma-facing surfaces in the divertor. The visible camera data suggest that, in the divertor volume, fluctuations in light emission above the X-point are strongest in the scrape-off layer (SOL). Conversely, in the region below the X-point, it is found that these fluctuations are strongest in the PFRmore » of the inner divertor leg. Detailed analysis of the appearance of these filaments in the camera data suggests that they are approximately circular, around 1–2 cm in diameter, but appear more elongated near the divertor target. The most probable toroidal quasi-mode number is between 2 and 3. These filaments eject plasma deeper into the private flux region, sometimes by the production of secondary filaments, moving at a speed of 0.5–1.0 km/s. Probe measurements at the inner divertor target suggest that the fluctuations in the particle flux to the inner target are strongest in the private flux region, and that the amplitude and distribution of these fluctuations are insensitive to the electron density of the core plasma, auxiliary heating and whether the plasma is single-null or double-null. It is found that the e-folding width of the time-average particle flux in the PFR decreases with increasing plasma current, but the fluctuations appear to be unaffected. At the outer divertor target, the fluctuations in particle and power fluxes are strongest in the SOL.« less

A multichannel visible spectroscopy system for the ITER-like W divertor on EAST

NASA Astrophysics Data System (ADS)

Mao, Hongmin; Ding, Fang; Luo, Guang-Nan; Hu, Zhenhua; Chen, Xiahua; Xu, Feng; Yang, Zhongshi; Chen, Jingbo; Wang, Liang; Ding, Rui; Zhang, Ling; Gao, Wei; Xu, Jichan; Wu, Chengrui

2017-04-01

To facilitate long-pulse high power operation, an ITER-like actively cooled tungsten (W) divertor was installed in Experimental Advanced Superconducting Tokamak (EAST) to replace the original upper graphite divertor in 2014. A dedicated multichannel visible spectroscopic diagnostic system has been accordingly developed for the characterization of the plasma and impurities in the W divertor. An array of 22 lines-of-sight (LOSs) provides a profile measurement of the light emitted from the plasma along upper outer divertor, and the other 17 vertical LOSs view the upper inner divertor, achieving a 13 mm poloidal resolution in both regions. The light emitted from the plasma is collected by a specially designed optical lens assembly and then transferred to a Czerny-Turner spectrometer via 40 m quartz fibers. At the end, the spectra dispersed by the spectrometer are recorded with an Electron-Multiplying Charge Coupled Device (EMCCD). The optical throughput and quantum efficiency of the system are optimized in the wavelength range 350-700 nm. The spectral resolution/coverage can be adjusted from 0.01 nm/3 nm to 0.41 nm/140 nm by switching the grating with suitable groove density. The frame rate depends on the setting of LOS number in EMCCD and can reach nearly 2 kHz for single LOS detection. The light collected by the front optical lens can also be divided and partly transferred to a photomultiplier tube array with specified bandpass filter, which can provide faster sampling rates by up to 200 kHz. The spectroscopic diagnostic is routinely operated in EAST discharges with absolute optical calibrations applied before and after each campaign, monitoring photon fluxes from impurities and H recycling in the upper divertor. This paper presents the technical details of the diagnostic and typical measurements during EAST discharges.

Blessing and curse of chaos in numerical turbulence simulations

NASA Astrophysics Data System (ADS)

Lee, Jon

1994-03-01

Because of the trajectory instability, time reversal is not possible beyond a certain evolution time and hence the time irreversibility prevails under the finite-accuracy trajectory computation. This therefore provides a practical reconciliation of the dynamic reversibility and macroscopic irreversibility (blessing of chaos). On the other hand, the trajectory instability is also responsible for a limited evolution time, so that finite-accuracy computation would yield a pseudo-orbit which is totally unrelated to the true trajectory (curse of chaos). For the inviscid 2D flow, however, we can accurately compute the long- time average of flow quantities with a pseudo-orbit by invoking the ergodic theorem.

Comment on "Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua".

PubMed

Felderhof, B U

2013-08-01

Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from the axis. We demonstrate that statistical mechanical arguments, involving Hamiltonian dynamics and ergodicity due to irregularity of the wall, lead instead to a thermal equilibrium state with uniform temperature. This is the situation to be expected in experiment.

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

NASA Astrophysics Data System (ADS)

Giordano, C. M.; Cincotta, P. M.

2018-05-01

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Various divertor biasing configurations and improved divertor performance with biasing on Tokamak de Varennes (TdeV)*

DOE Office of Scientific and Technical Information (OSTI.GOV)

Decoste, R.; Lachambre, J.; Abel, G.

1994-05-01

Electrically insulated divertor plates are used on TdeV (Tokamak de Varennes) [18[ital th] [ital EPS] [ital Conference] [ital on] [ital Controlled] [ital Fusion] [ital and] [ital Plasma] [ital Physics] Berlin (European Physical Society, Petit-Lancy, 1991), Vol. 15C, Part I, pp. 1--141] to produce various biasing configurations, which can be decomposed into two basic modes. Plasma biasing, with a radial electric field [ital E][sub [ital r

ADX: A high Power Density, Advanced RF-Driven Divertor Test Tokamak for PMI studies

NASA Astrophysics Data System (ADS)

Whyte, Dennis; ADX Team

2015-11-01

The MIT PSFC and collaborators are proposing an advanced divertor experiment, ADX; a divertor test tokamak dedicated to address critical gaps in plasma-material interactions (PMI) science, and the world fusion research program, on the pathway to FNSF/DEMO. Basic ADX design features are motivated and discussed. In order to assess the widest range of advanced divertor concepts, a large fraction (>50%) of the toroidal field volume is purpose-built with innovative magnetic topology control and flexibility for assessing different surfaces, including liquids. ADX features high B-field (>6 Tesla) and high global power density (P/S ~ 1.5 MW/m2) in order to access the full range of parallel heat flux and divertor plasma pressures foreseen for reactors, while simultaneously assessing the effect of highly dissipative divertors on core plasma/pedestal. Various options for efficiently achieving high field are being assessed including the use of Alcator technology (cryogenic cooled copper) and high-temperature superconductors. The experimental platform would also explore advanced lower hybrid current drive and ion-cyclotron range of frequency actuators located at the high-field side; a location which is predicted to greatly reduce the PMI effects on the launcher while minimally perturbing the core plasma. The synergistic effects of high-field launchers with high total B on current and flow drive can thus be studied in reactor-relevant boundary plasmas.

Active Control of Power Exhaust in Strongly Heated ASDEX Upgrade Plasmas

NASA Astrophysics Data System (ADS)

Dux, Ralph; Kallenbach, Arne; Bernert, Matthias; Eich, Thomas; Fuchs, Christoph; Giannone, Louis; Herrmann, Albrecht; Schweinzer, Josef; Treutterer, Wolfgang

2012-10-01

Due to the absence of carbon as an intrinsic low-Z radiator, and tight limits for the acceptable power load on the divertor target, ITER will rely on impurity seeding for radiative power dissipation and for generation of partial detachment. The injection of more than one radiating species is required to optimise the power removal in the main plasma and in the divertor region, i.e. a low-Z species for radiation in the divertor and a medium-Z species for radiation in the outer core plasma. In ASDEX Upgrade, a set of robust sensors, which is suitable to feedback control the radiated power in the main chamber and the divertor as well as the electron temperature at the target, has been developed. Different feedback schemes were applied in H-mode discharges with a maximum heating power of up to 23,W, i.e. at ITER values of P/R (power per major radius) to control all combinations of power flux into the divertor region, power flux onto the target or electron temperature at the target through injection of nitrogen as the divertor radiator and argon as the main chamber radiator. Even at the highest heating powers the peak heat flux density at the target is kept at benign values. The control schemes and the plasma behaviour in these discharges will be discussed.

Erosion and deposition in the JET divertor during the second ITER-like wall campaign

NASA Astrophysics Data System (ADS)

Mayer, M.; Krat, S.; Baron-Wiechec, A.; Gasparyan, Yu; Heinola, K.; Koivuranta, S.; Likonen, J.; Ruset, C.; de Saint-Aubin, G.; Widdowson, A.; Contributors, JET

2017-12-01

Erosion of plasma-facing materials and successive transport and redeposition of eroded material are crucial processes determining the lifetime of plasma-facing components and the trapped tritium inventory in redeposited material layers. Erosion and deposition in the JET divertor were studied during the second JET ITER-like wall campaign ILW-2 in 2013-2014 by using a poloidal row of specially prepared divertor marker tiles including the tungsten bulk tile 5. The marker tiles were analyzed using elastic backscattering with 3-4.5 MeV incident protons and nuclear reaction analysis using 0.8-4.5 MeV 3He ions before and after the campaign. The erosion/deposition pattern observed during ILW-2 is qualitatively comparable to the first campaign ILW-1 in 2011-2012: deposits consist mainly of beryllium with 5-20 at.% of carbon and oxygen and small amounts of Ni and W. The highest deposition with deposited layer thicknesses up to 30 μm per campaign is still observed on the upper and horizontal parts of the inner divertor. Outer divertor tiles 5, 6, 7 and 8 are net W erosion areas. The observed D inventory is roughly comparable to the inventory observed during ILW-1. The results obtained during ILW-2 therefore confirm the positive results observed in ILW-1 with respect to reduced material deposition and hydrogen isotopes retention in the divertor.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dr. Ricardo Maqueda; Dr. Fred M. Levinton

Nova Photonics, Inc. has a collaborative effort at the National Spherical Torus Experiment (NSTX). This collaboration, based on fast imaging of visible phenomena, has provided key insights on edge turbulence, intermittency, and edge phenomena such as edge localized modes (ELMs) and multi-faceted axisymmetric radiation from the edge (MARFE). Studies have been performed in all these areas. The edge turbulence/intermittency studies make use of the Gas Puff Imaging diagnostic developed by the Principal Investigator (Ricardo Maqueda) together with colleagues from PPPL. This effort is part of the International Tokamak Physics Activity (ITPA) edge, scrape-off layer and divertor group joint activity (DSOL-15:more » Inter-machine comparison of blob characteristics). The edge turbulence/blob study has been extended from the current location near the midplane of the device to the lower divertor region of NSTX. The goal of this effort was to study turbulence born blobs in the vicinity of the X-point region and their circuit closure on divertor sheaths or high density regions in the divertor. In the area of ELMs and MARFEs we have studied and characterized the mode structure and evolution of the ELM types observed in NSTX, as well as the study of the observed interaction between MARFEs and ELMs. This interaction could have substantial implications for future devices where radiative divertor regions are required to maintain detachment from the divertor plasma facing components.« less

Spectra of random operators with absolutely continuous integrated density of states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rio, Rafael del, E-mail: delrio@iimas.unam.mx, E-mail: delriomagia@gmail.com

2014-04-15

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the integrated density of states implies singular spectra of ergodic operators is either empty or of positive measure. Our results apply to Anderson and alloy type models, perturbed Landau Hamiltonians, almost periodic potentials, and models which are not ergodic.

Divertor Coil Design and Implementation on Pegasus

NASA Astrophysics Data System (ADS)

Shriwise, P. C.; Bongard, M. W.; Cole, J. A.; Fonck, R. J.; Kujak-Ford, B. A.; Lewicki, B. T.; Winz, G. R.

2012-10-01

An upgraded divertor coil system is being commissioned on the Pegasus Toroidal Experiment in conjunction with power system upgrades in order to achieve higher β plasmas, reduce impurities, and possibly achieve H-mode operation. Design points for the divertor coil locations and estimates of their necessary current ratings were found using predictive equilibrium modeling based upon a 300 kA target plasma. This modeling represented existing Pegasus coil locations and current drive limits. The resultant design calls for 125 kA-turns from the divertor system to support the creation of a double null magnetic topology in plasmas with Ip<=300 kA. Initial experiments using this system will employ 900 V IGBT power supply modules to provide IDIV<=4 kA. The resulting 20 kA-turn capability of the existing divertor coil will be augmented by a new coil providing additional A-turns in series. Induced vessel wall current modeling indicates the time response of a 28 turn augmentation coil remains fast compared to the poloidal field penetration rate through the vessel. First results operating the augmented system are shown.

Parallel Energy Transport in Detached DIII-D Divertor Plasmas

NASA Astrophysics Data System (ADS)

Leonard, A. W.; Lore, J. D.; Canik, J. M.; McLean, A. G.; Makowski, M. A.

2017-10-01

A comparison of experiment and modeling of detached divertor plasmas is examined in the context of parallel energy transport. Experimental estimates of power carried by electron thermal conduction versus plasma convection are experimentally inferred from power balance measurements of radiated power and target plate heat flux combined with Thomson scattering measurements of the Te profile along the divertor leg. Experimental profiles of Te exhibit relatively low gradients with Te < 15 eV from the X-point to the target implying transport dominated by convection. In contrast, fluid modeling with SOLPS produces sharp Te gradients for Te > 3 eV, characteristic of transport dominated by electron conduction through the bulk of the divertor. This discrepancy with experimental transport dominated by convection and modeling by conduction has significant implications for the radiative capacity of divertor plasmas and may explain at least part of the difficulty for fluid modeling to obtain the experimentally observed radiative losses. Comparisons are also made for helium plasmas where the match between experiment and modeling is much better. Work supported by the US DOE under DE-FC02-04ER54698.

Minimum magnetic curvature for resilient divertors using Compact Toroidal Hybrid geometry

DOE PAGES

Bader, Aaron; Hegna, C. C.; Cianciosa, Mark R.; ...

2018-03-16

The properties of resilient divertors are explored using equilibria derived from Compact Toroidal Hybrid (CTH) geometries. Resilience is defined here as the robustness of the strike point patterns as the plasma geometry and/or plasma profiles are changed. The addition of plasma current in the CTH configurations significantly alters the shape of the last closed flux surface and the rotational transform profile, however, it does not alter the strike point pattern on the target plates, and hence has resilient divertor features. The limits of when a configuration transforms to a resilient configuration is then explored. New CTH-like configurations are generated thatmore » vary from a perfectly circular cross section to configurations with increasing amounts of toroidal shaping. It is found that even small amounts of toroidal shaping lead to strike point localization that is similar to the standard CTH configuration. Lastly, these results show that only a small degree of three-dimensional shaping is necessary to produce a resilient divertor, implying that any highly shaped optimized stellarator will possess the resilient divertor property.« less

Designing divertor targets for uniform power load

NASA Astrophysics Data System (ADS)

Dekeyser, W.; Reiter, D.; Baelmans, M.

2015-08-01

Divertor design for next step fusion reactors heavily relies on 2D edge plasma modeling with codes as e.g. B2-EIRENE. While these codes are typically used in a design-by-analysis approach, in previous work we have shown that divertor design can alternatively be posed as a mathematical optimization problem, and solved very efficiently using adjoint methods adapted from computational aerodynamics. This approach has been applied successfully to divertor target shape design for more uniform power load. In this paper, the concept is further extended to include all contributions to the target power load, with particular focus on radiation. In a simplified test problem, we show the potential benefits of fully including the radiation load in the design cycle as compared to only assessing this load in a post-processing step.

Non-equilibrium theory of arrested spinodal decomposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olais-Govea, José Manuel; López-Flores, Leticia; Medina-Noyola, Magdaleno

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ramŕez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whosemore » high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.« less

Describing Directional Cell Migration with a Characteristic Directionality Time

PubMed Central

Loosley, Alex J.; O’Brien, Xian M.; Reichner, Jonathan S.; Tang, Jay X.

2015-01-01

Many cell types can bias their direction of locomotion by coupling to external cues. Characteristics such as how fast a cell migrates and the directedness of its migration path can be quantified to provide metrics that determine which biochemical and biomechanical factors affect directional cell migration, and by how much. To be useful, these metrics must be reproducible from one experimental setting to another. However, most are not reproducible because their numerical values depend on technical parameters like sampling interval and measurement error. To address the need for a reproducible metric, we analytically derive a metric called directionality time, the minimum observation time required to identify motion as directionally biased. We show that the corresponding fit function is applicable to a variety of ergodic, directionally biased motions. A motion is ergodic when the underlying dynamical properties such as speed or directional bias do not change over time. Measuring the directionality of nonergodic motion is less straightforward but we also show how this class of motion can be analyzed. Simulations are used to show the robustness of directionality time measurements and its decoupling from measurement errors. As a practical example, we demonstrate the measurement of directionality time, step-by-step, on noisy, nonergodic trajectories of chemotactic neutrophils. Because of its inherent generality, directionality time ought to be useful for characterizing a broad range of motions including intracellular transport, cell motility, and animal migration. PMID:25992908

Kinetic studies of divertor heat fluxes in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Bateman, G.; Kritz, A. H.; Rafiq, T.; Park, G. Y.; Chang, C. S.; Brunner, D.; Hughes, J. W.; Labombard, B.; Terry, J.

2010-11-01

The kinetic XGC0 code [C.S. Chang et al, Phys. Plasmas 11 (2004) 2649] is used to model the H- mode pedestal and SOL regions in Alcator C-Mod discharges. The self-consistent simulations in this study include kinetic neoclassical physics and anomalous transport models along with the ExB flow shear effects. The heat fluxes on the divertor plates are computed and the fluxes to the outer plate are compared with experimental observations. The dynamics of the radial electric field near the separatrix and in the SOL region are computed with the XGC0 code, and the effect of the anomalous transport on the heat fluxes in the SOL region is investigated. In particular, the particle and thermal diffusivities obtained in the analysis mode are compared with predictions from the theory-based anomalous transport models such as MMM95 [G. Bateman et al, Phys. Plasmas 5 (1998) 1793] and DRIBM [T. Rafiq et al, to appear in Phys. Plasmas (2010)]. It is found that there is a notable pinch effect in the inner separatrix region. Possible physical mechanisms for the particle and thermal pinches are discussed.

Tungsten dust impact on ITER-like plasma edge

DOE PAGES

Smirnov, R. D.; Krasheninnikov, S. I.; Pigarov, A. Yu.; ...

2015-01-12

The impact of tungsten dust originating from divertor plates on the performance of edge plasma in ITER-like discharge is evaluated using computer modeling with the coupled dust-plasma transport code DUSTT-UEDGE. Different dust injection parameters, including dust size and mass injection rates, are surveyed. It is found that tungsten dust injection with rates as low as a few mg/s can lead to dangerously high tungsten impurity concentrations in the plasma core. Dust injections with rates of a few tens of mg/s are shown to have a significant effect on edge plasma parameters and dynamics in ITER scale tokamaks. The large impactmore » of certain phenomena, such as dust shielding by an ablation cloud and the thermal force on tungsten ions, on dust/impurity transport in edge plasma and consequently on core tungsten contamination level is demonstrated. Lastly, it is also found that high-Z impurities provided by dust can induce macroscopic self-sustained plasma oscillations in plasma edge leading to large temporal variations of edge plasma parameters and heat load to divertor target plates.« less

Edge Mechanisms for Power Excursion Control in Burning Plasmas

NASA Astrophysics Data System (ADS)

Hill, M. D.; Stacey, W. M.

2017-10-01

ITER must have active and preferably also passive control mechanisms that will limit inadvertent plasma power excursions which could trigger runaway fusion heating. We are identifying and investigating the potential of ion-orbit loss, impurity seeding, and various divertor ``choking'' phenomena to control or limit sudden increases in plasma density or temperature by reducing energy confinement, increasing radiation loss, etc., with the idea that such mechanisms could be tested on DIII-D and other existing tokamaks. We are assembling an edge-divertor code (GTEDGE-2) with a neutral transport model and a burn dynamics code, for this purpose. One potential control mechanism is the enhanced ion orbit loss from the thermalized ion distribution that would result from heating of the thermalized plasma ion distribution. Another possibility is impurity seeding with ions whose emissivity would increase sharply if the edge temperature increased. Enhanced radiative losses should also reduce the thermal energy flux across the separatrix, perhaps dropping the plasma into the poorer L-mode confinement regime. We will present some initial calculations to quantify these ideas. Work supported by US DOE under DE-FC02-04ER54698.

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

DOE PAGES

Hu, Xiaohu; Hong, Liang; Smith, Micholas Dean; ...

2015-11-23

Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~10 2s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10 –12 to 10 –5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of themore » energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.« less

Extended slow dynamical regime close to the many-body localization transition

NASA Astrophysics Data System (ADS)

Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

2016-02-01

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L =28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S (t ) ∝t1 /z with a disorder-dependent exponent z ≥1 , in contrast with the pure ballistic growth z =1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t ) ∝t-ζ with a continuously varying disorder-dependent exponent ζ , vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.

Integrated simulations of H-mode operation in ITER including core fuelling, divertor detachment and ELM control

NASA Astrophysics Data System (ADS)

Polevoi, A. R.; Loarte, A.; Dux, R.; Eich, T.; Fable, E.; Coster, D.; Maruyama, S.; Medvedev, S. Yu.; Köchl, F.; Zhogolev, V. E.

2018-05-01

ELM mitigation to avoid melting of the tungsten (W) divertor is one of the main factors affecting plasma fuelling and detachment control at full current for high Q operation in ITER. Here we derive the ITER operational space, where ELM mitigation to avoid melting of the W divertor monoblocks top surface is not required and appropriate control of W sources and radiation in the main plasma can be ensured through ELM control by pellet pacing. We apply the experimental scaling that relates the maximum ELM energy density deposited at the divertor with the pedestal parameters and this eliminates the uncertainty related with the ELM wetted area for energy deposition at the divertor and enables the definition of the ITER operating space through global plasma parameters. Our evaluation is thus based on this empirical scaling for ELM power loads together with the scaling for the pedestal pressure limit based on predictions from stability codes. In particular, our analysis has revealed that for the pedestal pressure predicted by the EPED1  +  SOLPS scaling, ELM mitigation to avoid melting of the W divertor monoblocks top surface may not be required for 2.65 T H-modes with normalized pedestal densities (to the Greenwald limit) larger than 0.5 to a level of current of 6.5–7.5 MA, which depends on assumptions on the divertor power flux during ELMs and between ELMs that expand the range of experimental uncertainties. The pellet and gas fuelling requirements compatible with control of plasma detachment, core plasma tungsten accumulation and H-mode operation (including post-ELM W transient radiation) have been assessed by 1.5D transport simulations for a range of assumptions regarding W re-deposition at the divertor including the most conservative assumption of zero prompt re-deposition. With such conservative assumptions, the post-ELM W transient radiation imposes a very stringent limit on ELM energy losses and the associated minimum required ELM frequency. Depending on W transport assumptions during the ELM, a maximum ELM frequency is also identified above which core tungsten accumulation takes place.

Overview of the recent DiMES and MiMES experiments in DIII-D

NASA Astrophysics Data System (ADS)

Rudakov, D. L.; Wong, C. P. C.; Litnovsky, A.; Wampler, W. R.; Boedo, J. A.; Brooks, N. H.; Fenstermacher, M. E.; Groth, M.; Hollmann, E. M.; Jacob, W.; Krasheninnikov, S. I.; Krieger, K.; Lasnier, C. J.; Leonard, A. W.; McLean, A. G.; Marot, M.; Moyer, R. A.; Petrie, T. W.; Philipps, V.; Smirnov, R. D.; Stangeby, P. C.; Watkins, J. G.; West, W. P.; Yu, J. H.

2009-12-01

Divertor and midplane material evaluation systems (DiMES and MiMES) in the DIII-D tokamak are used to address a variety of plasma-material interaction (PMI) issues relevant to ITER. Among the topics studied are carbon erosion and re-deposition, hydrogenic retention in the gaps between plasma-facing components (PFCs), deterioration of diagnostic mirrors from carbon deposition and techniques to mitigate that deposition, and dynamics and transport of dust. An overview of the recent experimental results is presented.

Vapor shielding models and the energy absorbed by divertor targets during transient events

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skovorodin, D. I., E-mail: dskovorodin@gmail.com; Arakcheev, A. S.; Pshenov, A. A.

2016-02-15

The erosion of divertor targets caused by high heat fluxes during transients is a serious threat to ITER operation, as it is going to be the main factor determining the divertor lifetime. Under the influence of extreme heat fluxes, the surface temperature of plasma facing components can reach some certain threshold, leading to an onset of intense material evaporation. The latter results in formation of cold dense vapor and secondary plasma cloud. This layer effectively absorbs the energy of the incident plasma flow, turning it into its own kinetic and internal energy and radiating it. This so called vapor shieldingmore » is a phenomenon that may help mitigating the erosion during transient events. In particular, the vapor shielding results in saturation of energy (per unit surface area) accumulated by the target during single pulse of heat load at some level E{sub max}. Matching this value is one of the possible tests to verify complicated numerical codes, developed to calculate the erosion rate during abnormal events in tokamaks. The paper presents three very different models of vapor shielding, demonstrating that E{sub max} depends strongly on the heat pulse duration, thermodynamic properties, and evaporation energy of the irradiated target material. While its dependence on the other shielding details such as radiation capabilities of material and dynamics of the vapor cloud is logarithmically weak. The reason for this is a strong (exponential) dependence of the target material evaporation rate, and therefore the “strength” of vapor shield on the target surface temperature. As a result, the influence of the vapor shielding phenomena details, such as radiation transport in the vapor cloud and evaporated material dynamics, on the E{sub max} is virtually completely masked by the strong dependence of the evaporation rate on the target surface temperature. However, the very same details define the amount of evaporated particles, needed to provide an effective shielding to the target, and, therefore, strongly influence resulting erosion rate. Thus, E{sub max} cannot be used for validation of shielding models and codes, aimed at the target material erosion calculations.« less

Temperature specification in atomistic molecular dynamics and its impact on simulation efficacy

NASA Astrophysics Data System (ADS)

Ocaya, R. O.; Terblans, J. J.

2017-10-01

Temperature is a vital thermodynamical function for physical systems. Knowledge of system temperature permits assessment of system ergodicity, entropy, system state and stability. Rapid theoretical and computational developments in the fields of condensed matter physics, chemistry, material science, molecular biology, nanotechnology and others necessitate clarity in the temperature specification. Temperature-based materials simulations, both standalone and distributed computing, are projected to grow in prominence over diverse research fields. In this article we discuss the apparent variability of temperature modeling formalisms used currently in atomistic molecular dynamics simulations, with respect to system energetics,dynamics and structural evolution. Commercial simulation programs, which by nature are heuristic, do not openly discuss this fundamental question. We address temperature specification in the context of atomistic molecular dynamics. We define a thermostat at 400K relative to a heat bath at 300K firstly using a modified ab-initio Newtonian method, and secondly using a Monte-Carlo method. The thermostatic vacancy formation and cohesion energies, equilibrium lattice constant for FCC copper is then calculated. Finally we compare and contrast the results.

Search strategy in a complex and dynamic environment (the Indian Ocean case)

NASA Astrophysics Data System (ADS)

Loire, Sophie; Arbabi, Hassan; Clary, Patrick; Ivic, Stefan; Crnjaric-Zic, Nelida; Macesic, Senka; Crnkovic, Bojan; Mezic, Igor; UCSB Team; Rijeka Team

2014-11-01

The disappearance of Malaysia Airlines Flight 370 (MH370) in the early morning hours of 8 March 2014 has exposed the disconcerting lack of efficient methods for identifying where to look and how to look for missing objects in a complex and dynamic environment. The search area for plane debris is a remote part of the Indian Ocean. Searches, of the lawnmower type, have been unsuccessful so far. Lagrangian kinematics of mesoscale features are visible in hypergraph maps of the Indian Ocean surface currents. Without a precise knowledge of the crash site, these maps give an estimate of the time evolution of any initial distribution of plane debris and permits the design of a search strategy. The Dynamic Spectral Multiscale Coverage search algorithm is modified to search a spatial distribution of targets that is evolving with time following the dynamic of ocean surface currents. Trajectories are generated for multiple search agents such that their spatial coverage converges to the target distribution. Central to this DSMC algorithm is a metric for the ergodicity.

Minority games, evolving capitals and replicator dynamics

NASA Astrophysics Data System (ADS)

Galla, Tobias; Zhang, Yi-Cheng

2009-11-01

We discuss a simple version of the minority game (MG) in which agents hold only one strategy each, but in which their capitals evolve dynamically according to their success and in which the total trading volume varies in time accordingly. This feature is known to be crucial for MGs to reproduce stylized facts of real market data. The stationary states and phase diagram of the model can be computed, and we show that the ergodicity breaking phase transition common for MGs, and marked by a divergence of the integrated response, is present also in this simplified model. An analogous majority game turns out to be relatively void of interesting features, and the total capital is found to diverge in time. Introducing a restraining force leads to a model akin to the replicator dynamics of evolutionary game theory, and we demonstrate that here a different type of phase transition is observed. Finally we briefly discuss the relation of this model with one strategy per player to more sophisticated minority games with dynamical capitals and several trading strategies per agent.

Slow relaxation dynamics of clogs in a vibrated granular silo.

PubMed

Guerrero, B V; Pugnaloni, L A; Lozano, C; Zuriguel, I; Garcimartín, A

2018-04-01

We experimentally explore the vibration-induced unclogging of arches halting the flow in a two-dimensional silo. The endurance of arches is determined by carrying out a survival analysis of their breaking times. By analyzing the dynamics of two morphological variables, we demonstrate that arches evolve toward less regular structures and it seems that there may exist a certain degree of irregularity that the arch reaches before collapsing. Moreover, we put forward that σ (the standard deviation of all angles between consecutive beads) describes faithfully the morphological evolution of the arch. Focusing on long-lasting arches, we study σ calculating its two-time autocorrelation function and its mean-squared displacement. In particular, the apparent logarithmic increase of the correlation and the decrease of the mean-squared displacement of σ when the waiting time is increased reveal a slowing down of the dynamics. This behavior is a clear hallmark of aging phenomena and confirms the lack of ergodicity in the unclogging dynamics. Our findings provide new insights on how an arch tends to destabilize and how the probability that it breaks with a long sustained vibration decreases with time.

Slow relaxation dynamics of clogs in a vibrated granular silo

NASA Astrophysics Data System (ADS)

Guerrero, B. V.; Pugnaloni, L. A.; Lozano, C.; Zuriguel, I.; Garcimartín, A.

2018-04-01

We experimentally explore the vibration-induced unclogging of arches halting the flow in a two-dimensional silo. The endurance of arches is determined by carrying out a survival analysis of their breaking times. By analyzing the dynamics of two morphological variables, we demonstrate that arches evolve toward less regular structures and it seems that there may exist a certain degree of irregularity that the arch reaches before collapsing. Moreover, we put forward that σ (the standard deviation of all angles between consecutive beads) describes faithfully the morphological evolution of the arch. Focusing on long-lasting arches, we study σ calculating its two-time autocorrelation function and its mean-squared displacement. In particular, the apparent logarithmic increase of the correlation and the decrease of the mean-squared displacement of σ when the waiting time is increased reveal a slowing down of the dynamics. This behavior is a clear hallmark of aging phenomena and confirms the lack of ergodicity in the unclogging dynamics. Our findings provide new insights on how an arch tends to destabilize and how the probability that it breaks with a long sustained vibration decreases with time.

Simulation of turbulence in the divertor region of tokamak edge plasma

NASA Astrophysics Data System (ADS)

Umansky, M. V.; Rognlien, T. D.; Xu, X. Q.

2005-03-01

Results are presented for turbulence simulations with the fluid edge turbulence code BOUT [X.Q. Xu, R.H. Cohen, Contr. Plas. Phys. 36 (1998) 158]. The present study is focussed on turbulence in the divertor leg region and on the role of the X-point in the structure of turbulence. Results of the present calculations indicate that the ballooning effects are important for the divertor fluctuations. The X-point shear leads to weak correlation of turbulence across the X-point regions, in particular for large toroidal wavenumber. For the saturated amplitudes of the divertor region turbulence it is found that amplitudes of density fluctuations are roughly proportional to the local density of the background plasma. The amplitudes of electron temperature and electric potential fluctuations are roughly proportional to the local electron temperature of the background plasma.

Divertor with a third-order null of the poloidal field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryutov, D. D.; Umansky, M. V.

2013-09-15

A concept and preliminary feasibility analysis of a divertor with the third-order poloidal field null is presented. The third-order null is the point where not only the field itself but also its first and second spatial derivatives are zero. In this case, the separatrix near the null-point has eight branches, and the number of strike-points increases from 2 (as in the standard divertor) to six. It is shown that this magnetic configuration can be created by a proper adjustment of the currents in a set of three divertor coils. If the currents are somewhat different from the required values, themore » configuration becomes that of three closely spaced first-order nulls. Analytic approach, suitable for a quick orientation in the problem, is used. Potential advantages and disadvantages of this configuration are briefly discussed.« less

Initial development of the DIII–D snowflake divertor control

NASA Astrophysics Data System (ADS)

Kolemen, E.; Vail, P. J.; Makowski, M. A.; Allen, S. L.; Bray, B. D.; Fenstermacher, M. E.; Humphreys, D. A.; Hyatt, A. W.; Lasnier, C. J.; Leonard, A. W.; McLean, A. G.; Maingi, R.; Nazikian, R.; Petrie, T. W.; Soukhanovskii, V. A.; Unterberg, E. A.

2018-06-01

Simultaneous control of two proximate magnetic field nulls in the divertor region is demonstrated on DIII–D to enable plasma operations in an advanced magnetic configuration known as the snowflake divertor (SFD). The SFD is characterized by a second-order poloidal field null, created by merging two first-order nulls of the standard divertor configuration. The snowflake configuration has many magnetic properties, such as high poloidal flux expansion, large plasma-wetted area, and additional strike points, that are advantageous for divertor heat flux management in future fusion reactors. However, the magnetic configuration of the SFD is highly-sensitive to changes in currents within the plasma and external coils and therefore requires complex magnetic control. The first real-time snowflake detection and control system on DIII–D has been implemented in order to stabilize the configuration. The control algorithm calculates the position of the two nulls in real-time by locally-expanding the Grad–Shafranov equation in the divertor region. A linear relation between variations in the poloidal field coil currents and changes in the null locations is then analytically derived. This formulation allows for simultaneous control of multiple coils to achieve a desired SFD configuration. It is shown that the control enabled various snowflake configurations on DIII–D in scenarios such as the double-null advanced tokamak. The SFD resulted in a 2.5×  reduction in the peak heat flux for many energy confinement times (2–3 s) without any adverse effects on core plasma performance.

Nuclear analysis of structural damage and nuclear heating on enhanced K-DEMO divertor model

NASA Astrophysics Data System (ADS)

Park, J.; Im, K.; Kwon, S.; Kim, J.; Kim, D.; Woo, M.; Shin, C.

2017-12-01

This paper addresses nuclear analysis on the Korean fusion demonstration reactor (K-DEMO) divertor to estimate the overall trend of nuclear heating values and displacement damages. The K-DEMO divertor model was created and converted by the CAD (Pro-Engineer™) and Monte Carlo automatic modeling programs as a 22.5° sector of the tokamak. The Monte Carlo neutron photon transport and ADVANTG codes were used in this calculation with the FENDL-2.1 nuclear data library. The calculation results indicate that the highest values appeared on the upper outboard target (OT) area, which means the OT is exposed to the highest radiation conditions among the three plasma-facing parts (inboard, central and outboard) in the divertor. Especially, much lower nuclear heating values and displacement damages are indicated on the lower part of the OT area than others. These are important results contributing to thermal-hydraulic and thermo-mechanical analyses on the divertor and also it is expected that the copper alloy materials may be partially used as a heat sink only at the lower part of the OT instead of the reduced activation ferritic-martensitic steel due to copper alloy’s high thermal conductivity.

Power exhaust scenarios and control for projected high-power NSTX-U operation

NASA Astrophysics Data System (ADS)

Menard, Jonathan; Gerhardt, S. P.; Myers, C. E.; Reinke, M. L.; Brooks, A.; Mardenfeld, M.; NSTX Upgrade Team

2017-10-01

An important goal of the NSTX Upgrade (NSTX-U) research program is to characterize energy confinement in the low-aspect-ratio spherical tokamak configuration over a significantly expanded range of plasma current, toroidal field, and heating power, while increasing flattop durations up to 5 seconds. However, the narrowing of the scrape-off layer at higher current combined with an improved understanding of expected halo-current loads has motivated a significant re-design of NSTX-U plasma facing components in the high-heat-flux regions of the divertor. In order to reduce the expected divertor heat flux to acceptable levels, a combination of mitigation techniques will be used: increased divertor poloidal flux expansion, increased divertor radiation, and controlled strike-point sweeping. The machine requirements for these various mitigation techniques are studied here using a newly implemented reduced heat-flux model. Systematic equilibrium scans are used to quantify the required divertor coil currents and to verify vertical stability for a range of plasma shapes. Free-boundary control schemes to constrain the strike-point location and field-line angle-of-incidence will also be discussed. Work supported by DOE contract DE-AC02- 09CH11466.

A mechanism for large divertor plasma energy loss via lithium radiation in tokamaks

NASA Astrophysics Data System (ADS)

Rognlien, T. D.; Meier, E. T.; Soukhanovskii, V. A.

2012-10-01

Lithium has been used as a wall-conditioning element in a number of tokamaks over the years, including TFTR, FTU, and NSTX, where core plasma energy confinement and particle control are often found to improve following such conditioning. Here the possible role of Li in providing substantial energy loss for divertor plasmas via line radiation is reported. A multi-charge-state 2D UEDGE fluid model is used where the hydrogenic and Li ions and neutrals are each evolved as separate species and separate equations are solved for the electron and ion temperatures. It is shown that a sufficient level of Li neutrals evolving from the divertor surface via sputtering or evaporation can induce energy detachment of the divertor plasma, yielding a strongly radiating zone near the divertor where ionization and recombination from/to neutral Li can radiate most of the power flowing into the scrape-off layer while maintaining low core contamination. A local peaking of Li emissivity for electron temperatures near 1 eV appears to play an important role in the detachment of the mixed deuterium/Li plasma. Evidence of such behavior from NSTX discharges will be discussed.

Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fishman, S., E-mail: fishman@physics.technion.ac.il; Soffer, A., E-mail: soffer@math.rutgers.edu

2016-07-15

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

Ergodic channel capacity of spatial correlated multiple-input multiple-output free space optical links using multipulse pulse-position modulation

NASA Astrophysics Data System (ADS)

Wang, Huiqin; Wang, Xue; Cao, Minghua

2017-02-01

The spatial correlation extensively exists in the multiple-input multiple-output (MIMO) free space optical (FSO) communication systems due to the channel fading and the antenna space limitation. Wilkinson's method was utilized to investigate the impact of spatial correlation on the MIMO FSO communication system employing multipulse pulse-position modulation. Simulation results show that the existence of spatial correlation reduces the ergodic channel capacity, and the reception diversity is more competent to resist this kind of performance degradation.

Exposures of tungsten nanostructures to divertor plasmas in DIII-D

DOE PAGES

Rudakov, D. L.; Wong, C. P. C.; Doerner, R. P.; ...

2016-01-22

Tungsten nanostructures (W-fuzz) prepared in the PISCES-A linear device have been found to survive direct exposure to divertor plasmas in DIII-D. W-fuzz was exposed in the lower divertor of DIII-D using the divertor material evaluation system. Two samples were exposed in lower single null (LSN) deuterium H-mode plasmas. The first sample was exposed in three discharges terminated by vertical displacement event disruptions, and the second in two discharges near the lowered X-point. More recently, three samples were exposed near the lower outer strike point in predominantly helium H-mode LSN plasmas. In all cases, the W-fuzz survived plasma exposure with littlemore » obvious damage except in the areas where unipolar arcing occurred. In conclusion, arcing is effective in W-fuzz removal, and it appears that surfaces covered with W-fuzz can be more prone to arcing than smooth W surfaces.« less

Plasma transport in a simulated magnetic-divertor configuration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strawitch, C. M.

1981-03-01

The transport properties of plasma on magnetic field lines that intersect a conducting plate are studied experimentally in the Wisconsin internal ring D.C. machine. The magnetic geometry is intended to simulate certain aspects of plasma phenomena that may take place in a tokamak divertor. It is found by a variety of measurements that the cross field transport is non-ambipolar; this may have important implications in heat loading considerations in tokamak divertors. The undesirable effects of nonambipolar flow make it preferable to be able to eliminate it. However, we find that though the non-ambipolarity may be reduced, it is difficult tomore » eliminate entirely. The plasma flow velocity parallel to the magnetic field is found to be near the ion acoustic velocity in all cases. The experimental density and electron temperature profiles are compared to the solutions to a one dimensional transport model that is commonly used in divertor theory.« less

Structural investigation of re-deposited layers in JET

NASA Astrophysics Data System (ADS)

Likonen, J.; Vainonen-Ahlgren, E.; Khriachtchev, L.; Coad, J. P.; Rubel, M.; Renvall, T.; Arstila, K.; Hole, D. E.; Contributors to the EFDA-JET Work-programme

2008-07-01

JET Mk-II Gas Box divertor tiles exposed in 1998-2001 have been analysed with various ion beam techniques, secondary ion mass spectrometry (SIMS) and Raman spectroscopy. Inner divertor wall tiles removed in 2001 were covered with a duplex film. The inner layer was very rich in metallic impurities, with Be/C ˜ 1 and H-isotopes only present at low concentrations. The outer layer contained higher concentrations of D than normal for plasma-facing surfaces in JET (D/C ˜ 0.4), and Be/C ˜ 0.14. Raman and SIMS analyses show that the deposited films on inner divertor tiles are hydrogenated amorphous carbon with low sp 3 fractions. The deposits have polymeric structure and low density. Both Raman scattering and SIMS indicate that films on inner divertor wall Tiles 1 and 3, and on floor Tile 4 have some differences in the chemical structure of the deposited films

Density profiles in the Scrape-Off Layer interpreted through filament dynamics

NASA Astrophysics Data System (ADS)

Militello, Fulvio

2017-10-01

We developed a new theoretical framework to clarify the relation between radial Scrape-Off Layer density profiles and the fluctuations that generate them. The framework provides an interpretation of the experimental features of the profiles and of the turbulence statistics on the basis of simple properties of the filaments, such as their radial motion and their draining towards the divertor. L-mode and inter-ELM filaments are described as a Poisson process in which each event is independent and modelled with a wave function of amplitude and width statistically distributed according to experimental observations and evolving according to fluid equations. We will rigorously show that radially accelerating filaments, less efficient parallel exhaust and also a statistical distribution of their radial velocity can contribute to induce flatter profiles in the far SOL and therefore enhance plasma-wall interactions. A quite general result of our analysis is the resiliency of this non-exponential nature of the profiles and the increase of the relative fluctuation amplitude towards the wall, as experimentally observed. According to the framework, profile broadening at high fueling rates can be caused by interactions with neutrals (e.g. charge exchange) in the divertor or by a significant radial acceleration of the filaments. The framework assumptions were tested with 3D numerical simulations of seeded SOL filaments based on a two fluid model. In particular, filaments interact through the electrostatic field they generate only when they are in close proximity (separation comparable to their width in the drift plane), thus justifying our independence hypothesis. In addition, we will discuss how isolated filament motion responds to variations in the plasma conditions, and specifically divertor conditions. Finally, using the theoretical framework we will reproduce and interpret experimental results obtained on JET, MAST and HL-2A.

Initial development of the DIII–D snowflake divertor control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolemen, Egemen; Vail, P. J.; Makowski, M. A.

Simultaneous control of two proximate magnetic field nulls in the divertor region is demonstrated on DIII–D to enable plasma operations in an advanced magnetic configuration known as the snowflake divertor (SFD). The SFD is characterized by a second-order poloidal field null, created by merging two first-order nulls of the standard divertor configuration. The snowflake configuration has many magnetic properties, such as high poloidal flux expansion, large plasma-wetted area, and additional strike points, that are advantageous for divertor heat flux management in future fusion reactors. However, the magnetic configuration of the SFD is highly-sensitive to changes in currents within the plasmamore » and external coils and therefore requires complex magnetic control. The first real-time snowflake detection and control system on DIII–D has been implemented in order to stabilize the configuration. The control algorithm calculates the position of the two nulls in real-time by locally-expanding the Grad–Shafranov equation in the divertor region. A linear relation between variations in the poloidal field coil currents and changes in the null locations is then analytically derived. This formulation allows for simultaneous control of multiple coils to achieve a desired SFD configuration. It is shown that the control enabled various snowflake configurations on DIII–D in scenarios such as the double-null advanced tokamak. In conclusion, the SFD resulted in a 2.5×reduction in the peak heat flux for many energy confinement times (2–3s) without any adverse effects on core plasma performance.« less

Initial development of the DIII–D snowflake divertor control

DOE PAGES

Kolemen, Egemen; Vail, P. J.; Makowski, M. A.; ...

2018-04-11

Simultaneous control of two proximate magnetic field nulls in the divertor region is demonstrated on DIII–D to enable plasma operations in an advanced magnetic configuration known as the snowflake divertor (SFD). The SFD is characterized by a second-order poloidal field null, created by merging two first-order nulls of the standard divertor configuration. The snowflake configuration has many magnetic properties, such as high poloidal flux expansion, large plasma-wetted area, and additional strike points, that are advantageous for divertor heat flux management in future fusion reactors. However, the magnetic configuration of the SFD is highly-sensitive to changes in currents within the plasmamore » and external coils and therefore requires complex magnetic control. The first real-time snowflake detection and control system on DIII–D has been implemented in order to stabilize the configuration. The control algorithm calculates the position of the two nulls in real-time by locally-expanding the Grad–Shafranov equation in the divertor region. A linear relation between variations in the poloidal field coil currents and changes in the null locations is then analytically derived. This formulation allows for simultaneous control of multiple coils to achieve a desired SFD configuration. It is shown that the control enabled various snowflake configurations on DIII–D in scenarios such as the double-null advanced tokamak. In conclusion, the SFD resulted in a 2.5×reduction in the peak heat flux for many energy confinement times (2–3s) without any adverse effects on core plasma performance.« less

The Design and Use of Tungsten Coated TZM Molybdenum Tile Inserts in the DIII-D Tokamak Divertor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murphy, Christopher; Nygren, R. E.; Chrobak, C P.

Future tokamak devices are envisioned to utilize a high-Z metal divertor with tungsten as theleading candidate. However, tokamak experiments with tungsten divertors have seen significantdetrimental effects on plasma performance. The DIII-D tokamak presently has carbon as theplasma facing surface but to study the effect of tungsten on the plasma and its migration aroundthe vessel, two toroidal rows of carbon tiles in the divertor region were modified with high-Zmetal inserts, composed of a molybdenum alloy (TZM) coated with tungsten. A dedicated twoweek experimental campaign was run with the high-Z metal inserts. One row was coated withtungsten containing naturally occurring levels ofmore » isotopes. The second row was coated withtungsten where the isotope 182W was enhanced from the natural level of 26% up to greater than90%. The different isotopic concentrations enabled the experiment to differentiate between thetwo different sources of metal migration from the divertor. Various coating methods wereexplored for the deposition of the tungsten coating, including chemical vapor deposition,electroplating, vacuum plasma spray, and electron beam physical vapor deposition. The coatingswere tested to see if they were robust enough to act as a divertor target for the experiment. Testsincluded cyclic thermal heating using a high power laser and high-fluence deuterium plasmabombardment. The issues associate with the design of the inserts (tile installation, thermal stress,arcing, leading edges, surface preparation, etc.), are reviewed. The results of the tests used toselect the coating method and preliminary experimental observations are presented.« less

Unbiased Sampling of Globular Lattice Proteins in Three Dimensions

NASA Astrophysics Data System (ADS)

Jacobsen, Jesper Lykke

2008-03-01

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 643=262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system.

Physical aspects of biophotons.

PubMed

Popp, F A; Li, K H; Mei, W P; Galle, M; Neurohr, R

1988-07-15

By comparing the theoretically expected results of photon emission from a chaotic (thermal) field and those of an ordered (fully coherent) field with the actual experimental data, one finds ample indications for the hypothesis that 'biophotons' originate from a coherent field occurring within living tissues. A direct proof may be seen in the hyperbolic relaxation dynamics of spectral delayed luminescence under ergodic conditions. A possible mechanism has to be founded on Einstein's balance equation and, under stationary conditions, on energy conservation including a photochemical potential. It is shown that the considered equations deliver, besides the thermal equilibrium, a conditionally stable region far away from equilibrium, which can help to describe both 'biophoton emission' and biological regulation.

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

Three-dimensional modeling of plasma edge transport and divertor fluxes during application of resonant magnetic perturbations on ITER

NASA Astrophysics Data System (ADS)

Schmitz, O.; Becoulet, M.; Cahyna, P.; Evans, T. E.; Feng, Y.; Frerichs, H.; Loarte, A.; Pitts, R. A.; Reiser, D.; Fenstermacher, M. E.; Harting, D.; Kirschner, A.; Kukushkin, A.; Lunt, T.; Saibene, G.; Reiter, D.; Samm, U.; Wiesen, S.

2016-06-01

Results from three-dimensional modeling of plasma edge transport and plasma-wall interactions during application of resonant magnetic perturbation (RMP) fields for control of edge-localized modes in the ITER standard 15 MA Q  =  10 H-mode are presented. The full 3D plasma fluid and kinetic neutral transport code EMC3-EIRENE is used for the modeling. Four characteristic perturbed magnetic topologies are considered and discussed with reference to the axisymmetric case without RMP fields. Two perturbation field amplitudes at full and half of the ITER ELM control coil current capability using the vacuum approximation are compared to a case including a strongly screening plasma response. In addition, a vacuum field case at high q 95  =  4.2 featuring increased magnetic shear has been modeled. Formation of a three-dimensional plasma boundary is seen for all four perturbed magnetic topologies. The resonant field amplitudes and the effective radial magnetic field at the separatrix define the shape and extension of the 3D plasma boundary. Opening of the magnetic field lines from inside the separatrix establishes scrape-off layer-like channels of direct parallel particle and heat flux towards the divertor yielding a reduction of the main plasma thermal and particle confinement. This impact on confinement is most accentuated at full RMP current and is strongly reduced when screened RMP fields are considered, as well as for the reduced coil current cases. The divertor fluxes are redirected into a three-dimensional pattern of helical magnetic footprints on the divertor target tiles. At maximum perturbation strength, these fingers stretch out as far as 60 cm across the divertor targets, yielding heat flux spreading and the reduction of peak heat fluxes by 30%. However, at the same time substantial and highly localized heat fluxes reach divertor areas well outside of the axisymmetric heat flux decay profile. Reduced RMP amplitudes due to screening or reduced RMP coil current yield a reduction of the width of the divertor flux spreading to about 20-25 cm and cause increased peak heat fluxes back to values similar to those in the axisymmetric case. The dependencies of these features on the divertor recycling regime and the perpendicular transport assumptions, as well as toroidal averaged effects mimicking rotation of the RMP field, are discussed in the paper.

On base station cooperation using statistical CSI in jointly correlated MIMO downlink channels

NASA Astrophysics Data System (ADS)

Zhang, Jun; Jiang, Bin; Jin, Shi; Gao, Xiqi; Wong, Kai-Kit

2012-12-01

This article studies the transmission of a single cell-edge user's signal using statistical channel state information at cooperative base stations (BSs) with a general jointly correlated multiple-input multiple-output (MIMO) channel model. We first present an optimal scheme to maximize the ergodic sum capacity with per-BS power constraints, revealing that the transmitted signals of all BSs are mutually independent and the optimum transmit directions for each BS align with the eigenvectors of the BS's own transmit correlation matrix of the channel. Then, we employ matrix permanents to derive a closed-form tight upper bound for the ergodic sum capacity. Based on these results, we develop a low-complexity power allocation solution using convex optimization techniques and a simple iterative water-filling algorithm (IWFA) for power allocation. Finally, we derive a necessary and sufficient condition for which a beamforming approach achieves capacity for all BSs. Simulation results demonstrate that the upper bound of ergodic sum capacity is tight and the proposed cooperative transmission scheme increases the downlink system sum capacity considerably.

Safety characteristics of the monolithic CFC divertor

NASA Astrophysics Data System (ADS)

Zucchetti, M.; Merola, M.; Matera, R.

1994-09-01

The main distinguishing feature of the monolithic CFC divertor is the use of a single material, a carbon fibre reinforced carbon, for the protective armour, the heat sink and the cooling channels. This removes joint interface problems which are one of the most important concerns related to the reference solutions of the ITER CDA divertor. An activation analysis of the different coolant options for this concept is presented. It turns out that neither short-term nor long-term activation are a concern for any coolants investigated. Therefore the proposed concept proves to be attractive from a safety stand-point also.

Numerical Study of High Heat Flux Performances of Flat-Tile Divertor Mock-ups with Hypervapotron Cooling Concept

NASA Astrophysics Data System (ADS)

Chen, Lei; Liu, Xiang; Lian, Youyun; Cai, Laizhong

2015-09-01

The hypervapotron (HV), as an enhanced heat transfer technique, will be used for ITER divertor components in the dome region as well as the enhanced heat flux first wall panels. W-Cu brazing technology has been developed at SWIP (Southwestern Institute of Physics), and one W/CuCrZr/316LN component of 450 mm×52 mm×166 mm with HV cooling channels will be fabricated for high heat flux (HHF) tests. Before that a relevant analysis was carried out to optimize the structure of divertor component elements. ANSYS-CFX was used in CFD analysis and ABAQUS was adopted for thermal-mechanical calculations. Commercial code FE-SAFE was adopted to compute the fatigue life of the component. The tile size, thickness of tungsten tiles and the slit width among tungsten tiles were optimized and its HHF performances under International Thermonuclear Experimental Reactor (ITER) loading conditions were simulated. One brand new tokamak HL-2M with advanced divertor configuration is under construction in SWIP, where ITER-like flat-tile divertor components are adopted. This optimized design is expected to supply valuable data for HL-2M tokamak. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2011GB110001 and 2011GB110004)

Feedback system for divertor impurity seeding based on real-time measurements of surface heat flux in the Alcator C-Mod tokamak

NASA Astrophysics Data System (ADS)

Brunner, D.; Burke, W.; Kuang, A. Q.; LaBombard, B.; Lipschultz, B.; Wolfe, S.

2016-02-01

Mitigation of the intense heat flux to the divertor is one of the outstanding problems in fusion energy. One technique that has shown promise is impurity seeding, i.e., the injection of low-Z gaseous impurities (typically N2 or Ne) to radiate and dissipate the power before it arrives to the divertor target plate. To this end, the Alcator C-Mod team has created a first-of-its-kind feedback system to control the injection of seed gas based on real-time surface heat flux measurements. Surface thermocouples provide real-time measurements of the surface temperature response to the plasma heat flux. The surface temperature measurements are inputted into an analog computer that "solves" the 1-D heat transport equation to deliver accurate, real-time signals of the surface heat flux. The surface heat flux signals are sent to the C-Mod digital plasma control system, which uses a proportional-integral-derivative (PID) algorithm to control the duty cycle demand to a pulse width modulated piezo valve, which in turn controls the injection of gas into the private flux region of the C-Mod divertor. This paper presents the design and implementation of this new feedback system as well as initial results using it to control divertor heat flux.

Feedback system for divertor impurity seeding based on real-time measurements of surface heat flux in the Alcator C-Mod tokamak.

PubMed

Brunner, D; Burke, W; Kuang, A Q; LaBombard, B; Lipschultz, B; Wolfe, S

2016-02-01

Mitigation of the intense heat flux to the divertor is one of the outstanding problems in fusion energy. One technique that has shown promise is impurity seeding, i.e., the injection of low-Z gaseous impurities (typically N2 or Ne) to radiate and dissipate the power before it arrives to the divertor target plate. To this end, the Alcator C-Mod team has created a first-of-its-kind feedback system to control the injection of seed gas based on real-time surface heat flux measurements. Surface thermocouples provide real-time measurements of the surface temperature response to the plasma heat flux. The surface temperature measurements are inputted into an analog computer that "solves" the 1-D heat transport equation to deliver accurate, real-time signals of the surface heat flux. The surface heat flux signals are sent to the C-Mod digital plasma control system, which uses a proportional-integral-derivative (PID) algorithm to control the duty cycle demand to a pulse width modulated piezo valve, which in turn controls the injection of gas into the private flux region of the C-Mod divertor. This paper presents the design and implementation of this new feedback system as well as initial results using it to control divertor heat flux.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

Damage of target edges in brush-like geometry in the course of ELM-like plasma pulses in QSPA Kh-50

NASA Astrophysics Data System (ADS)

Makhlaj, V. A.; Garkusha, I. E.; Aksenov, N. N.; Bazylev, B.; Byrka, O. V.; Chebotarev, V. V.; Landman, I.; Herashchenko, S. S.; Staltsov, V. V.

2015-08-01

Castellated edges of macro-brush armour elements of ITER divertor can be a source of molten/solid dust particles which are injected into the plasma. The targets that combined in brush-like geometry have been irradiated under different inclination angles in QSPA Kh-50. The cubic brushes element has typical size of 1 cm. The titanium was used to investigate dynamics of mountains' formation. The onset of dust particles ejection from the exposed castellated targets has been studied. Formation of resolidified bridges through the gaps of brush-like targets due to the melt motion is studied in dynamics. With following plasma impacts such resolidified bridges became additional source of dust.

NSTX Disruption Simulations of Detailed Divertor and Passive Plate Models by Vector Potential Transfer from OPERA Global Analysis Results

DOE Office of Scientific and Technical Information (OSTI.GOV)

P. H. Titus, S. Avasaralla, A.Brooks, R. Hatcher

2010-09-22

The National Spherical Torus Experiment (NSTX) project is planning upgrades to the toroidal field, plasma current and pulse length. This involves the replacement of the center-stack, including the inner legs of the TF, OH, and inner PF coils. A second neutral beam will also be added. The increased performance of the upgrade requires qualification of the remaining components including the vessel, passive plates, and divertor for higher disruption loads. The hardware needing qualification is more complex than is typically accessible by large scale electromagnetic (EM) simulations of the plasma disruptions. The usual method is to include simplified representations of componentsmore » in the large EM models and attempt to extract forces to apply to more detailed models. This paper describes a more efficient approach of combining comprehensive modeling of the plasma and tokamak conducting structures, using the 2D OPERA code, with much more detailed treatment of individual components using ANSYS electromagnetic (EM) and mechanical analysis. This capture local eddy currents and resulting loads in complex details, and allows efficient non-linear, and dynamic structural analyses.« less

Advanced simulation of mixed-material erosion/evolution and application to low and high-Z containing plasma facing components

NASA Astrophysics Data System (ADS)

Brooks, J. N.; Hassanein, A.; Sizyuk, T.

2013-07-01

Plasma interactions with mixed-material surfaces are being analyzed using advanced modeling of time-dependent surface evolution/erosion. Simulations use the REDEP/WBC erosion/redeposition code package coupled to the HEIGHTS package ITMC-DYN mixed-material formation/response code, with plasma parameter input from codes and data. We report here on analysis for a DIII-D Mo/C containing tokamak divertor. A DIII-D/DiMES probe experiment simulation predicts that sputtered molybdenum from a 1 cm diameter central spot quickly saturates (˜4 s) in the 5 cm diameter surrounding carbon probe surface, with subsequent re-sputtering and transport to off-probe divertor regions, and with high (˜50%) redeposition on the Mo spot. Predicted Mo content in the carbon agrees well with post-exposure probe data. We discuss implications and mixed-material analysis issues for Be/W mixing at the ITER outer divertor, and Li, C, Mo mixing at an NSTX divertor.

Constrained ripple optimization of Tokamak bundle divertors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hively, L.M.; Rome, J.A.; Lynch, V.E.

1983-02-01

Magnetic field ripple from a tokamak bundle divertor is localized to a small toroidal sector and must be treated differently from the usual (distributed) toroidal field (TF) coil ripple. Generally, in a tokamak with an unoptimized divertor design, all of the banana-trapped fast ions are quickly lost due to banana drift diffusion or to trapping between the 1/R variation in absolute value vector B ..xi.. B and local field maxima due to the divertor. A computer code has been written to optimize automatically on-axis ripple subject to these constraints, while varying up to nine design parameters. Optimum configurations have lowmore » on-axis ripple (<0.2%) so that, now, most banana-trapped fast ions are confined. Only those ions with banana tips near the outside region (absolute value theta < or equal to 45/sup 0/) are lost. However, because finite-sized TF coils have not been used in this study, the flux bundle is not expanded.« less

Initial results from divertor heat-flux instrumentation on Alcator C-Mod

NASA Astrophysics Data System (ADS)

Labombard, B.; Brunner, D.; Payne, J.; Reinke, M.; Terry, J. L.; Hughes, J. W.; Lipschultz, B.; Whyte, D.

2009-11-01

Physics-based plasma transport models that can accurately simulate the heat-flux power widths observed in the tokamak boundary are lacking at the present time. Yet this quantity is of fundamental importance for ITER and most critically important for DEMO, a reactor similar to ITER but with ˜4 times the power exhaust. In order to improve our understanding, C-Mod, DIII-D and NSTX will aim experiments in FY10 towards characterizing the divertor ``footprint'' and its connection to conditions ``upstream'' in the boundary and core plasmas [2]. Standard IR-based heat-flux measurements are particularly difficult in C-Mod, due to its vertical-oriented divertor targets. To overcome this, a suite of embedded heat-flux sensor probes (tile thermocouples, calorimeters, surface thermocouples) combined with IR thermography was installed during the FY09 opening, along with a new divertor bolometer system. This paper will report on initial experiments aimed at unfolding the heat-flux dependencies on plasma operating conditions. [2] a proposed US DoE Joint Facilities Milestone.

HSX as an example of a resilient non-resonant divertor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bader, A.; Boozer, A. H.; Hegna, C. C.

This study describes an initial description of the resilient divertor properties of quasi-symmetric (QS) stellarators using the HSX (Helically Symmetric eXperiment) configuration as a test-case. Divertors in high-performance QS stellarators will need to be resilient to changes in plasma configuration that arise due to evolution of plasma pressure profiles and bootstrap currents for divertor design. Resiliency is tested by examining the changes in strike point patterns from the field line following, which arise due to configurational changes. A low strike point variation with high configuration changes corresponds to high resiliency. The HSX edge displays resilient properties with configuration changes arisingmore » from the (1) wall position, (2) plasma current, and (3) external coils. The resilient behavior is lost if large edge islands intersect the wall structure. The resilient edge properties are corroborated by heat flux calculations from the fully 3-D plasma simulations using EMC3-EIRENE. Additionally, the strike point patterns are found to correspond to high curvature regions of magnetic flux surfaces.« less

Definition of acceptance criteria for the ITER divertor plasma-facing components through systematic experimental analysis

NASA Astrophysics Data System (ADS)

Escourbiac, F.; Richou, M.; Guigon, R.; Constans, S.; Durocher, A.; Merola, M.; Schlosser, J.; Riccardi, B.; Grosman, A.

2009-12-01

Experience has shown that a critical part of the high-heat flux (HHF) plasma-facing component (PFC) is the armour to heat sink bond. An experimental study was performed in order to define acceptance criteria with regards to thermal hydraulics and fatigue performance of the International Thermonuclear Experimental Reactor (ITER) divertor PFCs. This study, which includes the manufacturing of samples with calibrated artificial defects relevant to the divertor design, is reported in this paper. In particular, it was concluded that defects detectable with non-destructive examination (NDE) techniques appeared to be acceptable during HHF experiments relevant to heat fluxes expected in the ITER divertor. On the basis of these results, a set of acceptance criteria was proposed and applied to the European vertical target medium-size qualification prototype: 98% of the inspected carbon fibre composite (CFC) monoblocks and 100% of tungsten (W) monoblock and flat tiles elements (i.e. 80% of the full units) were declared acceptable.

Experiences with tungsten coatings in high heat flux tests and under plasma load in ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Herrmann, A.; Greuner, H.; Fuchs, J. C.; de Marné, P.; Neu, R.; ASDEX Upgrade Team

2009-12-01

ASDEX Upgrade was operated with about 6400 s plasma discharge during the scientific program in 2007/2008 exploring tungsten as a first wall material in tokamaks. In the first phase, the heating power was restricted to 10 MW. It was increased to 15 MW in the second phase. During this operational period, a delamination of the 200 μm W-VPS coating happened at 2 out of 128 tiles of the outer divertor and an unscheduled opening was required. In the third phase, ASDEX Upgrade was operated with partly predamaged tiles and up to 15 MW heating power. The target load was actively controlled by N2-seeding. This paper presents the screening test of target tiles in the high heat flux test facility GLADIS, experiences with operation and detected damages of the outer divertor as well as the heat load to the outer divertor and the reasons for the toroidal asymmetry of the divertor load.

Design of snowflake-diverted equilibria of CFETR

NASA Astrophysics Data System (ADS)

Hang, LI; Xiang, GAO; Guoqiang, LI; Zhengping, LUO; Damao, YAO; Yong, GUO

2018-03-01

The Chinese Fusion Engineering Test Reactor (CFETR) represents the next generation of full superconducting fusion reactors in China. Recently, CFETR was redesigned with a larger size and will be operated in two phases. To reduce the heat flux on the target plate, a snowflake (SF) divertor configuration is proposed. In this paper we show that by adding two dedicated poloidal field (PF) coils, the SF configuration can be achieved in both phases. The equilibria were calculated by TEQ code for a range of self-inductances l i3. The coil currents were calculated at some fiducial points in the flattop phase. The results indicate that the PF coil system has the ability to maintain a long flattop phase in 7.5 and 10 MA inductive scenarios for the single null divertor (SND) and SF divertor configurations. The properties of the SF configuration were also analyzed. The connection length and flux expansion of the SF divertor were both increased significantly over the SND.

HSX as an example of a resilient non-resonant divertor

DOE PAGES

Bader, A.; Boozer, A. H.; Hegna, C. C.; ...

2017-03-16

This study describes an initial description of the resilient divertor properties of quasi-symmetric (QS) stellarators using the HSX (Helically Symmetric eXperiment) configuration as a test-case. Divertors in high-performance QS stellarators will need to be resilient to changes in plasma configuration that arise due to evolution of plasma pressure profiles and bootstrap currents for divertor design. Resiliency is tested by examining the changes in strike point patterns from the field line following, which arise due to configurational changes. A low strike point variation with high configuration changes corresponds to high resiliency. The HSX edge displays resilient properties with configuration changes arisingmore » from the (1) wall position, (2) plasma current, and (3) external coils. The resilient behavior is lost if large edge islands intersect the wall structure. The resilient edge properties are corroborated by heat flux calculations from the fully 3-D plasma simulations using EMC3-EIRENE. Additionally, the strike point patterns are found to correspond to high curvature regions of magnetic flux surfaces.« less

Divertor extreme ultraviolet (EUV) survey spectroscopy in DIII-D

NASA Astrophysics Data System (ADS)

McLean, Adam; Allen, Steve; Ellis, Ron; Jarvinen, Aaro; Soukhanovskii, Vlad; Boivin, Rejean; Gonzales, Eduardo; Holmes, Ian; Kulchar, James; Leonard, Anthony; Williams, Bob; Taussig, Doug; Thomas, Dan; Marcy, Grant

2017-10-01

An extreme ultraviolet spectrograph measuring resonant emissions of D and C in the lower divertor has been added to DIII-D to help resolve an 2X discrepancy between bolometrically measured radiated power and that predicted by boundary codes for DIII-D, JET and ASDEX-U. With 290 and 450 gr/mm gratings, the DivSPRED spectrometer, an 0.3 m flat-field McPherson model 251, measures ground state transitions for D (the Lyman series) and C (e.g., C IV, 155 nm) which account for >75% of radiated power in the divertor. Combined with Thomson scattering and imaging in the DIII-D divertor, measurements of position, temperature and fractional power emission from plasma components are made and compared to UEDGE/SOLPS-ITER. Mechanical, optical, electrical, vacuum, and shielding aspects of DivSPRED are presented. Work supported under USDOE Cooperative Agreement DE-FC02-04ER54698 and DE-AC52-07NA27344, and by the LLNL Laboratory Directed R&D Program, project #17-ERD-020.

Hierarchical layered and semantic-based image segmentation using ergodicity map

NASA Astrophysics Data System (ADS)

Yadegar, Jacob; Liu, Xiaoqing

2010-04-01

Image segmentation plays a foundational role in image understanding and computer vision. Although great strides have been made and progress achieved on automatic/semi-automatic image segmentation algorithms, designing a generic, robust, and efficient image segmentation algorithm is still challenging. Human vision is still far superior compared to computer vision, especially in interpreting semantic meanings/objects in images. We present a hierarchical/layered semantic image segmentation algorithm that can automatically and efficiently segment images into hierarchical layered/multi-scaled semantic regions/objects with contextual topological relationships. The proposed algorithm bridges the gap between high-level semantics and low-level visual features/cues (such as color, intensity, edge, etc.) through utilizing a layered/hierarchical ergodicity map, where ergodicity is computed based on a space filling fractal concept and used as a region dissimilarity measurement. The algorithm applies a highly scalable, efficient, and adaptive Peano- Cesaro triangulation/tiling technique to decompose the given image into a set of similar/homogenous regions based on low-level visual cues in a top-down manner. The layered/hierarchical ergodicity map is built through a bottom-up region dissimilarity analysis. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level of detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanisms for contextual topological object/region relationship generation. Experiments have been conducted within the maritime image environment where the segmented layered semantic objects include the basic level objects (i.e. sky/land/water) and deeper level objects in the sky/land/water surfaces. Experimental results demonstrate the proposed algorithm has the capability to robustly and efficiently segment images into layered semantic objects/regions with contextual topological relationships.

Design of an advanced bundle divertor for the Demonstration Tokamak Hybrid Reactor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, T.F.; Lee, A.Y.; Ruck, G.W.

1979-01-25

The conclusion of this work is that a bundle divertor, using an improved method of designing the magnetic field configuration, is feasible for the Demonstration Tokamak Hybrid Reactor (DTHR) investigated by Westinghouse. The most significant achievement of this design is the reduction in current density (1 kA/cm/sup 2/) in the divertor coils in comparison to the overall averaged current densities per tesla of field to be nulled for DITE (25 kA/cm/sup 2/) and for ISX-B/sup 2/ (11 kA/cm/sup 2/). Therefore, superconducting magnets can be built into the tight space available with a sound mechanical structure.

Anosov C-systems and random number generators

NASA Astrophysics Data System (ADS)

Savvidy, G. K.

2016-08-01

We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.

Extended applications of track irregularity probabilistic model and vehicle-slab track coupled model on dynamics of railway systems

NASA Astrophysics Data System (ADS)

Xu, Lei; Zhai, Wanming; Gao, Jianmin

2017-11-01

Track irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel-rail interactions. For depicting the dynamic behaviours of vehicle-track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle-track coupled model by properly considering the wheel-rail nonlinear contact mechanisms. In the present study, the vehicle-track coupled model is programmed by combining finite element method with wheel-rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.

Ergodic properties of spiking neuronal networks with delayed interactions

NASA Astrophysics Data System (ADS)

Palmigiano, Agostina; Wolf, Fred

The dynamical stability of neuronal networks, and the possibility of chaotic dynamics in the brain pose profound questions to the mechanisms underlying perception. Here we advance on the tractability of large neuronal networks of exactly solvable neuronal models with delayed pulse-coupled interactions. Pulse coupled delayed systems with an infinite dimensional phase space can be studied in equivalent systems of fixed and finite degrees of freedom by introducing a delayer variable for each neuron. A Jacobian of the equivalent system can be analytically obtained, and numerically evaluated. We find that depending on the action potential onset rapidness and the level of heterogeneities, the asynchronous irregular regime characteristic of balanced state networks loses stability with increasing delays to either a slow synchronous irregular or a fast synchronous irregular state. In networks of neurons with slow action potential onset, the transition to collective oscillations leads to an increase of the exponential rate of divergence of nearby trajectories and of the entropy production rate of the chaotic dynamics. The attractor dimension, instead of increasing linearly with increasing delay as reported in many other studies, decreases until eventually the network reaches full synchrony

Dimensionality and entropy of spontaneous and evoked rate activity

NASA Astrophysics Data System (ADS)

Engelken, Rainer; Wolf, Fred

Cortical circuits exhibit complex activity patterns both spontaneously and evoked by external stimuli. Finding low-dimensional structure in population activity is a challenge. What is the diversity of the collective neural activity and how is it affected by an external stimulus? Using concepts from ergodic theory, we calculate the attractor dimensionality and dynamical entropy production of these networks. We obtain these two canonical measures of the collective network dynamics from the full set of Lyapunov exponents. We consider a randomly-wired firing-rate network that exhibits chaotic rate fluctuations for sufficiently strong synaptic weights. We show that dynamical entropy scales logarithmically with synaptic coupling strength, while the attractor dimensionality saturates. Thus, despite the increasing uncertainty, the diversity of collective activity saturates for strong coupling. We find that a time-varying external stimulus drastically reduces both entropy and dimensionality. Finally, we analytically approximate the full Lyapunov spectrum in several limiting cases by random matrix theory. Our study opens a novel avenue to characterize the complex dynamics of rate networks and the geometric structure of the corresponding high-dimensional chaotic attractor. received funding from Evangelisches Studienwerk Villigst, DFG through CRC 889 and Volkswagen Foundation.

OEDGE Modeling of Collector Probe measurements in L-mode from the DIII-D tungsten ring campaign

NASA Astrophysics Data System (ADS)

Elder, J. D.; Stangeby, P. C.; Unterberg, Z.; Donovan, D.; Wampler, W. R.; Watkins, J.; Abrams, T.; McLean, A. G.

2017-10-01

During the tungsten ring campaign on DIII-D, a collector probe system with multiple diameter, dual-facing collector rods was inserted into the far scrape off layer (SOL) near the outer midplane to measure the plasma tungsten content. For most probes more tungsten was observed on the side connected along field lines to the inner divertor, with the larger probes showing largest divertor-facing asymmetries The OEDGE code is used to model the tungsten erosion, transport and deposition. It has been enhanced with (i) a peripheral particle transport and deposition model to record the impurity content in the peripheral region outside the regular mesh, and (ii) a collector probe model. The OEDGE results approximately reproduce both the divertor-facing asymmetries and the radial decay of each collector probe profile. The effect of changing impurity transport assumptions and wall location are examined. The measured divertor-facing asymmetries imply a higher tungsten density in the plasma upstream of the probe; this was expected theoretically from the effect of the parallel ion temperature gradient force driving upstream transport of tungsten from the outer divertor and was also found in the code analysis. Work supported by the US Department of Energy under DE-FC02-04ER54698, DE-NA0003525, DE-AC05-00OR22725, and DE-AC52-07NA27344.

Characterization of chemical sputtering using the Mark II DiMES porous plug injector in attached and semi-detached divertor plasmas of DIII-D

NASA Astrophysics Data System (ADS)

McLean, A. G.; Davis, J. W.; Stangeby, P. C.; Allen, S. L.; Boedo, J. A.; Bray, B. D.; Brezinsek, S.; Brooks, N. H.; Fenstermacher, M. E.; Groth, M.; Haasz, A. A.; Hollmann, E. M.; Isler, R. C.; Lasnier, C. J.; Mu, Y.; Petrie, T. W.; Rudakov, D. L.; Watkins, J. G.; West, W. P.; Whyte, D. G.; Wong, C. P. C.

2009-06-01

An improved, self-contained gas injection system for the divertor material evaluation system (DiMES) on DIII-D has been employed for in situ study of chemical erosion in the tokamak divertor environment. To minimize perturbation to local plasma, the Mark II porous plug injector (PPI) releases methane through a porous graphite surface at the outer strike point at a rate precisely controlled by a micro-orifice flow restrictor to be approximately equal as that predicted for intrinsic chemical sputtering. Effective photon efficiencies resulting from CH 4 are found to be 58 ± 12 in an attached divertor ( ne ˜ 1.5 × 10 13/cm 3, Te ˜ 25 eV, Tsurf ˜ 450 K), and 94 ± 20 in a semi-detached cold divertor ( ne ˜ 6.0 × 10 13/cm 3, Te ˜ 2-3 eV, Tsurf ˜ 350 K). These values are significantly more than previous measurements in similar plasma conditions, indicating the importance of the injection rate and local re-erosion for the integrity of this analysis. The contribution of chemical versus physical sputtering to the source of C + at the target is assessed through simultaneous measurement of CII line, and CD plus CH-band emissions during release of CH 4 from the PPI, then compared with that seen in intrinsic sputtering.

Characterizing Tungsten Sourcing and SOL Transport during the Metal Rings Campaign

NASA Astrophysics Data System (ADS)

Thomas, D. M.; Abrams, T.; Unterberg, E. A.; Donovan, D.; Elder, J. D.; Wampler, W. R.; DIII-D Team

2017-10-01

The Metal Rings Campaign on DIII-D utilized two isotopically and poloidally distinct toroidal arrays of tungsten coated inserts in the lower divertor to study W divertor erosion near the outer strike point (OSP) and divertor entrance and subsequent migration in a mixed-material (C-W) environment. In AT hybrid discharges (PAUX = 14 MW, H98 = 1.6, βN = 3.7) with rapid ELMs (fELM 200 Hz, δW/W 0.7%) W impurities are seen to reach the midplane predominantly from the OSP region rather than the divertor entrance (far-SOL). Conversely, in scenarios with less frequent larger ELMs (fELM 60 Hz, δW/W 3.6%), the W impurities are found to transport equally from the OSP and entrance region. ELM-resolved spectroscopic measurements of W sourcing indicate that large ELMs can source W at many times the inter ELM rate. The peak W erosion rate can shift radially outwards consistent with the ELM energy flux, thereby shifting the balance between strikepoint and far-SOL sources. Changes in the peak erosion locations between forward and reversed Bt discharges are consistent with ExB ion drift effects. Evidence for a near-SOL impurity buildup between the divertors driven by the parallel grad-Ti force is also seen. Work supported under USDOE Cooperative Agreement DE-FC02-04ER54698.

Controlling marginally detached divertor plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eldon, David; Kolemen, Egemen; Barton, Joseph L.

A new control system at DIII-D has stabilized the inter-ELM detached divertor plasma state for H-mode in close proximity to the threshold for reattachment, thus demonstrating the ability to maintain detachment with minimal gas puffing. When the same control system was instead ordered to hold the plasma at the threshold (here defined as T e = 5 eV near the divertor target plate), the resulting T e profiles separated into two groups with one group consistent with marginal detachment, and the other with marginal attachment. The plasma dithers between the attached and detached states when the control system attempts to hold at the threshold. The control system is upgraded from the one described in and it handles ELMing plasmas by using real time D α measurements to remove during-ELM slices from real time T e measurements derived from divertor Thomson scattering. The difference between measured and requested inter-ELM T e is passed to a PID (proportionalintegral-derivative) controller to determine gas puff commands. While some degree of detachment is essential for the health of ITER’s divertor, more deeply detached plasmas have greater radiative losses and, at the extreme, confinement degradation, making it desirable to limit detachment to the minimum level needed to protect the target plate. However, the observed bifurcation in plasma conditions at the outer strike point with the ion B ×more » $$\

Progress in extrapolating divertor heat fluxes towards large fusion devices

NASA Astrophysics Data System (ADS)

Sieglin, B.; Faitsch, M.; Eich, T.; Herrmann, A.; Suttrop, W.; Collaborators, JET; the MST1 Team; the ASDEX Upgrade Team

2017-12-01

Heat load to the plasma facing components is one of the major challenges for the development and design of large fusion devices such as ITER. Nowadays fusion experiments can operate with heat load mitigation techniques, e.g. sweeping, impurity seeding, but do not generally require it. For large fusion devices however, heat load mitigation will be essential. This paper presents the current progress of the extrapolation of steady state and transient heat loads towards large fusion devices. For transient heat loads, so-called edge localized modes are considered a serious issue for the lifetime of divertor components. In this paper, the ITER operation at half field (2.65 T) and half current (7.5 MA) will be discussed considering the current material limit for the divertor peak energy fluence of 0.5 {MJ}/{{{m}}}2. Recent studies were successful in describing the observed energy fluence in the JET, MAST and ASDEX Upgrade using the pedestal pressure prior to the ELM crash. Extrapolating this towards ITER results in a more benign heat load compared to previous scalings. In the presence of magnetic perturbation, the axisymmetry is broken and a 2D heat flux pattern is induced on the divertor target, leading to local increase of the heat flux which is a concern for ITER. It is shown that for a moderate divertor broadening S/{λ }{{q}}> 0.5 the toroidal peaking of the heat flux disappears.

The contribution of radio-frequency rectification to field-aligned losses of high-harmonic fast wave power to the divertor in the National Spherical Torus eXperiment

DOE PAGES

Perkins, R. J.; Hosea, J. C.; Jaworski, M. A.; ...

2015-04-13

The National Spherical Torus eXperiment (NSTX) can exhibit a major loss of high-harmonic fast wave (HHFW) power along scrape-off layer (SOL) field lines passing in front of the antenna, resulting in bright and hot spirals on both the upper and lower divertor regions. One possible mechanism for this loss is RF sheaths forming at the divertors. We demonstrate that swept-voltage Langmuir probe characteristics for probes under the spiral are shifted relative to those not under the spiral in a manner consistent with RF rectification. We estimate both the magnitude of the RF voltage across the sheath and the sheath heatmore » flux transmission coefficient in the presence of the RF field. Though the precise comparison between computed heat flux and infrared (IR) thermography cannot yet be made, the computed heat deposition compares favorably with the projections from IR camera measurements. The RF sheath losses are significant and contribute substantially to the total SOL losses of HHFW power to the divertor for the cases studied. Our work will guide future experimentation on NSTX-U, where a wide-angle IR camera and a dedicated set of coaxial Langmuir probes for measuring the RF sheath voltage directly will quantify the contribution of RF sheath rectification to the heat deposition from the SOL to the divertor.« less

Numerical analyses of baseline JT-60SA design concepts with the COREDIV code

NASA Astrophysics Data System (ADS)

Zagórski, R.; Gałązka, K.; Ivanova-Stanik, I.; Stępniewski, W.; Garzotti, L.; Giruzzi, G.; Neu, R.; Romanelli, M.

2017-06-01

JT-60SA reference design scenarios at high (#3) and low (#2) density have been analyzed with the help of the self-consistent COREDIV code. Simulations results for a standard C wall and full W wall have been compared in terms of the influence of impurities, both intrinsic (C, W) and seeded (N, Ar, Ne, Kr), on the radiation losses and plasma parameters. For scenario #3 in a C environment, the regime of detachment on divertor plates can be achieved with N or Ne seeding, whereas for the low density and high power scenario (#2), the C and seeding impurity radiation does not effectively reduce power to the targets. In this case, only an increase of either average density or edge density together with Kr seeding might help to develop conditions with strong radiation losses and semi-detached conditions in the divertor. The calculations show that, in the case of a W divertor, the power load to the plate is mitigated by seeding and the central plasma dilution is smaller compared to the C divertor. For the high density case (#3) with Ne seeding, operation in full detachment mode is predicted. Ar seems to be an optimal choice for the low-density high-power scenario #2, showing a wide operating window, whereas Ne leads to high plasma dilution at high seeding levels albeit not achieving semi-detached conditions in the divertor.

Quiescence near the X-point of MAST measured by high speed visible imaging

NASA Astrophysics Data System (ADS)

Walkden, N. R.; Harrison, J.; Silburn, S. A.; Farley, T.; Henderson, S. S.; Kirk, A.; Militello, F.; Thornton, A.; The MAST Team

2017-12-01

Using high speed imaging of the divertor volume, the region close to the X-point in MAST is shown to be quiescent. This is confirmed by three different analysis techniques and the quiescent X-point region (QXR) spans from the separatrix to the \\psiN = 1.02 flux surface. Local reductions to the atomic density and effects associated with the camera viewing geometry are ruled out as causes of the QXR, leaving quiescence in the local plasma conditions as being the most likely cause. The QXR is found to be ubiquitous across a significant operational space in MAST including L-mode and H-mode discharges across maximal ranges of 9.8×1019~m-2 in line integrated density, 0.36 MA in plasma current, 0.11 T in toroidal magnetic field and 3.2 MW in NBI power. When mapped to the divertor target the QXR occupies approximately an e-folding length of the heat-flux profile, containing  ∼60% of the total heat flux to the target, and also shows a tendency towards higher frequency shorter lived fluctuations in the ion-saturation current. This is consistent with short-lived divertor localised filamentary structures observed further down the outer divertor leg in the camera images, and suggests a complex multi-region picture of filamentary transport in the divertor.

Controlling marginally detached divertor plasmas

DOE PAGES

Eldon, David; Kolemen, Egemen; Barton, Joseph L.; ...

2017-05-04

A new control system at DIII-D has stabilized the inter-ELM detached divertor plasma state for H-mode in close proximity to the threshold for reattachment, thus demonstrating the ability to maintain detachment with minimal gas puffing. When the same control system was instead ordered to hold the plasma at the threshold (here defined as T e = 5 eV near the divertor target plate), the resulting T e profiles separated into two groups with one group consistent with marginal detachment, and the other with marginal attachment. The plasma dithers between the attached and detached states when the control system attempts to hold at the threshold. The control system is upgraded from the one described in and it handles ELMing plasmas by using real time D α measurements to remove during-ELM slices from real time T e measurements derived from divertor Thomson scattering. The difference between measured and requested inter-ELM T e is passed to a PID (proportionalintegral-derivative) controller to determine gas puff commands. While some degree of detachment is essential for the health of ITER’s divertor, more deeply detached plasmas have greater radiative losses and, at the extreme, confinement degradation, making it desirable to limit detachment to the minimum level needed to protect the target plate. However, the observed bifurcation in plasma conditions at the outer strike point with the ion B ×more » $$\

Parametric analyses of DEMO Divertor using two dimensional transient thermal hydraulic modelling

NASA Astrophysics Data System (ADS)

Domalapally, Phani; Di Caro, Marco

2018-05-01

Among the options considered for cooling of the Plasma facing components of the DEMO reactor, water cooling is a conservative option because of its high heat removal capability. In this work a two-dimensional transient thermal hydraulic code is developed to support the design of the divertor for the projected DEMO reactor with water as a coolant. The mathematical model accounts for transient 2D heat conduction in the divertor section. Temperature-dependent properties are used for more accurate analysis. Correlations for single phase flow forced convection, partially developed subcooled nucleate boiling, fully developed subcooled nucleate boiling and film boiling are used to calculate the heat transfer coefficients on the channel side considering the swirl flow, wherein different correlations found in the literature are compared against each other. Correlation for the Critical Heat Flux is used to estimate its limit for a given flow conditions. This paper then investigates the results of the parametric analysis performed, whereby flow velocity, diameter of the coolant channel, thickness of the coolant pipe, thickness of the armor material, inlet temperature and operating pressure affect the behavior of the divertor under steady or transient heat fluxes. This code will help in understanding the basic parameterś effect on the behavior of the divertor, to achieve a better design from a thermal hydraulic point of view.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Microscopic pressure-cooker model for studying molecules in confinement

NASA Astrophysics Data System (ADS)

Santamaria, Ruben; Adamowicz, Ludwik; Rosas-Acevedo, Hortensia

2015-04-01

A model for a system of a finite number of molecules in confinement is presented and expressions for determining the temperature, pressure, and volume of the system are derived. The present model is a generalisation of the Zwanzig-Langevin model because it includes pressure effects in the system. It also has general validity, preserves the ergodic hypothesis, and provides a formal framework for previous studies of hydrogen clusters in confinement. The application of the model is illustrated by an investigation of a set of prebiotic compounds exposed to varying pressure and temperature. The simulations performed within the model involve the use of a combination of molecular dynamics and density functional theory methods implemented on a computer system with a mixed CPU-GPU architecture.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Quantitative quasiperiodicity

NASA Astrophysics Data System (ADS)

Das, Suddhasattwa; Saiki, Yoshitaka; Sander, Evelyn; Yorke, James A.

2017-11-01

The Birkhoff ergodic theorem concludes that time averages, i.e. Birkhoff averages, B_N( f):=Σn=0N-1 f(x_n)/N of a function f along a length N ergodic trajectory (x_n) of a function T converge to the space average \\int f dμ , where μ is the unique invariant probability measure. Convergence of the time average to the space average is slow. We use a modified average of f(x_n) by giving very small weights to the ‘end’ terms when n is near 0 or N-1 . When (x_n) is a trajectory on a quasiperiodic torus and f and T are C^∞ , our weighted Birkhoff average (denoted \

A proof of the log-concavity conjecture related to the computation of the ergodic capacity of MIMO channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurvitis, Leonid

2009-01-01

An upper bound on the ergodic capacity of MIMO channels was introduced recently in [1]. This upper bound amounts to the maximization on the simplex of some multilinear polynomial p({lambda}{sub 1}, ..., {lambda}{sub n}) with non-negative coefficients. In general, such maximizations problems are NP-HARD. But if say, the functional log(p) is concave on the simplex and can be efficiently evaluated, then the maximization can also be done efficiently. Such log-concavity was conjectured in [1]. We give in this paper self-contained proof of the conjecture, based on the theory of H-Stable polynomials.

Decryption of pure-position permutation algorithms.

PubMed

Zhao, Xiao-Yu; Chen, Gang; Zhang, Dan; Wang, Xiao-Hong; Dong, Guang-Chang

2004-07-01

Pure position permutation image encryption algorithms, commonly used as image encryption investigated in this work are unfortunately frail under known-text attack. In view of the weakness of pure position permutation algorithm, we put forward an effective decryption algorithm for all pure-position permutation algorithms. First, a summary of the pure position permutation image encryption algorithms is given by introducing the concept of ergodic matrices. Then, by using probability theory and algebraic principles, the decryption probability of pure-position permutation algorithms is verified theoretically; and then, by defining the operation system of fuzzy ergodic matrices, we improve a specific decryption algorithm. Finally, some simulation results are shown.

Electric Field-Induced Large Strain in Ni/Sb-co Doped (Bi0.5Na0.5) TiO3-Based Lead-Free Ceramics

NASA Astrophysics Data System (ADS)

Li, Liangliang; Hao, Jigong; Xu, Zhijun; Li, Wei; Chu, Ruiqing

2018-02-01

Lead-free piezoelectric ceramics (Bi0.5Na0.5)0.935Ba0.065Ti1- x (Ni0.5Sb0.5) x O3 (BNBT6.5- xNS) have been fabricated using conventional solid sintering technique. The effect of (Ni, Sb) doping on the phase structure and electrical properties of BNBT6.5 ceramics were systematically investigated. Results show that the addition of (Ni, Sb) destroyed the ferroelectric long-range order of BNBT6.5 and shifted the ferroelectric-relaxor transition temperature ( T F-R) down to room temperature. Thus, this process induced an ergodic relaxor phase at zero field in samples with x = 0.005. Under the electric field, the ergodic relaxor phase could reversibly transform to ferroelectric phase, which promotes the strain response with peak value of 0.38% (at 80 kV/cm, corresponding to d 33 * = 479 pm/V) at x = 0.005. Temperature-dependent measurements of both polarization and strain confirmed that the large strain originated from a reversible field-induced ergodic relaxor to ferroelectric phase transformation. The proposed material exhibits potential for nonlinear actuators.

Ergodicity, hidden bias and the growth rate gain

NASA Astrophysics Data System (ADS)

Rochman, Nash D.; Popescu, Dan M.; Sun, Sean X.

2018-05-01

Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the ‘von Foerster equation’ for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble. We show that one common definition for the term ergodicity, ‘a single individual observed over many generations recapitulates the behavior of the entire ensemble’ is implied by the other, ‘the probability of observing any state is conserved across time and over all individuals’ in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate. Finally, we explore the ‘growth rate gain’—the phenomenon that variations in the cell cycle duration leads to an improved population-level growth rate—in this context. We highlight that, fundamentally, this effect is due to asymmetric division.

Adaptive multi-node multiple input and multiple output (MIMO) transmission for mobile wireless multimedia sensor networks.

PubMed

Cho, Sunghyun; Choi, Ji-Woong; You, Cheolwoo

2013-10-02

Mobile wireless multimedia sensor networks (WMSNs), which consist of mobile sink or sensor nodes and use rich sensing information, require much faster and more reliable wireless links than static wireless sensor networks (WSNs). This paper proposes an adaptive multi-node (MN) multiple input and multiple output (MIMO) transmission to improve the transmission reliability and capacity of mobile sink nodes when they experience spatial correlation. Unlike conventional single-node (SN) MIMO transmission, the proposed scheme considers the use of transmission antennas from more than two sensor nodes. To find an optimal antenna set and a MIMO transmission scheme, a MN MIMO channel model is introduced first, followed by derivation of closed-form ergodic capacity expressions with different MIMO transmission schemes, such as space-time transmit diversity coding and spatial multiplexing. The capacity varies according to the antenna correlation and the path gain from multiple sensor nodes. Based on these statistical results, we propose an adaptive MIMO mode and antenna set switching algorithm that maximizes the ergodic capacity of mobile sink nodes. The ergodic capacity of the proposed scheme is compared with conventional SN MIMO schemes, where the gain increases as the antenna correlation and path gain ratio increase.

Adaptive Multi-Node Multiple Input and Multiple Output (MIMO) Transmission for Mobile Wireless Multimedia Sensor Networks

PubMed Central

Cho, Sunghyun; Choi, Ji-Woong; You, Cheolwoo

2013-01-01

Mobile wireless multimedia sensor networks (WMSNs), which consist of mobile sink or sensor nodes and use rich sensing information, require much faster and more reliable wireless links than static wireless sensor networks (WSNs). This paper proposes an adaptive multi-node (MN) multiple input and multiple output (MIMO) transmission to improve the transmission reliability and capacity of mobile sink nodes when they experience spatial correlation. Unlike conventional single-node (SN) MIMO transmission, the proposed scheme considers the use of transmission antennas from more than two sensor nodes. To find an optimal antenna set and a MIMO transmission scheme, a MN MIMO channel model is introduced first, followed by derivation of closed-form ergodic capacity expressions with different MIMO transmission schemes, such as space-time transmit diversity coding and spatial multiplexing. The capacity varies according to the antenna correlation and the path gain from multiple sensor nodes. Based on these statistical results, we propose an adaptive MIMO mode and antenna set switching algorithm that maximizes the ergodic capacity of mobile sink nodes. The ergodic capacity of the proposed scheme is compared with conventional SN MIMO schemes, where the gain increases as the antenna correlation and path gain ratio increase. PMID:24152920

Making sense of snapshot data: ergodic principle for clonal cell populations

PubMed Central

2017-01-01

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations. PMID:29187636

Making sense of snapshot data: ergodic principle for clonal cell populations.

PubMed

Thomas, Philipp

2017-11-01

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations. © 2017 The Author(s).

The Entropy of Non-Ergodic Complex Systems — a Derivation from First Principles

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Hanel, Rudolf

In information theory the 4 Shannon-Khinchin1,2 (SK) axioms determine Boltzmann Gibbs entropy, S -∑i pilog pi, as the unique entropy. Physics is different from information in the sense that physical systems can be non-ergodic or non-Markovian. To characterize such strongly interacting, statistical systems - complex systems in particular - within a thermodynamical framework it might be necessary to introduce generalized entropies. A series of such entropies have been proposed in the past decades. Until now the understanding of their fundamental origin and their deeper relations to complex systems remains unclear. To clarify the situation we note that non-ergodicity explicitly violates the fourth SK axiom. We show that by relaxing this axiom the entropy generalizes to, S ∑i Γ(d + 1, 1 - c log pi), where Γ is the incomplete Gamma function, and c and d are scaling exponents. All recently proposed entropies compatible with the first 3 SK axioms appear to be special cases. We prove that each statistical system is uniquely characterized by the pair of the two scaling exponents (c, d), which defines equivalence classes for all systems. The corresponding distribution functions are special forms of Lambert-W exponentials containing, as special cases, Boltzmann, stretched exponential and Tsallis distributions (power-laws) - all widely abundant in nature. This derivation is the first ab initio justification for generalized entropies. We next show how the phasespace volume of a system is related to its generalized entropy, and provide a concise criterion when it is not of Boltzmann-Gibbs type but assumes a generalized form. We show that generalized entropies only become relevant when the dynamically (statistically) relevant fraction of degrees of freedom in a system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen. Systems governed by generalized entropies are therefore systems whose phasespace volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for accelerating random walks, and a spin system on a constant-conectancy network. We argue that generalized entropies should be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

The snowflake divertor

NASA Astrophysics Data System (ADS)

Ryutov, D. D.; Soukhanovskii, V. A.

2015-11-01

The snowflake magnetic configuration is characterized by the presence of two closely spaced poloidal field nulls that create a characteristic hexagonal (reminiscent of a snowflake) separatrix structure. The magnetic field properties and the plasma behaviour in the snowflake are determined by the simultaneous action of both nulls, this generating a lot of interesting physics, as well as providing a chance for improving divertor performance. Among potential beneficial effects of this geometry are: increased volume of a low poloidal field around the null, increased connection length, and the heat flux sharing between multiple divertor channels. The authors summarise experimental results obtained with the snowflake configuration on several tokamaks. Wherever possible, relation to the existing theoretical models is described.

Suppression of tritium retention in remote areas of ITER by nonperturbative reactive gas injection.

PubMed

Tabarés, F L; Ferreira, J A; Ramos, A; van Rooij, G; Westerhout, J; Al, R; Rapp, J; Drenik, A; Mozetic, M

2010-10-22

A technique based on reactive gas injection in the afterglow region of the divertor plasma is proposed for the suppression of tritium-carbon codeposits in remote areas of ITER when operated with carbon-based divertor targets. Experiments in a divertor simulator plasma device indicate that a 4  nm/min deposition can be suppressed by addition of 1  Pa·m³ s⁻¹ ammonia flow at 10 cm from the plasma. These results bolster the concept of nonperturbative scavenger injection for tritium inventory control in carbon-based fusion plasma devices, thus paving the way for ITER operation in the active phase under a carbon-dominated, plasma facing component background.

Erosion of tungsten armor after multiple intense transient events in ITER

NASA Astrophysics Data System (ADS)

Bazylev, B. N.; Janeschitz, G.; Landman, I. S.; Pestchanyi, S. E.

2005-03-01

Macroscopic erosion by melt motion is the dominating damage mechanism for tungsten armour under high-heat loads with energy deposition W > 1 MJ/m 2 and τ > 0.1 ms. For ITER divertor armour the results of a fluid dynamics simulation of the melt motion erosion after repetitive stochastically varying plasma heat loads of consecutive disruptions interspaced by ELMs are presented. The heat loads for particular single transient events are numerically simulated using the two-dimensional MHD code FOREV-2D. The whole melt motion is calculated by the fluid dynamics code MEMOS-1.5D. In addition for the ITER dome melt motion erosion of tungsten armour caused by the lateral radiation impact from the plasma shield at the disruption and ELM heat loads is estimated.

Divertor sheath power studies in DIII-D using fixed Langmuir probes and three-dimensional modeling of tile heat flows

NASA Astrophysics Data System (ADS)

Donovan, D.; Nygren, R.; Buchenauer, D.; Watkins, J.; Rudakov, D.; Leonard, A.; Wong, C. P. C.; Makowski, M.

2014-04-01

Experimental results are presented from the three-Langmuir probe (LP) diagnostic head of the divertor material evaluation system (DiMES) on DIII-D that confirm the size of the projected current collection area of the LPs, which is essential for properly measuring ion saturation current density (Jsat) and the sheath power transmission factor (SPTF). Also using the 3-LP DiMES head, the hypothesis that collisional effects on plasma density occurring in the magnetic sheath of the tile are responsible for a lower than expected SPTF is tested and deemed not to have a significant impact on the SPTF. Three-dimensional thermal modeling of wall tiles is presented that accounts for lateral heat conduction, temperature dependence of tile material properties and radiative heat loss from the tile surface. This modeling was developed to be used in the analysis of temperature profiles of the divertor embedded thermocouple (TC) array to obtain more accurate interpretations of TC temperature profiles to infer divertor surface heat flux than have previously been accomplished using more basic one-dimensional methods.

Fast plasma shutdown by killer pellet injection in JT-60U with reduced heat flux on the divertor plate and avoiding runaway electron generation

NASA Astrophysics Data System (ADS)

Yoshino, R.; Kondoh, T.; Neyatani, Y.; Itami, K.; Kawano, Y.; Isei, N.

1997-02-01

A killer pellet is an impurity pellet that is injected into a tokamak plasma in order to terminate a discharge without causing serious damage to the tokamak machine. In JT-60U neon ice pellets have been injected into OH and NB heated plasmas and fast plasma shutdowns have been demonstrated without large vertical displacement. The heat pulse on the divertor plate has been greatly reduced by killer pellet injection (KPI), but a low-power heat flux tail with a long time duration is observed. The total energy on the divertor plate increases with longer heat flux tail, so it has been reduced by shortening the tail. Runaway electron (RE) generation has been observed just after KPI and/or in the later phase of the plasma current quench. However, RE generation has been avoided when large magnetic perturbations are excited. These experimental results clearly show that KPI is a credible fast shutdown method avoiding large vertical displacement, reducing heat flux on the divertor plate, and avoiding (or minimizing) RE generation.

ADX - Advanced Divertor and RF Tokamak Experiment

NASA Astrophysics Data System (ADS)

Greenwald, Martin; Labombard, Brian; Bonoli, Paul; Irby, Jim; Terry, Jim; Wallace, Greg; Vieira, Rui; Whyte, Dennis; Wolfe, Steve; Wukitch, Steve; Marmar, Earl

2015-11-01

The Advanced Divertor and RF Tokamak Experiment (ADX) is a design concept for a compact high-field tokamak that would address boundary plasma and plasma-material interaction physics challenges whose solution is critical for the viability of magnetic fusion energy. This device would have two crucial missions. First, it would serve as a Divertor Test Tokamak, developing divertor geometries, materials and operational scenarios that could meet the stringent requirements imposed in a fusion power plant. By operating at high field, ADX would address this problem at a level of power loading and other plasma conditions that are essentially identical to those expected in a future reactor. Secondly, ADX would investigate the physics and engineering of high-field-side launch of RF waves for current drive and heating. Efficient current drive is an essential element for achieving steady-state in a practical, power producing fusion device and high-field launch offers the prospect of higher efficiency, better control of the current profile and survivability of the launching structures. ADX would carry out this research in integrated scenarios that simultaneously demonstrate the required boundary regimes consistent with efficient current drive and core performance.

FLIT: Flowing LIquid metal Torus

NASA Astrophysics Data System (ADS)

Kolemen, Egemen; Majeski, Richard; Maingi, Rajesh; Hvasta, Michael

2017-10-01

The design and construction of FLIT, Flowing LIquid Torus, at PPPL is presented. FLIT focuses on a liquid metal divertor system suitable for implementation and testing in present-day fusion systems, such as NSTX-U. It is designed as a proof-of-concept fast-flowing liquid metal divertor that can handle heat flux of 10 MW/m2 without an additional cooling system. The 72 cm wide by 107 cm tall torus system consisting of 12 rectangular coils that give 1 Tesla magnetic field in the center and it can operate for greater than 10 seconds at this field. Initially, 30 gallons Galinstan (Ga-In-Sn) will be recirculated using 6 jxB pumps and flow velocities of up to 10 m/s will be achieved on the fully annular divertor plate. FLIT is designed as a flexible machine that will allow experimental testing of various liquid metal injection techniques, study of flow instabilities, and their control in order to prove the feasibility of liquid metal divertor concept for fusion reactors. FLIT: Flowing LIquid metal Torus. This work is supported by the US DOE Contract No. DE-AC02-09CH11466.

Using Divertor Strike Point Splitting to Study Plasma Response and Its Sensitivity to Equilibrium Uncertainties

NASA Astrophysics Data System (ADS)

Teklu, Abraham; Orlov, D. M.; Moyer, R. A.; Bykov, I.; Evans, T. E.; Wu, W.; Trevisan, G. L.; Lyons, B. C.; Abrams, T.; Makowski, M. A.; Lasnier, C. S.; Fenstermacher, M. E.

2017-10-01

Resonant magnetic perturbations (RMPs) from 3D coils have been varied to modify the splitting of the divertor strike points in DIII-D. This splitting is imaged in filtered visible and infrared emission from the divertor to determine the particle and heat flux patterns on the target plates. The observed splitting is compared to vacuum and plasma response modeling in discharges where a subset of the RMP coils were ramped to shift the divertor footprints from dominantly n = 3 to n = 2 pattern. These results will be used to determine if the plasma response model can be validated with the measured splitting. We will also study the sensitivity of the modeled splitting to details of the 2D equilibrium. This RMP ramp technique could be used in ITER to spread out the heat flux while avoiding excessive forces on the RMP coils. Work supported by U.S. DOE under the Science Undergraduate Laboratory Internship (SULI) program and DE-FC02-04ER54698, DE-FG02-07ER54917, DE-FG02-05ER54809 and DE-AC52-07NA27344.

One-Time Pad as a nonlinear dynamical system

NASA Astrophysics Data System (ADS)

Nagaraj, Nithin

2012-11-01

The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.

Double density dynamics: realizing a joint distribution of a physical system and a parameter system

NASA Astrophysics Data System (ADS)

Fukuda, Ikuo; Moritsugu, Kei

2015-11-01

To perform a variety of types of molecular dynamics simulations, we created a deterministic method termed ‘double density dynamics’ (DDD), which realizes an arbitrary distribution for both physical variables and their associated parameters simultaneously. Specifically, we constructed an ordinary differential equation that has an invariant density relating to a joint distribution of the physical system and the parameter system. A generalized density function leads to a physical system that develops under nonequilibrium environment-describing superstatistics. The joint distribution density of the physical system and the parameter system appears as the Radon-Nikodym derivative of a distribution that is created by a scaled long-time average, generated from the flow of the differential equation under an ergodic assumption. The general mathematical framework is fully discussed to address the theoretical possibility of our method, and a numerical example representing a 1D harmonic oscillator is provided to validate the method being applied to the temperature parameters.

Equidistribution for Nonuniformly Expanding Dynamical Systems, and Application to the Almost Sure Invariance Principle

NASA Astrophysics Data System (ADS)

Korepanov, Alexey

2017-12-01

Let {T : M \\to M} be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let {v : M \\to R^d} be an observable and {v_n = \\sum_{k=0}^{n-1} v circ T^k} denote the Birkhoff sums. Given a probability measure {μ} on M, we consider v n as a discrete time random process on the probability space {(M, μ)} . In smooth ergodic theory there are various natural choices of {μ} , such as the Lebesgue measure, or the absolutely continuous T-invariant measure. They give rise to different random processes. We investigate relation between such processes. We show that in a large class of measures, it is possible to couple (redefine on a new probability space) every two processes so that they are almost surely close to each other, with explicit estimates of "closeness". The purpose of this work is to close a gap in the proof of the almost sure invariance principle for nonuniformly hyperbolic transformations by Melbourne and Nicol.

Modeling of divertor power footprint widths on EAST by SOLPS5.0/B2.5-Eirene

NASA Astrophysics Data System (ADS)

Deng, Guozhong; Liu, Xiaoju; Wang, Liang; Liu, Shaocheng; Xu, Jichan; Feng, Wei; Liu, Jianbin; Liu, Huan; Gao, Xiang

2017-04-01

The edge plasma code package SOLPS5.0 is employed to simulate the divertor power footprint widths of the experimental advanced superconducting tokamak (EAST) L-mode and ELM-free H-mode plasmas. The divertor power footprint widths, which consist of the scrape-off layer (SOL) width λ q and heat spreading S, are important physical parameters for edge plasmas. In this work, a plasma current scan is implemented in the simulation to obtain the dependence of the divertor power footprint width on the plasma current I p. Strong inverse scaling of the SOL width with I p has been achieved for both L-mode and H-mode plasmas in the forms of {λ }q,{{L}\\text-\\text{mode}}=4.98× {I}{{p}}-0.68 and {λ }q,{{H}\\text-\\text{mode}}=1.86× {I}{{p}}-1.08. Similar trends have also been demonstrated in the study of heat spreading with {S}{{L}\\text-\\text{mode}}=1.95× {I}{{p}}-0.542 and {S}{{H}\\text-\\text{mode}}=0.756× {I}{{p}}-0.872. In addition, studies on divertor peak heat load and the magnetic flux expansion factor show that both of them are proportional to plasma current. The simulation work here can act as a way to explore the power footprint widths of future tokamak fusion devices such as ITER and the China Fusion Engineering Test Reactor (CFETR).

Overview of decade-long development of plasma-facing components at ASIPP

NASA Astrophysics Data System (ADS)

Luo, G.-N.; Liu, G. H.; Li, Q.; Qin, S. G.; Wang, W. J.; Shi, Y. L.; Xie, C. Y.; Chen, Z. M.; Missirlian, M.; Guilhem, D.; Richou, M.; Hirai, T.; Escourbiac, F.; Yao, D. M.; Chen, J. L.; Wang, T. J.; Bucalossi, J.; Merola, M.; Li, J. G.; EAST Team

2017-06-01

The first EAST (Experimental Advanced Superconducting Tokamak) plasma ignited in 2006 with non-actively cooled steel plates as the plasma-facing materials and components (PFMCs) which were then upgraded into full graphite tiles bolted onto water-cooled copper heat sinks in 2008. The first wall was changed further into molybdenum alloy in 2012, while keeping the graphite for both the upper and lower divertors. With the rapid increase in heating and current driving power in EAST, the W/Cu divertor project was launched around the end of 2012, aiming at achieving actively cooled full W/Cu-PFCs for the upper divertor, with heat removal capability up to 10 MW m-2. The W/Cu upper divertor was finished in the spring of 2014, consisting of 80 cassette bodies toroidally assembled. Commissioning of the EAST upper W/Cu divertor in 2014 was unsatisfactory and then several practical measures were implemented to improve the design, welding quality and reliability, which helped us achieve successful commissioning in the 2015 Spring Campaign. In collaboration with the IO and CEA teams, we have demonstrated our technological capability to remove heat loads of 5000 cycles at 10 MW m-2 and 1000 cycles at 20 MW m-2 for the small scale monoblock mockups, and surprisingly over 300 cycles at 20 MW m-2 for the flat-tile ones. The experience and lessons we learned from batch production and commissioning are undoubtedly valuable for ITER (International Thermonuclear Experimental Reactor) engineering validation and tungsten-related plasma physics.

Controlling marginally detached divertor plasmas

NASA Astrophysics Data System (ADS)

Eldon, D.; Kolemen, E.; Barton, J. L.; Briesemeister, A. R.; Humphreys, D. A.; Leonard, A. W.; Maingi, R.; Makowski, M. A.; McLean, A. G.; Moser, A. L.; Stangeby, P. C.

2017-06-01

A new control system at DIII-D has stabilized the inter-ELM detached divertor plasma state for H-mode in close proximity to the threshold for reattachment, thus demonstrating the ability to maintain detachment with minimal gas puffing. When the same control system was instead ordered to hold the plasma at the threshold (here defined as T e  =  5 eV near the divertor target plate), the resulting T e profiles separated into two groups with one group consistent with marginal detachment, and the other with marginal attachment. The plasma dithers between the attached and detached states when the control system attempts to hold at the threshold. The control system is upgraded from the one described in Kolemen et al (2015 J. Nucl. Mater. 463 1186) and it handles ELMing plasmas by using real time D α measurements to remove during-ELM slices from real time T e measurements derived from divertor Thomson scattering. The difference between measured and requested inter-ELM T e is passed to a PID (proportional-integral-derivative) controller to determine gas puff commands. While some degree of detachment is essential for the health of ITER’s divertor, more deeply detached plasmas have greater radiative losses and, at the extreme, confinement degradation, making it desirable to limit detachment to the minimum level needed to protect the target plate (Kolemen et al 2015 J. Nucl. Mater. 463 1186). However, the observed bifurcation in plasma conditions at the outer strike point with the ion B   ×  \

Lesson from Tungsten Leading Edge Heat Load Analysis in KSTAR Divertor

NASA Astrophysics Data System (ADS)

Hong, Suk-Ho; Pitts, Richard Anthony; Lee, Hyeong-Ho; Bang, Eunnam; Kang, Chan-Soo; Kim, Kyung-Min; Kim, Hong-Tack; ITER Organization Collaboration; Kstar Team Team

2016-10-01

An important design issue for the ITER tungsten (W) divertor and in fact for all such components using metallic plasma-facing elements and which are exposed to high parallel power fluxes, is the question of surface shaping to avoid melting of leading edges. We have fabricated a series of tungsten blocks with a variety of leading edge heights (0.3, 0.6, 1.0, and 2.0 mm), from the ITER worst case to heights even beyond the extreme value tested on JET. They are mounted into adjacent, inertially cooled graphite tile installed in the central divertor region of KSTAR, within the field of view of an infra-red (IR) thermography system with a spatial resolution to 0.4 mm/pixel. Adjustment of the outer divertor strike point position is used to deposit power on the different blocks in different discharges. The measured power flux density on flat regions of the surrounding graphite tiles is used to obtain the parallel power flux, q|| impinging on the various W blocks. Experiments have been performed in Type I ELMing H-mode with Ip = 600 kA, BT = 2 T, PNBI = 3.5 MW, leading to a hot attached divertor with typical pulse lengths of 10 s. Three dimensional ANSYS simulations using q|| and assuming geometric projection of the heat flux are found to be consistent with the observed edge loading. This research was partially supported by Ministry of Science, ICT, and Future Planning under KSTAR project.

Changes in divertor conditions in response to changing core density with RMPs

DOE PAGES

Briesemeister, Alexis R.; Ahn, Joon -Wook; Canik, John M.; ...

2017-06-07

The effects of changes in core density on divertor electron temperature, density and heat flux when resonant magnetic perturbations (RMPs) are applied are presented, notably a reduction in RMP induced secondary radial peaks in the electron temperature profile at the target plate is observed when the core density is increased, which is consistent with modeling. RMPs is used here to indicated non-axisymmetric magnetic field perturbations, created using in-vessel control coils, which have components which has at least one but typically many resonances with the rotational transform of the plasma. RMPs are found to alter inter-ELM heat flux to the divertormore » by modifying the core plasma density. It is shown that applying RMPs reduces the core density and increases the inter-ELM heat flux to both the inner and outer targets. Using gas puffing to return the core density to the pre-RMP levels more than eliminates the increase in inter-ELM heat flux, but a broadening of the heat flux to the outer target remains. These measurements were made at a single toroidal location, but the peak in the heat flux profile was found near the outer strike point where simulations indicate little toroidal variation should exist and tangentially viewing diagnostics showed no evidence of strong asymmetries. In experiments where divertor Thomson scattering measurements were available it is shown that, local secondary peaks in the divertor electron temperature profile near the target plate are reduced as the core density is increased, while peaks in the divertor electron density profile near the target are increased. Furthermore, these trends observed in the divertor electron temperature and density are qualitatively reproduced by scanning the upstream density in EMC3-Eirene modeling. Measurements are presented showing that higher densities are needed to induce detachment of the outer strike point in a case where an increase in electron temperature, likely due to a change in MHD activity, is seen after RMPs are applied.« less

Effects of low-Z and high-Z impurities on divertor detachment and plasma confinement

DOE PAGES

Wang, H. Q.; Guo, Houyang Y.; Petrie, Thomas W.; ...

2017-03-18

The impurity-seeded detached divertor is essential for heat exhaust in ITER and other reactor-relevant devices. Dedicated experiments with injection of N 2, Ne and Ar have been performed in DIII-D to assess the impact of the different impurities on divertor detachment and confinement. Seeding with N 2, Ne and Ar all promote divertor detachment, greatly reducing heat flux near the strike point. The upstream plasma density at the onset of detachment decreases with increasing impurity-puffing flow rates. For all injected impurity species, the confinement and pedestal pressure are correlated with the impurity content and the ratio of separatrix loss powermore » to the L-H transition threshold power. As the divertor plasma approaches detachment, the high-Z impurity seeding tends to degrade the core confinement owing to the increased core radiation. In particular, Ar injection leads to an increase in core radiation, up to 50% of the injected power, and a reduction in pedestal temperature over 60%, thus significantly degrading the confinement, i.e., with H 98 reducing from 1.1 to below 0.7. As for Ne seeding, H 98 near 0.8 can be maintained during the detachment phase with the pedestal temperature being reduced by about 50%. In contrast, in the N 2 seeded plasmas, radiation is predominately confined in the boundary plasma, with up to 50% of heating power being radiated in the divertor region and less than 25% in the core at the onset of detachment. In the case of strong N 2 gas puffing, the confinement recovers during the detachment, from ~20% reduction at the onset of the detachment to greater than that before the seeding. The core and pedestal temperatures feature a reduction of 30% from the initial attached phase and remain nearly constant during the detachment phase. The improvement in confinement appears to arise from the increase in pedestal and core density despite the temperature reduction.« less

Fabrication of divertor mock-up with ODS-Cu and W by the improved brazing technique

NASA Astrophysics Data System (ADS)

Tokitani, M.; Hamaji, Y.; Hiraoka, Y.; Masuzaki, S.; Tamura, H.; Noto, H.; Tanaka, T.; Muroga, T.; Sagara, A.; FFHR Design Group

2017-07-01

Copper alloy has been considered as a divertor cooling tube or heat sink not only in the helical reactor FFHR-d1 but also in the tokamak DEMO reactor, because it has a high thermal conductivity. This work focused on applying an oxide dispersion strengthened copper alloy (ODS-Cu), GlidCop® (Cu-0.3 wt%Al2O3) as the divertor heat sink material of FFHR-d1. This alloy has superior high temperature yield strength exceeding 300 MPa at room temperature even after annealing up to ~1000 °C. The change in material properties of Pure-Cu, GlidCop® and CuCrZr by neutron irradiation are summarized in this paper. A primary dose limit is the radiation-induced hardening/softening (~0.2 dpa/1-2 dpa) which has a temperature dependence. According to such an evaluation, the GlidCop® can be selected as the current best candidate material in the commercial base of the divertor heat sink, and its temperature should be maintained as close as possible to 300 °C during operation. Bonding between the W armour and the GlidCop® heat sink was successfully performed by using an improved brazing technique with BNi-6 (Ni-11%P) filler material. The bonding strength was measured by a three-point bending test and reached up to approximately 200 MPa. Surprisingly, several specimens showed an obvious yield point. This means that the BNi-6 brazing (bonding) layer caused relaxation of the applied stress. The small-scale divertor mock-up of the W/BNi-6/GlidCop® was successfully fabricated by using the improved brazing technique. The heat loading test was carried out by the electron beam device ACT2 in NIFS. The mock-up showed an excellent heat removal capability for use in the FFHR-d1 divertor.

Changes in divertor conditions in response to changing core density with RMPs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Briesemeister, Alexis R.; Ahn, Joon -Wook; Canik, John M.

The effects of changes in core density on divertor electron temperature, density and heat flux when resonant magnetic perturbations (RMPs) are applied are presented, notably a reduction in RMP induced secondary radial peaks in the electron temperature profile at the target plate is observed when the core density is increased, which is consistent with modeling. RMPs is used here to indicated non-axisymmetric magnetic field perturbations, created using in-vessel control coils, which have components which has at least one but typically many resonances with the rotational transform of the plasma. RMPs are found to alter inter-ELM heat flux to the divertormore » by modifying the core plasma density. It is shown that applying RMPs reduces the core density and increases the inter-ELM heat flux to both the inner and outer targets. Using gas puffing to return the core density to the pre-RMP levels more than eliminates the increase in inter-ELM heat flux, but a broadening of the heat flux to the outer target remains. These measurements were made at a single toroidal location, but the peak in the heat flux profile was found near the outer strike point where simulations indicate little toroidal variation should exist and tangentially viewing diagnostics showed no evidence of strong asymmetries. In experiments where divertor Thomson scattering measurements were available it is shown that, local secondary peaks in the divertor electron temperature profile near the target plate are reduced as the core density is increased, while peaks in the divertor electron density profile near the target are increased. Furthermore, these trends observed in the divertor electron temperature and density are qualitatively reproduced by scanning the upstream density in EMC3-Eirene modeling. Measurements are presented showing that higher densities are needed to induce detachment of the outer strike point in a case where an increase in electron temperature, likely due to a change in MHD activity, is seen after RMPs are applied.« less

Infrared Camera Diagnostic for Heat Flux Measurements on NSTX

DOE Office of Scientific and Technical Information (OSTI.GOV)

D. Mastrovito; R. Maingi; H.W. Kugel

2003-03-25

An infrared imaging system has been installed on NSTX (National Spherical Torus Experiment) at the Princeton Plasma Physics Laboratory to measure the surface temperatures on the lower divertor and center stack. The imaging system is based on an Indigo Alpha 160 x 128 microbolometer camera with 12 bits/pixel operating in the 7-13 {micro}m range with a 30 Hz frame rate and a dynamic temperature range of 0-700 degrees C. From these data and knowledge of graphite thermal properties, the heat flux is derived with a classic one-dimensional conduction model. Preliminary results of heat flux scaling are reported.

Elastic-plastic adhesive impacts of tungsten dust with metal surfaces in plasma environments

NASA Astrophysics Data System (ADS)

Ratynskaia, S.; Tolias, P.; Shalpegin, A.; Vignitchouk, L.; De Angeli, M.; Bykov, I.; Bystrov, K.; Bardin, S.; Brochard, F.; Ripamonti, D.; den Harder, N.; De Temmerman, G.

2015-08-01

Dust-surface collisions impose size selectivity on the ability of dust grains to migrate in scrape-off layer and divertor plasmas and to adhere to plasma-facing components. Here, we report first experimental evidence of dust impact phenomena in plasma environments concerning low-speed collisions of tungsten dust with tungsten surfaces: re-bouncing, adhesion, sliding and rolling. The results comply with the predictions of the model of elastic-perfectly plastic adhesive spheres employed in the dust dynamics code MIGRAINe for sub- to several meters per second impacts of micrometer-range metal dust.

Exploring the engineering limit of heat flux of a W/RAFM divertor target for fusion reactors

NASA Astrophysics Data System (ADS)

Mao, X.; Fursdon, M.; Chang, X. B.; Zhang, J. W.; Liu, P.; Ellwood, G.; Qian, X. Y.; Qin, S. J.; Peng, X. B.; Barrett, T. R.; Liu, P.

2018-06-01

The design and development of a fusion reactor divertor plasma facing component (PFC) is one of the many challenging issues on the road to commercial use of fusion energy. The divertor PFC is expected to exhaust steady state heat loads in the region of 10 MW m‑2 while keeping temperatures and thermo-mechanical stresses in its structure within the allowable limits. For ITER (International Thermo-Nuclear Experimental Reactor) a water cooled W/CuCrZr divertor PFC concept has been developed. However, this concept is not necessarily assured for use in future fusion reactors mainly because the neutron radiation dose would be at least an order magnitude higher, resulting in limited thermo-mechanical performance and considerably more activated waste products. In the present study, a water cooled divertor PFC using reduced activation ferritic-martensitic (RAFM) steel as the heat sink pipe has been designed with pressurised water reactor-like cooling conditions (pressure of 15.5 MPa, velocity of 10–20 m s‑1 and temperature of 300 °C). The PFC is made up of a number of rectangular tungsten tiles, each with an inner circular hole (so-called monoblocks), joined onto a RAFM steel pipe with copper interlayers. The thermo-mechanical performance of the PFC has been studied in detail. The heat transfer coefficient between the RAFM pipe inner surface and the water was calculated using published correlations. Geometric parameters and water velocity were optimized with finite element (FE) thermal analysis, to achieve acceptable temperatures in the structure given the target exhaust heat load of 10 MW m‑2. Under this heat load and the optimised thermal design parameters, the structure of the PFC was further assessed by mechanical analysis. We find that under these conditions the RAFM steel pipe experiences cyclic plasticity, and fails the common linear elastic ratchetting (3 Sm) rule. Nevertheless, the designed W/RAFM divertor PFU can withstand 10 MW m‑2 heat load, albeit with a fatigue life of approximately 0.55 years based on the expected operation scenario of a prototype or test reactor. This study extends the state of knowledge of the technological limit of a divertor based on a RAFM steel pipe structure.

Liquid lithium loop system to solve challenging technology issues for fusion power plant

DOE PAGES

Ono, Masayuki; Majeski, Richard P.; Jaworski, Michael A.; ...

2017-07-12

Here, steady-state fusion power plant designs present major divertor technology challenges, including high divertor heat flux both in steady-state and during transients. In addition to these concerns, there are the unresolved technology issues of long term dust accumulation and associated tritium inventory and safety issues. It has been suggested that radiation-based liquid lithium (LL) divertor concepts with a modest lithium-loop could provide a possible solution for these outstanding fusion reactor technology issues, while potentially improving reactor plasma performance. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peakmore » heat flux while maintaining essentially Li-free core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid lithium divertor (RLLD) concept and its variant, the active liquid lithium divertor concept (ARLLD), taking advantage of the enhanced or non-coronal Li radiation in relatively poorly confined divertor plasmas. To maintain the LL purity in a 1 GW-electric class fusion power plant, a closed LL loop system with a modest circulating capacity of ~ 1 liter/second (l/sec) is envisioned. We examined two key technology issues: 1) dust or solid particle removal and 2) real time recovery of tritium from LL while keeping the tritium inventory level to an acceptable level. By running the LL-loop continuously, it can carry the dust particles and impurities generated in the vacuum vessel to the outside where the dust / impurities can be removed by relatively simple dust filter, cold trap and/or centrifugal separation systems. With ~ 1 l/sec LL flow, even a small 0.1% dust content by weight (or 0.5 g per sec) suggests that the LL-loop could carry away nearly 16 tons of dust per year. In a 1 GW-electric (or ~ 3 GW fusion power) fusion power plant, about 0.5 g / sec of tritium is needed to maintain the fusion fuel cycle assuming ~ 1 % fusion burn efficiency. It appears feasible to recover tritium (T) in real time from LL while maintaining an acceptable T inventory level. Laboratory tests are being conducted to investigate T recovery feasibility with the surface cold trap (SCT) concept.« less

Liquid lithium loop system to solve challenging technology issues for fusion power plant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ono, Masayuki; Majeski, Richard P.; Jaworski, Michael A.

Here, steady-state fusion power plant designs present major divertor technology challenges, including high divertor heat flux both in steady-state and during transients. In addition to these concerns, there are the unresolved technology issues of long term dust accumulation and associated tritium inventory and safety issues. It has been suggested that radiation-based liquid lithium (LL) divertor concepts with a modest lithium-loop could provide a possible solution for these outstanding fusion reactor technology issues, while potentially improving reactor plasma performance. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peakmore » heat flux while maintaining essentially Li-free core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid lithium divertor (RLLD) concept and its variant, the active liquid lithium divertor concept (ARLLD), taking advantage of the enhanced or non-coronal Li radiation in relatively poorly confined divertor plasmas. To maintain the LL purity in a 1 GW-electric class fusion power plant, a closed LL loop system with a modest circulating capacity of ~ 1 liter/second (l/sec) is envisioned. We examined two key technology issues: 1) dust or solid particle removal and 2) real time recovery of tritium from LL while keeping the tritium inventory level to an acceptable level. By running the LL-loop continuously, it can carry the dust particles and impurities generated in the vacuum vessel to the outside where the dust / impurities can be removed by relatively simple dust filter, cold trap and/or centrifugal separation systems. With ~ 1 l/sec LL flow, even a small 0.1% dust content by weight (or 0.5 g per sec) suggests that the LL-loop could carry away nearly 16 tons of dust per year. In a 1 GW-electric (or ~ 3 GW fusion power) fusion power plant, about 0.5 g / sec of tritium is needed to maintain the fusion fuel cycle assuming ~ 1 % fusion burn efficiency. It appears feasible to recover tritium (T) in real time from LL while maintaining an acceptable T inventory level. Laboratory tests are being conducted to investigate T recovery feasibility with the surface cold trap (SCT) concept.« less

Liquid lithium loop system to solve challenging technology issues for fusion power plant

NASA Astrophysics Data System (ADS)

Ono, M.; Majeski, R.; Jaworski, M. A.; Hirooka, Y.; Kaita, R.; Gray, T. K.; Maingi, R.; Skinner, C. H.; Christenson, M.; Ruzic, D. N.

2017-11-01

Steady-state fusion power plant designs present major divertor technology challenges, including high divertor heat flux both in steady-state and during transients. In addition to these concerns, there are the unresolved technology issues of long term dust accumulation and associated tritium inventory and safety issues. It has been suggested that radiation-based liquid lithium (LL) divertor concepts with a modest lithium-loop could provide a possible solution for these outstanding fusion reactor technology issues, while potentially improving reactor plasma performance. The application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and reduction in the divertor peak heat flux while maintaining essentially Li-free core plasma operation even during H-modes. These promising results in NSTX and related modeling calculations motivated the radiative liquid lithium divertor concept and its variant, the active liquid lithium divertor concept, taking advantage of the enhanced or non-coronal Li radiation in relatively poorly confined divertor plasmas. To maintain the LL purity in a 1 GW-electric class fusion power plant, a closed LL loop system with a modest circulating capacity of ~1 l s-1 is envisioned. We examined two key technology issues: (1) dust or solid particle removal and (2) real time recovery of tritium from LL while keeping the tritium inventory level to an acceptable level. By running the LL-loop continuously, it can carry the dust particles and impurities generated in the vacuum vessel to the outside where the dust/impurities can be removed by relatively simple dust filter, cold trap and/or centrifugal separation systems. With ~1 l s-1 LL flow, even a small 0.1% dust content by weight (or 0.5 g s-1) suggests that the LL-loop could carry away nearly 16 tons of dust per year. In a 1 GW-electric (or ~3 GW fusion power) fusion power plant, about 0.5 g s-1 of tritium is needed to maintain the fusion fuel cycle assuming ~1% fusion burn efficiency. It appears feasible to recover tritium (T) in real time from LL while maintaining an acceptable T inventory level. Laboratory tests are being conducted to investigate T recovery feasibility with the surface cold trap concept.

Lithium As Plasma Facing Component for Magnetic Fusion Research

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masayuki Ono

The use of lithium in magnetic fusion confinement experiments started in the 1990's in order to improve tokamak plasma performance as a low-recycling plasma-facing component (PFC). Lithium is the lightest alkali metal and it is highly chemically reactive with relevant ion species in fusion plasmas including hydrogen, deuterium, tritium, carbon, and oxygen. Because of the reactive properties, lithium can provide strong pumping for those ions. It was indeed a spectacular success in TFTR where a very small amount (~ 0.02 gram) of lithium coating of the PFCs resulted in the fusion power output to improve by nearly a factor ofmore » two. The plasma confinement also improved by a factor of two. This success was attributed to the reduced recycling of cold gas surrounding the fusion plasma due to highly reactive lithium on the wall. The plasma confinement and performance improvements have since been confirmed in a large number of fusion devices with various magnetic configurations including CDX-U/LTX (US), CPD (Japan), HT-7 (China), EAST (China), FTU (Italy), NSTX (US), T-10, T-11M (Russia), TJ-II (Spain), and RFX (Italy). Additionally, lithium was shown to broaden the plasma pressure profile in NSTX, which is advantageous in achieving high performance H-mode operation for tokamak reactors. It is also noted that even with significant applications (up to 1,000 grams in NSTX) of lithium on PFCs, very little contamination (< 0.1%) of lithium fraction in main fusion plasma core was observed even during high confinement modes. The lithium therefore appears to be a highly desirable material to be used as a plasma PFC material from the magnetic fusion plasma performance and operational point of view. An exciting development in recent years is the growing realization of lithium as a potential solution to solve the exceptionally challenging need to handle the fusion reactor divertor heat flux, which could reach 60 MW/m2 . By placing the liquid lithium (LL) surface in the path of the main divertor heat flux (divertor strike point), the lithium is evaporated from the surface. The evaporated lithium is quickly ionized by the plasma and the ionized lithium ions can provide a strongly radiative layer of plasma ("radiative mantle"), thus could significantly reduce the heat flux to the divertor strike point surfaces, thus protecting the divertor surface. The protective effects of LL have been observed in many experiments and test stands. As a possible reactor divertor candidate, a closed LL divertor system is described. Finally, it is noted that the lithium applications as a PFC can be quite flexible and broad. The lithium application should be quite compatible with various divertor configurations, and it can be also applied to protecting the presently envisioned tungsten based solid PFC surfaces such as the ones for ITER. Lithium based PFCs therefore have the exciting prospect of providing a cost effective flexible means to improve the fusion reactor performance, while providing a practical solution to the highly challenging divertor heat handling issue confronting the steadystate magnetic fusion reactors.« less

The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics

NASA Astrophysics Data System (ADS)

Hopkins, Paul; Fortini, Andrea; Archer, Andrew J.; Schmidt, Matthias

2010-12-01

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.

Fuzzy fractals, chaos, and noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

Dynamics of a family of transcendental meromorphic functions having rational Schwarzian derivative

NASA Astrophysics Data System (ADS)

Sajid, M.; Kapoor, G. P.

2007-02-01

In the present paper, a class of critically finite transcendental meromorphic functions having rational Schwarzian derivative is introduced and the dynamics of functions in one parameter family is investigated. It is found that there exist two parameter values [lambda]*=[phi](0)>0 and , where and is the real root of [phi]'(x)=0, such that the Fatou sets of f[lambda](z) for [lambda]=[lambda]* and [lambda]=[lambda]** contain parabolic domains. A computationally useful characterization of the Julia set of the function f[lambda](z) as the complement of the basin of attraction of an attracting real fixed point of f[lambda](z) is established and applied for the generation of the images of the Julia sets of f[lambda](z). Further, it is observed that the Julia set of explodes to whole complex plane for [lambda]>[lambda]**. Finally, our results found in the present paper are compared with the recent results on dynamics of one parameter families [lambda]tanz, [R.L. Devaney, L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative, Ann. Sci. Ecole Norm. Sup. 22 (4) (1989) 55-79; L. Keen, J. Kotus, Dynamics of the family [lambda]tan(z), Conform. Geom. Dynam. 1 (1997) 28-57; G.M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions, J. London Math. Soc. 49 (1994) 281-295] and , [lambda]>0 [G.P. Kapoor, M. Guru Prem Prasad, Dynamics of : The Julia set and bifurcation, Ergodic Theory Dynam. Systems 18 (1998) 1363-1383].

DSMC simulations of vapor transport toward development of the lithium vapor box divertor concept

NASA Astrophysics Data System (ADS)

Jagoe, Christopher; Schwartz, Jacob; Goldston, Robert

2016-10-01

The lithium vapor divertor box concept attempts to achieve volumetric dissipation of the high heat efflux from a fusion power system. The vapor extracts the heat of the incoming plasma by ionization and radiation, while remaining localized in the vapor box due to differential pumping based on rapid condensation. Preliminary calculations with lithium vapor at densities appropriate for an NSTX-U-scale machine give Knudsen numbers between 0.01 and 1, outside both the range of continuum fluid dynamics and of collisionless Monte Carlo. The direct-simulation Monte Carlo (DSMC) method, however, can simulate rarefied gas flows in this regime. Using the solver contained in the OpenFOAM package, pressure-driven flows of water vapor will be analyzed. The use of water vapor in the relevant range of Knudsen number allows for a flexible similarity experiment to verify the reliability of the code before moving to tests with lithium. The simulation geometry consists of chains of boxes on a temperature gradient, connected by slots with widths that are a representative fraction of the dimensions of the box. We expect choked flow, sonic shocks, and order-of-magnitude pressure and density drops from box to box, but this expectation will be tested in the simulation and then experiment. This work is supported by the Princeton Environmental Institute.

Constructing local integrals of motion in the many-body localized phase

NASA Astrophysics Data System (ADS)

Chandran, Anushya; Kim, Isaac H.; Vidal, Guifre; Abanin, Dmitry A.

2015-02-01

Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body-localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin-flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, in both experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin-chain model. We show that the resulting LIOMs are quasilocal and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.

Interacting with an artificial partner: modeling the role of emotional aspects.

PubMed

Cattinelli, Isabella; Goldwurm, Massimiliano; Borghese, N Alberto

2008-12-01

In this paper we introduce a simple model based on probabilistic finite state automata to describe an emotional interaction between a robot and a human user, or between simulated agents. Based on the agent's personality, attitude, and nature, and on the emotional inputs it receives, the model will determine the next emotional state displayed by the agent itself. The probabilistic and time-varying nature of the model yields rich and dynamic interactions, and an autonomous adaptation to the interlocutor. In addition, a reinforcement learning technique is applied to have one agent drive its partner's behavior toward desired states. The model may also be used as a tool for behavior analysis, by extracting high probability patterns of interaction and by resorting to the ergodic properties of Markov chains.

Texture Analysis of Chaotic Coupled Map Lattices Based Image Encryption Algorithm

NASA Astrophysics Data System (ADS)

Khan, Majid; Shah, Tariq; Batool, Syeda Iram

2014-09-01

As of late, data security is key in different enclosures like web correspondence, media frameworks, therapeutic imaging, telemedicine and military correspondence. In any case, a large portion of them confronted with a few issues, for example, the absence of heartiness and security. In this letter, in the wake of exploring the fundamental purposes of the chaotic trigonometric maps and the coupled map lattices, we have presented the algorithm of chaos-based image encryption based on coupled map lattices. The proposed mechanism diminishes intermittent impact of the ergodic dynamical systems in the chaos-based image encryption. To assess the security of the encoded image of this scheme, the association of two nearby pixels and composition peculiarities were performed. This algorithm tries to minimize the problems arises in image encryption.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

Surface heat flux feedback controlled impurity seeding experiments with Alcator C-Mod’s high-Z vertical target plate divertor: performance, limitations and implications for fusion power reactors

NASA Astrophysics Data System (ADS)

Brunner, D.; Wolfe, S. M.; LaBombard, B.; Kuang, A. Q.; Lipschultz, B.; Reinke, M. L.; Hubbard, A.; Hughes, J.; Mumgaard, R. T.; Terry, J. L.; Umansky, M. V.; The Alcator C-Mod Team

2017-08-01

The Alcator C-Mod team has recently developed a feedback system to measure and control surface heat flux in real-time. The system uses real-time measurements of surface heat flux from surface thermocouples and a pulse-width modulated piezo valve to inject low-Z impurities (typically N2) into the private flux region. It has been used in C-Mod to mitigate peak surface heat fluxes  >40 MW m-2 down to  <10 MW m-2 while maintaining excellent core confinement, H 98  >  1. While the system works quite well under relatively steady conditions, use of it during transients has revealed important limitations on feedback control of impurity seeding in conventional vertical target plate divertors. In some cases, the system is unable to avoid plasma reattachment to the divertor plate or the formation of a confinement-damaging x-point MARFE. This is due to the small operational window for mitigated heat flux in the parameters of incident plasma heat flux, plasma density, and impurity density as well as the relatively slow response of the impurity gas injection system compared to plasma transients. Given the severe consequences for failure of such a system to operate reliably in a reactor, there is substantial risk that the conventional vertical target plate divertor will not provide an adequately controllable system in reactor-class devices. These considerations motivate the need to develop passively stable, highly compliant divertor configurations and experimental facilities that can test such possible solutions.

Achievement of radiative feedback control for long-pulse operation on EAST

NASA Astrophysics Data System (ADS)

Wu, K.; Yuan, Q. P.; Xiao, B. J.; Wang, L.; Duan, Y. M.; Chen, J. B.; Zheng, X. W.; Liu, X. J.; Zhang, B.; Xu, J. C.; Luo, Z. P.; Zang, Q.; Li, Y. Y.; Feng, W.; Wu, J. H.; Yang, Z. S.; Zhang, L.; Luo, G.-N.; Gong, X. Z.; Hu, L. Q.; Hu, J. S.; Li, J.

2018-05-01

The active feedback control of radiated power to prevent divertor target plates overheating during long-pulse operation has been developed and implemented on EAST. The radiation control algorithm, with impurity seeding via a supersonic molecular beam injection (SMBI) system, has shown great success in both reliability and stability. By seeding a sequence of short neon (Ne) impurity pulses with the SMBI from the outer mid-plane, the radiated power of the bulk plasma can be well controlled, and the duration of radiative control (feedforward and feedback) is 4.5 s during a discharge of 10 s. Reliable control of the total radiated power of bulk plasma has been successfully achieved in long-pulse upper single null (USN) discharges with a tungsten divertor. The achieved control range of {{f}rad} is 20%–30% in L-mode regimes and 18%–36% in H-mode regimes. The temperature of the divertor target plates was maintained at a low level during the radiative control phase. The peak particle flux on the divertor target was decreased by feedforward Ne injection in the L-mode discharges, while the Ne pulses from the SMBI had no influence on the peak particle flux because of the very small injecting volume. It is shown that although the radiated power increased, no serious reduction of plasma-stored energy or confinement was observed during the control phase. The success of the radiation control algorithm and current experiments in radiated power control represents a significant advance for steady-state divertor radiation and heat flux control on EAST for near-future long-pulse operation.

Principle of Parsimony, Fake Science, and Scales

NASA Astrophysics Data System (ADS)

Yeh, T. C. J.; Wan, L.; Wang, X. S.

2017-12-01

Considering difficulties in predicting exact motions of water molecules, and the scale of our interests (bulk behaviors of many molecules), Fick's law (diffusion concept) has been created to predict solute diffusion process in space and time. G.I. Taylor (1921) demonstrated that random motion of the molecules reach the Fickian regime in less a second if our sampling scale is large enough to reach ergodic condition. Fick's law is widely accepted for describing molecular diffusion as such. This fits the definition of the parsimony principle at the scale of our concern. Similarly, advection-dispersion or convection-dispersion equation (ADE or CDE) has been found quite satisfactory for analysis of concentration breakthroughs of solute transport in uniformly packed soil columns. This is attributed to the solute is often released over the entire cross-section of the column, which has sampled many pore-scale heterogeneities and met the ergodicity assumption. Further, the uniformly packed column contains a large number of stationary pore-size heterogeneity. The solute thus reaches the Fickian regime after traveling a short distance along the column. Moreover, breakthrough curves are concentrations integrated over the column cross-section (the scale of our interest), and they meet the ergodicity assumption embedded in the ADE and CDE. To the contrary, scales of heterogeneity in most groundwater pollution problems evolve as contaminants travel. They are much larger than the scale of our observations and our interests so that the ergodic and the Fickian conditions are difficult. Upscaling the Fick's law for solution dispersion, and deriving universal rules of the dispersion to the field- or basin-scale pollution migrations are merely misuse of the parsimony principle and lead to a fake science ( i.e., the development of theories for predicting processes that can not be observed.) The appropriate principle of parsimony for these situations dictates mapping of large-scale heterogeneities as detailed as possible and adapting the Fick's law for effects of small-scale heterogeneity resulting from our inability to characterize them in detail.

Low temperature tungsten spectroscopy on a Penning Ionization Discharge

NASA Astrophysics Data System (ADS)

Kumar, Deepak; Englesbe, Alexander; Stutman, Dan; Finkenthal, Michael

2011-10-01

Complete Tungsten divertor operation is being planned on many tokamaks including Tore Supra and ITER. Thus, low temperature tungsten spectroscopy is important for aiding the divertor diagnostics on larger machines. A Penning Ionization Discharge (PID) at the Johns Hopkins University produces steady state plasmas with Te ~ 2 eV, ne ~1013 cm-3 and a fast electron fraction at ~ 10 s eV. Similar bi-Maxwellian distributions, but with slightly higher electron temperatures, are found in the divertor plasmas of tokamaks. The two significant populating mechanisms for higher charge states in the PID are: (a) collisional excitation from bulk electrons, and (b) inner shell ionization from the fast electrons. The PID is diagnosed in a wide wavelength range - XUV, VUV and visible, to differentiate the two populating mechanisms. W is introduced in the PID by the sputtering of cathodes made of CuW alloy. Spectral emission from significantly higher charge states of W (up to W IV) has been observed in the experiment. This poster will describe results indicating the populating mechanism of W ions and also describe plans on upgrading the experiment to achieve higher temperatures which are closer to the divertor conditions. Supported by USDOE.

Carbon Deposition in the Inner JET Divertor Measured by Means of Quartz Microbalance

NASA Astrophysics Data System (ADS)

Esser, H. G.; Philipps, V.; Freisinger, M.; Coad, P.; Matthews, G. F.; Neill, G.; JET EFDA Contributors

A Quartz Microbalance (QMB) system was implemented in the inner divertor region of JET in order to measure in situ and time resolved (minimum exposure time ≥0.1 s) material fluxes (mainly carbon) and layer deposition. The system has been developed to operate at temperatures up to 200°C. The aim is to investigate carbon transport to the remote areas, and hence the tritium retention in dependence on plasma conditions. This question is still a major concern for the ITER operation. The mass sensitivity of the system is Sm = 1.5 A~— 10-8 [g/Hz cm2]. First reliable measurements were made during the C5 campaign (March–May 2002; â‰e1000 plasma discharges). The results presented are based on 74 selected exposures (694 s) under various conditions (strike point position, input power, neutral pressure, ELM frequency). Most influencing on the carbon deposition in the remote area seems to be the geometry i.e. the strike point position on the divertor tiles. In average 1.9 A~— 10-4 C-atom are deposited per deuterium ion flowing into the inner divertor.

Characterization of edge turbulence in different states of divertor detachment using reflectometry in the ASDEX Upgrade tokamak

NASA Astrophysics Data System (ADS)

Nikolaeva, V.; Guimarais, L.; Manz, P.; Carralero, D.; Manso, M. E.; Stroth, U.; Silva, C.; Conway, G. D.; Seliunin, E.; Vicente, J.; Brida, D.; Aguiam, D.; Santos, J.; Silva, A.; ASDEX Upgrade team; MST1 team

2018-05-01

Transport in the scrape-off layer (SOL) depends on the state of divertor detachment. L-mode discharges were analyzed where the state of divertor detachment is varied through a density ramp-up. By means of reflectometry measurements at the low (LFS) and the high field side (HFS), midplane density fluctuations are studied for the first time in ASDEX Upgrade simultaneously at both sides of the tokamak. Radial density fluctuation profiles (δ {n}e/{n}e) increase with radius in both the HFS and the LFS. It is found that in the SOL density fluctuations at the LFS have about a factor of two larger amplitude than at the HFS in agreement with ballooned transport. Density fluctuations at the LFS show a modest variation with increasing background density resulting mainly from a rise of low frequency components. Experimental results are in good agreement with an enhanced convection of filaments at the LFS at the beginning of outer divertor detachment leading to a flatter SOL density profile. In this phase of the discharge, density fluctuations measured at the HFS far-SOL display a strong increase, which may be associated with the presence of faster filaments originated at the LFS.

Heat removal capability of divertor coaxial tube assembly

NASA Astrophysics Data System (ADS)

Shibui, Masanao; Nakahira, Masataka; Tada, Eisuke; Takatsu, Hideyuki

1994-05-01

To deal with high power flowing in the divertor region, an advanced divertor concept with gas target has been proposed for use in ITER/EDA. The concept uses a divertor channel to remove the radiated power while allowing neutrals to recirculate. Candidate channel wall designs include a tube array design where many coaxial tubes are arranged in the toroidal direction to make louver. The coaxial tube consists of a Be protection tube encases many supply tubes wound helically around a return tube. V-alloy and hardened Cu-alloy have been proposed for use in the supply and return tubes. Some coolants have also been proposed for the design including pressurized He and liquid metals, because these coolants are consistent with the selection of coolants for the blanket and also meet the requirement of high temperature operation. In the coaxial tube design, the coolant area is restricted and brittle Be material is used under severe thermal cyclings. Thus, to obtain the coaxial tube with sufficient safety margin for the expected fusion power excursion, it is essential to understand its applicability limit. The paper discusses heat removal capability of the coaxial tube and recommends some design modifications.

Overview of the JET results

NASA Astrophysics Data System (ADS)

Romanelli, F.; JET Contributors,

2015-10-01

Since the installation of an ITER-like wall, the JET programme has focused on the consolidation of ITER design choices and the preparation for ITER operation, with a specific emphasis given to the bulk tungsten melt experiment, which has been crucial for the final decision on the material choice for the day-one tungsten divertor in ITER. Integrated scenarios have been progressed with the re-establishment of long-pulse, high-confinement H-modes by optimizing the magnetic configuration and the use of ICRH to avoid tungsten impurity accumulation. Stationary discharges with detached divertor conditions and small edge localized modes have been demonstrated by nitrogen seeding. The differences in confinement and pedestal behaviour before and after the ITER-like wall installation have been better characterized towards the development of high fusion yield scenarios in DT. Post-mortem analyses of the plasma-facing components have confirmed the previously reported low fuel retention obtained by gas balance and shown that the pattern of deposition within the divertor has changed significantly with respect to the JET carbon wall campaigns due to the absence of thermally activated chemical erosion of beryllium in contrast to carbon. Transport to remote areas is almost absent and two orders of magnitude less material is found in the divertor.

Influence of impurity seeding on the plasma radiation in the EAST tokamak

NASA Astrophysics Data System (ADS)

Liping, DONG; Yanmin, DUAN; Kaiyun, CHEN; Xiuda, YANG; Ling, ZHANG; Feng, XU; Jingbo, CHEN; Songtao, MAO; Zhenwei, WU; Liqun, HU

2018-04-01

Plasma radiation characteristics in EAST argon (Ar) gas and neon (Ne) gas seeding experiments are studied. The radiation profiles reconstructed from the fast bolometer measurement data by tomography method are compared with the ones got from the simulation program based on corona model. And the simulation results coincide roughly with the experimental data. For Ar seeding discharges, the substantial enhanced radiations can be generally observed in the edge areas at normalized radius ρ pol∼0.7–0.9, while the enhanced regions are more outer for Ne seeding discharges. The influence of seeded Ar gas on the core radiation is related to the injected position. In discharges with LSN divertor configuration, the Ar ions can permeate into the core region more easily when being injected from the opposite upper divertor ports. In USN divertor configuration, the W impurity sputtered from the upper divertor target plates are observed to be an important contributor to the increase of the core radiation no matter impurity seeding from any ports. The maximum radiated power fractions f rad (P rad/P heat) about 60%–70% have been achieved in the recent EAST experimental campaign in 2015–2016.

Rapid change of blob structure in the outer scrape-off layer (SOL)

NASA Astrophysics Data System (ADS)

Cohen, R. H.

2005-10-01

Nonlinear structures (``blobs'') driven by the magnetic field curvature and highly elongated along the field lines may exist in the tokamak SOL.footnotetextS.I. Krasheninnikov. Phys. Lett. A 283, 368 (2001) The contact of the blob end with the divertor plate significantly affects the blob structure and velocity. However, the strong shearing of the flux-tube near the X-point makes impossible direct electrical contact of the blob in the upper SOL and the divertor, so that the sheath boundary condition (BC) has to be replaced by a BC imposed near the X point.footnotetextD. Ryutov, R.H. Cohen. Contr. Pl. Phys 44, 168 (2004) We show that, at larger distances from the separatrix, in the far SOL, the connection between the upper SOL and the divertor plate is re-established, and the sheath BC becomes again relevant. During the blob's outward radial motion, this event is reflected in a sudden change of its length, from the blob extending only to the X point to the blob extending down to the plate. Likewise, a blob initially existing only in the divertor leg becomes suddenly longer, and extends to the whole SOL.

Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dekeyser, W., E-mail: Wouter.Dekeyser@kuleuven.be; Reiter, D.; Baelmans, M.

As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation ofmore » the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.« less

Development of high poloidal beta, steady-state scenario with ITER-like tungsten divertor on EAST

NASA Astrophysics Data System (ADS)

Garofalo, A. M.; Gong, X. Z.; Qian, J.; Chen, J.; Li, G.; Li, K.; Li, M. H.; Zhai, X.; Bonoli, P.; Brower, D.; Cao, L.; Cui, L.; Ding, S.; Ding, W. X.; Guo, W.; Holcomb, C.; Huang, J.; Hyatt, A.; Lanctot, M.; Lao, L. L.; Liu, H.; Lyu, B.; McClenaghan, J.; Peysson, Y.; Ren, Q.; Shiraiwa, S.; Solomon, W.; Zang, Q.; Wan, B.

2017-07-01

Recent experiments on EAST have achieved the first long pulse H-mode (61 s) with zero loop voltage and an ITER-like tungsten divertor, and have demonstrated access to broad plasma current profiles by increasing the density in fully-noninductive lower hybrid current-driven discharges. These long pulse discharges reach wall thermal and particle balance, exhibit stationary good confinement (H 98y2 ~ 1.1) with low core electron transport, and are only possible with optimal active cooling of the tungsten armors. In separate experiments, the electron density was systematically varied in order to study its effect on the deposition profile of the external lower hybrid current drive (LHCD), while keeping the plasma in fully-noninductive conditions and with divertor strike points on the tungsten divertor. A broadening of the current profile is found, as indicated by lower values of the internal inductance at higher density. A broad current profile is attractive because, among other reasons, it enables internal transport barriers at large minor radius, leading to improved confinement as shown in companion DIII-D experiments. These experiments strengthen the physics basis for achieving high performance, steady state discharges in future burning plasmas.

Impact of the impurity seeding for divertor protection on the performance of fusion reactors

NASA Astrophysics Data System (ADS)

Siccinio, Mattia; Fable, Emiliano; Angioni, Clemente; Saarelma, Samuli; Scarabosio, Andrea; Zohm, Hartmut

2017-10-01

A 0D divertor and scrape-off layer (SOL) model has been coupled to the 1.5D core transport code ASTRA. The resulting numerical tool has been employed for various parameter scans in order to identify the most convenient choices for the operation of electricity producing fusion devices with seeded impurities for the divertor protection. In particular, the repercussions of such radiative species on the main plasma through the fuel dilution have been taken into account. The main result we found is that, when the limits on the maximum tolerable divertor heat flux are enforced, the curves at constant electrical power output are closed on themselves in the R-BT plane, i.e. no improvement would descend from a further increase of R or BT once the maximum has been reached. This occurrence appears as an intrinsic physical limit for all devices where a radiative SOL is needed to deal with the power exhaust. Furthermore, the relative importance of the different power loss channels (e.g. hydrogen radiation, charge exchange, perpendicular transport and impurity radiation), through which the power entering the SOL is dissipated before reaching the target plate, is investigated with our model.

Analysis of a multi-machine database on divertor heat fluxesa)

NASA Astrophysics Data System (ADS)

Makowski, M. A.; Elder, D.; Gray, T. K.; LaBombard, B.; Lasnier, C. J.; Leonard, A. W.; Maingi, R.; Osborne, T. H.; Stangeby, P. C.; Terry, J. L.; Watkins, J.

2012-05-01

A coordinated effort to measure divertor heat flux characteristics in fully attached, similarly shaped H-mode plasmas on C-Mod, DIII-D, and NSTX was carried out in 2010 in order to construct a predictive scaling relation applicable to next step devices including ITER, FNSF, and DEMO. Few published scaling laws are available and those that have been published were obtained under widely varying conditions and divertor geometries, leading to conflicting predictions for this critically important quantity. This study was designed to overcome these deficiencies. Analysis of the combined data set reveals that the primary dependence of the parallel heat flux width is robustly inverse with Ip, which all three tokamaks independently demonstrate. An improved Thomson scattering system on DIII-D has yielded very accurate scrape off layer (SOL) profile measurements from which tests of parallel transport models have been made. It is found that a flux-limited model agrees best with the data at all collisionalities, while a Spitzer resistivity model agrees at higher collisionality where it is more valid. The SOL profile measurements and divertor heat flux scaling are consistent with a heuristic drift based model as well as a critical gradient model.

Development of high poloidal beta, steady-state scenario with ITER-like tungsten divertor on EAST

DOE PAGES

Garofalo, Andrea M.; Gong, X. Z.; Qian, J.; ...

2017-06-07

Recent experiments on EAST have achieved the first long pulse H-mode (61 s) with zero loop voltage and an ITER-like tungsten divertor, and have demonstrated access to broad plasma current profiles by increasing the density in fully-noninductive lower hybrid current-driven discharges. These long pulse discharges reach wall thermal and particle balance, exhibit stationary good confinement (H 98y2~1.1) with low core electron transport, and are only possible with optimal active cooling of the tungsten armors. In separate experiments, the electron density was systematically varied in order to study its effect on the deposition profile of the external lower hybrid current drivemore » (LHCD), while keeping the plasma in fully-noninductive conditions and with divertor strike points on the tungsten divertor. A broadening of the current profile is found, as indicated by lower values of the internal inductance at higher density. A broad current profile is attractive because, among other reasons, it enables internal transport barriers at large minor radius, leading to improved confinement as shown in companion DIII-D experiments. These experiments strengthen the physics basis for achieving high performance, steady state discharges in future burning plasmas.« less

Effects of low and high mode number tearing modes in divertor tokamaks

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima; Boozer, Allen; Evans, Todd

2007-08-01

The topological effects of magnetic perturbations on a divertor tokamak, such as DIII-D, are studied using field-line maps that were developed by Punjabi et al. [A. Punjabi, A. Verma, and A. Boozer, Phys. Rev. Lett. 69, 3322 (1992)]. The studies consider both long-wavelength perturbations, such as those of m =1, n =1 tearing modes, and localized perturbations, which are represented as a magnetic dipole. The parameters of the dipole map are set using DIII-D data from shot 115467 in which the C-coils were activated [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The long-wavelength perturbations alter the structure of the interception of magnetic field lines with the divertor plates, but the interception is in sharp lines. The dipole perturbations cause a spreading of the interception of the field lines with the divertor plates, which alleviates problems associated with heat deposition. Magnetic field lines are the trajectories of a one-and-a-half degree of freedom Hamiltonian, which strongly constrains the topological features of the lines. Although the field line maps that we use do not accurately represent the trajectories through ordinary space of individual field lines, they do represent their topological structure.

Preliminary Results on the Heat Deposition on Divertor Plate using Low MN Map

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2003-10-01

The study of magnetic field line behavior and the closely related plasma behavior are important not only for their tokamak application but also for their application to other Hamiltonian, or near-Hamiltonian, systems. The behavior of field lines near a tokamak separatrix has been studied extensively using various approaches. Our approach is called method of maps. In this paper, we introduce an area-preserving map called Low MN map. We first derive the map from the general theory of maps /1/, and then use it to calculate the effects of m = 1, n = 1 perturbations on the stochastic layer and magnetic footprint in single-null divertor tokamaks. We show that there are self-similarities, singularities, and topological equivalences in the pattern of physical parameters that characterize the stochastic layer and the magnetic footprint. Preliminary results in the investigation on the heat distribution on the divertor plate indicate multiple peaked in heat flux profile distributed radially across the divertor target when the amplitude is 10-3. This, and other features, are in good agreement with experimental observations. This work is done under the DOE grant number DE-FG02-01ER54624. 1. A. Punjabi et al, J. Plasma Phys. 52, 91 (1994).

Two-point modeling of SOL losses of HHFW power in NSTX

NASA Astrophysics Data System (ADS)

Kish, Ayden; Perkins, Rory; Ahn, Joon-Wook; Diallo, Ahmed; Gray, Travis; Hosea, Joel; Jaworski, Michael; Kramer, Gerrit; Leblanc, Benoit; Sabbagh, Steve

2017-10-01

High-harmonic fast-wave (HHFW) heating is a heating and current-drive scheme on the National Spherical Torus eXperiment (NSTX) complimentary to neutral beam injection. Previous experiments suggest that a significant fraction, up to 50%, of the HHFW power is promptly lost to the scrape-off layer (SOL). Research indicates that the lost power reaches the divertor via wave propagation and is converted to a heat flux at the divertor through RF rectification rather than heating the SOL plasma at the midplane. This counter-intuitive hypothesis is investigated using a simplified two-point model, relating plasma parameters at the divertor to those at the midplane. Taking measurements at the divertor region of NSTX as input, this two-point model is used to predict midplane parameters, using the predicted heat flux as an indicator of power input to the SOL. These predictions are compared to measurements at the midplane to evaluate the extent to which they are consistent with experiment. This work was made possible by funding from the Department of Energy for the Summer Undergraduate Laboratory Internship (SULI) program. This work is supported by the US DOE Contract No. DE-AC02-09CH11466.

Measurements of tungsten migration in the DIII-D divertor

NASA Astrophysics Data System (ADS)

Wampler, W. R.; Rudakov, D. L.; Watkins, J. G.; McLean, A. G.; Unterberg, E. A.; Stangeby, P. C.

2017-12-01

An experimental study of migration of tungsten in the DIII-D divertor is described, in which the outer strike point of L-mode plasmas was positioned on a toroidal ring of tungsten-coated metal inserts. Net deposition of tungsten on the divertor just outside the strike point was measured on graphite samples exposed to various plasma durations using the divertor materials evaluation system. Tungsten coverage, measured by Rutherford backscattering spectroscopy (RBS), was found to be low and nearly independent of both radius and exposure time closer to the strike point, whereas farther from the strike point the W coverage was much larger and increased with exposure time. Depth profiles from RBS show this was due to accumulation of thicker mixed-material deposits farther from the strike point where the plasma temperature is lower. These results are consistent with a low near-surface steady-state coverage on graphite undergoing net erosion, and continuing accumulation in regions of net deposition. This experiment provides data needed to validate, and further improve computational simulations of erosion and deposition of material on plasma-facing components and transport of impurities in magnetic fusion devices. Such simulations are underway and will be reported later.

Predictive modelling of JT-60SA high-beta steady-state plasma with impurity accumulation

NASA Astrophysics Data System (ADS)

Hayashi, N.; Hoshino, K.; Honda, M.; Ide, S.

2018-06-01

The integrated modelling code TOPICS has been extended to include core impurity transport, and applied to predictive modelling of JT-60SA high-beta steady-state plasma with the accumulation of impurity seeded to reduce the divertor heat load. In the modelling, models and conditions are selected for a conservative prediction, which considers a lower bound of plasma performance with the maximum accumulation of impurity. The conservative prediction shows the compatibility of impurity seeding with core plasma with high-beta (β N  >  3.5) and full current drive conditions, i.e. when Ar seeding reduces the divertor heat load below 10 MW m‑2, its accumulation in the core is so moderate that the core plasma performance can be recovered by additional heating within the machine capability to compensate for Ar radiation. Due to the strong dependence of accumulation on the pedestal density gradient, high separatrix density is important for the low accumulation as well as the low divertor heat load. The conservative prediction also shows that JT-60SA has enough capability to explore the divertor heat load control by impurity seeding in high-beta steady-state plasmas.

Extreme Ultraviolet Spectra of Few-Times Ionized Tungsten for Divertor Plasma Diagnostics

DOE PAGES

Clementson, Joel; Lennartsson, Thomas; Beiersdorfer, Peter

2015-09-09

The extreme ultraviolet (EUV) emission from few-times ionized tungsten atoms has been experimentally studied at the Livermore electron beam ion trap facility. The ions were produced and confined during low-energy operations of the EBIT-I electron beam ion trap. By varying the electron-beam energy from around 30–300 eV, tungsten ions in charge states expected to be abundant in tokamak divertor plasmas were excited, and the resulting EUV emission was studied using a survey spectrometer covering 120–320 Å. It is found that the emission strongly depends on the excitation energy; below 150 eV, it is relatively simple, consisting of strong isolated linesmore » from a few charge states, whereas at higher energies, it becomes very complex. For divertor plasmas with tungsten impurity ions, this emission should prove useful for diagnostics of tungsten flux rates and charge balance, as well as for radiative cooling of the divertor volume. Several lines in the 194–223 Å interval belonging to the spectra of five- and seven-times ionized tungsten (Tm-like W VI and Ho-like W VIII) were also measured using a high-resolution spectrometer.« less

The near infrared imaging system for the real-time protection of the JET ITER-like wall

NASA Astrophysics Data System (ADS)

Huber, A.; Kinna, D.; Huber, V.; Arnoux, G.; Balboa, I.; Balorin, C.; Carman, P.; Carvalho, P.; Collins, S.; Conway, N.; McCullen, P.; Jachmich, S.; Jouve, M.; Linsmeier, Ch; Lomanowski, B.; Lomas, P. J.; Lowry, C. G.; Maggi, C. F.; Matthews, G. F.; May-Smith, T.; Meigs, A.; Mertens, Ph; Nunes, I.; Price, M.; Puglia, P.; Riccardo, V.; Rimini, F. G.; Sergienko, G.; Tsalas, M.; Zastrow, K.-D.; contributors, JET

2017-12-01

This paper describes the design, implementation and operation of the near infrared (NIR) imaging diagnostic system of the JET ITER-like wall (JET-ILW) plasma experiment and its integration into the existing JET protection architecture. The imaging system comprises four wide-angle views, four tangential divertor views, and two top views of the divertor covering 66% of the first wall and up to 43% of the divertor. The operation temperature ranges which must be observed by the NIR protection cameras are, for the materials used on JET: Be 700 °C-1400 °C W coating 700 °C-1370 °C W bulk 700 °C-1400 °C. The Real-Time Protection system operates routinely since 2011 and successfully demonstrated its capability to avoid the overheating of the main chamber beryllium wall as well as of the divertor W and W-coated carbon fibre composite (CFC) tiles. During this period, less than 0.5% of the terminated discharges were aborted by a malfunction of the system. About 2%-3% of the discharges were terminated due to the detection of actual hot spots.

Predictions of VRF on a Langmuir Probe under the RF Heating Spiral on the Divertor Floor on NSTX-U

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hosea, J C; Perkins, R J; Jaworski, M A

RF heating deposition spirals are observed on the divertor plates on NSTX as shown in for a NB plus RF heating case. It has been shown that the RF spiral is tracked quite well by the spiral mapping of the strike points on the divertor plate of magnetic field lines passing in front of the high harmonic fast wave (HHFW) antenna on NSTX. Indeed, both current instrumented tiles and Langmuir probes respond to the spiral when it is positioned over them. In particular, a positive increment in tile current (collection of electrons) is obtained when the spiral is over themore » tile. This current can be due to RF rectification and/or RF heating of the scrape off layer (SOL) plasma along the magnetic field lines passing in front of the the HHFW antenna. It is important to determine quantitatively the relative contributions of these processes. Here we explore the properties of the characteristics of probes on the lower divertor plate to determine the likelyhood that the primary cause of the RF heat deposition is RF rectification.« less

Molecular dynamics simulations of hydrogen bombardment of tungsten carbide surfaces

NASA Astrophysics Data System (ADS)

Träskelin, P.; Juslin, N.; Erhart, P.; Nordlund, K.

2007-05-01

The interaction between energetic hydrogen and tungsten carbide (WC) is of interest both due to the use of hydrogen-containing plasmas in thin-film manufacturing and due to the presence of WC in the divertor of fusion reactors. In order to study this interaction, we have carried out molecular dynamics simulations of the low-energy bombardment of deuterium impinging onto crystalline as well as amorphous WC surfaces. We find that prolonged bombardment leads to the formation of an amorphous WC surface layer, regardless of the initial structure of the WC sample. Loosely bound hydrocarbons, which can erode by swift chemical sputtering, are formed at the surface. Carbon-terminated surfaces show larger sputtering yields than tungsten-terminated surfaces. In both cumulative and noncumulative simulations, C is seen to sputter preferentially. Implications for mixed material erosion in ITER are discussed.

A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse

DOE PAGES

Shi, E. L.; Hakim, A. H.; Hammett, G. W.

2015-02-03

An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. We focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cellequations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheathboundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. Finally, this test problem also helps illustratemore » some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.« less

Thermalization dynamics in a quenched many-body state

NASA Astrophysics Data System (ADS)

Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus

2016-05-01

Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.

Dynamical manifestations of quantum chaos: correlation hole and bulge

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; Santos, Lea F.

2017-10-01

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

A study of X-divertor in NSTX-U with SOLPS simulations

NASA Astrophysics Data System (ADS)

Chen, Zhong-Ping; Kotschenreuther, Mike; Mahajan, Swadesh; Gerhardt, Stefan

2018-03-01

The X-divertor (XD) geometry in NSTX-U is demonstrated, via SOLPS simulations, to perform better than the standard divertor (SD); in particular, it allows detachment at a lower upstream density and stabilizes the detachment front near the target, away from the main X-point. Consequently a stable detached operation becomes possible—the localization near the plate allows a vast reduction of heat fluxes without degrading the core plasma. Indeed, it is confirmed by our simulation that at similar states of detachment the XD outperforms the SD by reducing the heat fluxes to the target and maintaining higher upstream temperatures, resulting in scrape-off layers that are more favorable for advanced tokamak operation. These advantages are attributed to the unique geometric characteristics of XD—poloidal flaring near the target.