X. Z. Tang
2000-12-18
Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given.
Neoclassical toroidal viscosity in perturbed equilibria with general tokamak geometry
NASA Astrophysics Data System (ADS)
Logan, Nikolas C.; Park, Jong-Kyu; Kim, Kimin; Wang, Zhirui; Berkery, John W.
2013-12-01
This paper presents a calculation of neoclassical toroidal viscous torque independent of large-aspect-ratio expansions across kinetic regimes. The Perturbed Equilibrium Nonambipolar Transport (PENT) code was developed for this purpose, and is compared to previous combined regime models as well as regime specific limits and a drift kinetic δf guiding center code. It is shown that retaining general expressions, without circular large-aspect-ratio or other orbit approximations, can be important at experimentally relevant aspect ratio and shaping. The superbanana plateau, a kinetic resonance effect recently recognized for its relevance to ITER, is recovered by the PENT calculations and shown to require highly accurate treatment of geometric effects.
Modeling of Neoclassical Tearing Mode Stability for Generalized Toroidal Geometry
A.L. Rosenberg; D.A. Gates; A. Pletzer; J.E. Menard; S.E. Kruger; C.C. Hegna; F. Paoletti; S. Sabbagh
2002-08-21
Neoclassical tearing modes (NTMs) can lead to disruption and loss of confinement. Previous analysis of these modes used large aspect ratio, low beta (plasma pressure/magnetic pressure) approximations to determine the effect of NTMs on tokamak plasmas. A more accurate tool is needed to predict the onset of these instabilities. As a follow-up to recent theoretical work, a code has been written which computes the tearing mode island growth rate for arbitrary tokamak geometry. It calls PEST-3 [A. Pletzer et al., J. Comput. Phys. 115, 530 (1994)] to compute delta prime, the resistive magnetohydrodynamic (MHD) matching parameter. The code also calls the FLUXGRID routines in NIMROD [A.H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)] for Dnc, DI and DR [C.C. Hegna, Phys. Plasmas 6, 3980 (1999); A.H. Glasser et al., Phys. Fluids 18, 875 (1975)], which are the bootstrap current driven term and the ideal and resistive interchange mode criterion, respectively. In addition to these components, the NIMROD routines calculate alphas-H, a new correction to the Pfirsch-Schlter term. Finite parallel transport effects were added and a National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] equilibrium was analyzed. Another program takes the output of PEST-3 and allows the user to specify the rational surface, island width, and amount of detail near the perturbed surface to visualize the total helical flux. The results of this work will determine the stability of NTMs in an spherical torus (ST) [Y.-K.M. Peng et al., Nucl. Fusion 26, 769 (1986)] plasma with greater accuracy than previously achieved.
Gyrokinetic calculations of ITG turbulence in general toroidal geometry within the Summit Framework
NASA Astrophysics Data System (ADS)
Leboeuf, Jean-Noel; Decyk, Viktor; Dimits, Andris; Shumaker, Dan
2003-10-01
The Summit Framework is a gyrokinetic particle-in-cell turbulence simulation environment written in Fortran90 providing a unified object-based facility for sharing common components in a massively parallel setting [http://www.nersc.gov/scidac/summit/]. The Summit Framework is part of the US Department of Energy SciDAC Plasma Microturbulence Project. Work is under way to include kinetic electron models and electromagnetic effects, realistic magnetic geometry and global effects under one software environment. General geometry, realistic equilibria capabilities are being incorporated in the Summit Framework through the pg3eq_nc module, itself an extension of the circular geometry pg3eq module [Dimits et al. Phys. Rev. Letts 77, 71 (1996)]. These modules use quasi-ballooning coordinates to solve the three-dimensional, toroidal, delta-f, gyrokinetic equations for ions in order to model ITG turbulence. Realistic geometry is introduced through an interface to data from the EFIT equilibrium code[ http://fusion.gat.com/efit/]. Massively parallel implementation has been effected using MPI. Successful nonlinear comparisons for a sample shaped and finite beta equilibrium have yielded equivalent results between serial, one-processor and multi-processor parallel implementations. Linear and nonlinear tests are currently under way between the general geometry and circular geometry modules with a circular equilibrium which can be accommodated in both modules. Results from all of these tests will be reported, along with strategies for the global extension of both the circular and general geometry modules.
SUMMIT Framework: Gyrokinetic calculations of ITG turbulence in general toroidal geometry
NASA Astrophysics Data System (ADS)
Leboeuf, Jean-Noel; Decyk, Viktor; Dimits, Andris; Shumaker, Dan
2004-11-01
The SUMMIT Framework [http://www.nersc.gov/scidac/summit/] is a gyrokinetic particle-in-cell turbulence simulation environment written in Fortran90 providing a unified object-based facility for sharing common components in a massively parallel setting. The SUMMIT Framework was part of the US Department of Energy SciDAC Plasma Microturbulence Project. General geometry, realistic equilibria capabilities are being incorporated in the SUMMIT Framework through the pg3eq_nc module, itself an extension of the circular geometry pg3eq module [Dimits et al., Phys. Rev. Letts 77, 71 (1996)]. These modules use quasi-ballooning coordinates to solve the three-dimensional, toroidal, delta-f, gyrokinetic equations for ions in order to model ITG turbulence. Realistic geometry is introduced through an interface to data from the EFIT equilibrium code [http://fusion.gat.com/efit/] which is currently being upgraded. Massively parallel implementation of the pg3eq_nc module has been effected using MPI. Successful nonlinear comparisons for a sample shaped and finite beta equilibrium have yielded equivalent results between serial, one-processor and multi-processor parallel implementations. Linear and nonlinear tests have also been successfully performed between the general geometry and circular geometry modules with a circular equilibrium which can be accommodated in both modules. Results from all of these upgrades and tests will be reported.
Nonlinear particle simulation of ion cyclotron waves in toroidal geometry
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.
2015-12-10
Global particle simulation model has been developed in this work to provide a first-principles tool for studying the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation with realistic electron-to-ion mass ratio. Boris push scheme for the ion motion has been developed in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron and ion Bernstein waves in global gyrokinetic toroidal code (GTC). The nonlinear simulation capability is applied to study the parametric decay instability of a pump wave into an ion Bernstein wave side band and a low frequency ion cyclotron quasi mode.
Neoclassical viscosity effects on resistive magnetohydrodynamic modes in toroidal geometry
Yang, J.G.; Oh, Y.H.; Choi, D.I. ); Kim, J.Y.; Horton, W. )
1992-03-01
The flux-surface-averaged linearized resistive magnetohydrodynamic (MHD) boundary-layer equations including the compressibility, diamagnetic drift, and neoclassical viscosity terms are derived in toroidal geometry. These equations describe the resistive layer dynamics of resistive MHD modes over the collisionality regime between the banana plateau and the Pfirsch--Schlueter. From the resulting equations, the effects of neoclassical viscosity on the stability of the tearing and resistive ballooning modes are investigated numerically. Also, a study is given for the problem of how the neoclassical resistive MHD mode is generated as the collisionality is reduced. It is shown that the neoclassical viscosity terms give a significant destabilizing effect for the tearing and resistive ballooning modes. This destabilization comes mainly from the reduction of the stabilizing effect of the parallel ion sound compression by the ion neoclassical viscosity. In the banana-plateau collisionality limit, where the compressibility is negligible, the dispersion relations of the tearing and resistive ballooning modes reduce to the same form, with the threshold value of the driving force given by {Delta}{sub {ital c}}=0. On the other hand, with the finite neoclassical effect it is found that the neoclassical resistive MHD instability is generated in agreement with previous results. Furthermore, it is shown that this later instability can be generated in a wide range of the collisionality including near the Pfirsch--Schlueter regime as well as the banana-plateau regime, suggesting that this mode is a probable cause of anomalous transport.
Full-wave calculations in flux coordinates for toroidal geometry
Carreras, B.A.; Lynch, V.E.; Jaeger, E.F.; Batchelor, D.B.
1988-01-01
A new 2-D full-wave code, HYPERION, employing a poloidal and toroidal mode expansion and including the toroidal terms arising in the wave equation has been developed. It is based on the existing modules developed for the MHD stability codes and uses as input the tokamak equilibria calculated with the RSTEQ code. At present the plasma response is described by the collisionally broadened cold plasma conductivity. However, the code is written in straight field line coordinates, this permits the accurate representation of k /sub /parallel// and as a consequence allows the incorporation of the plasma Z functions. This code also retains the E/sub /parallel// component of the electric field which will allow the study of the low density region of the plasma. We have done detailed benchmarking of the HYPERION code in the cold plasma limit with the existing finite difference ORION full-wave code. The agreement is very good.
The universal instability in general geometry
Helander, P.; Plunk, G. G.
2015-09-15
The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.
Electron cyclotron heating and current drive in toroidal geometry
Kritz, A.H.
1993-03-01
The Principal Investigator has continued to work on problems associated both with the deposition and with the emission of electron cyclotron heating power electron cyclotron heating in toroidal plasmas. Inparticular, the work has focused on the use of electron cyclotron heating to stabilize q = 1 and q = 2 instabilities in tokamaks and on the use of electron cyclotron emission as a plasma diagnostic. The research described in this report has been carried out in collaboration with scientists at Princeton, MIT and Livermore. The Principal Investigator is now employed at Lehigh University, and a small group effort on electron cyclotron heating in plasmas has begun to evolve at Lehigh involving undergraduate and graduate students. Work has also been done in support of the electron cyclotron heating and current drive program at the Center for Research in Plasma Physics in Lausanne, Switzerland.
Modeling of Feedback Stabilization of External MHD Modes in Toroidal Geometry
NASA Astrophysics Data System (ADS)
Chu, M. S.; Chance, M. S.; Okabayashi, M.
2000-10-01
The intelligent shell feedback scheme(C.M. Bishop, Plasma Phys. Contr. Nucl. Fusion 31), 1179 (1989). seeks to utilize external coils to suppress the unstable MHD modes slowed down by the resistive shell. We present a new formulation and numerical results of the interaction between the plasma and its outside vacuum region, with complete plasma response and the inclusion of a resistive vessel in general toroidal geometry. This is achieved by using the Green's function technique, which is a generalization of that previously used for the VACUUM(M.S. Chance, Phys. Plasmas 4), 2161 (1997). code and coupled with the ideal MHD code GATO. The effectiveness of different realizations of the intelligent shell concept is gauged by their ability to minimize the available free energy to drive the MHD mode. Computations indicate poloidal coverage of 30% of the total resistive wall surface area and 6 or 7 segments of ``intelligent coil'' arrays superimposed on the resistive wall will allow recovery of up to 90% the effectiveness of the ideal shell in stabilizing the ideal external kink.
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Geometry of generalized depolarizing channels
Burrell, Christian K.
2009-10-15
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
MHD Stability Trends from Perturbed Equilibria: Possible Limitations with Toroidal Geometry
NASA Astrophysics Data System (ADS)
Comer, K. J.; Callen, J. D.; Hegna, C. C.; Turnbull, A. D.; Cowley, S.
2003-10-01
The effects of equilibrium changes on ideal MHD properties are usually studied using numerical parameter scans. Previously, we introduced a new technique to explore these dependencies: changes in the potential energy δ W due to equilibrium changes are found with an expansion of the energy principle, rather than an eigenvalue-solver code. Validation of the approach in toroidal geometry attempted to use GATO (an ideal MHD stability code) and DIII-D shot 87009. The approach should succeed with the global modes of 87009; however, ˜ 0.1% changes to qo predicted δ W rapidly increasing. Perturbing β of other toroidal equilibria resulted in similar behavior. We first review results for a cylindrical equilibrium and for 87009. Between the cylindrical case and 87009 lie several other equilibria, which should produce intermediate results. We examine several of these intermediate equilibria, starting with the cylindrical case and changing aspect ratio, shape and profiles until ending at 87009.
Solution of the Quiet Implicit Particle-In Moment Equations in Toroidal Geometry
NASA Astrophysics Data System (ADS)
Nystrom, William David
A computer program, QIP3D, has been developed to solve the Quiet Implicit Particle- in-cell (QIP) moment equations in three-dimensional toroidal geometry. This model provides an efficient algorithm for computing the time evolution of the full two-fluid (ion/electron) plasma. The coordinate system is based on a conformal mapping of the poloidal plane from a circular outer boundary and origin coincident with the magnetic axis to form a logically polar computational mesh. A Fourier, pseudospectral representation is employed for the poloidal and toroidal angles and finite differencing for the radial coordinate. The QIP equations are differenced implicitly in time and solved using a predictor -corrector algorithm. The implicit electric field equation (and other elliptic equations) are solved using advanced iterative methods. Efficient algorithms implement the required matrix-vector product and preconditioner. Two series of calculations in toroidal geometry with q_0 = 0.9 establish the two -fluid physics of the m = 1 internal kink mode where q _0 is the safety factor at the magnetic axis and m is the poloidal mode number. In each series, the mode is excited and exhibits the proper eigenmode structure. With the aspect ratio, A = R_0/a, constant at 10 and beta_0 varying from 0.0 to 0.01, the growth rate of the kink is found to increase with beta_0 and to be in quantitative agreement with previous calculations. Here, R _0 is the distance of the magnetic axis from the axis of rotational symmetry for the torus, a is the minor radius of the torus and beta_0 is the ratio of kinetic pressure to magnetic field pressure at the magnetic axis. With beta _0 = 0.0 and A varied from 5 to 10, the growth rate is found to be independent of A in agreement with theory.
Viscous damping of toroidal angular momentum in tokamaks
Stacey, W. M.
2014-09-15
The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various “neoclassical toroidal viscosity” mechanisms. In the process, it was verified that the parallel viscosity contribution to damping toroidal angular momentum still vanishes even in the presence of toroidal asymmetries, unless there are 3D radial magnetic fields.
Two-Dimensional x-y and r-z Geometry Multigroup Transport Code System for Large Toroidal Reactors.
1980-06-16
Version: 00 Although TRIDENT-CTR is a follow-on code to TRIDENT, it has incorporated several features that make it significantly different. It can handle a wide range of irregular geometric domains in both x-y and r-z geometries. However, it was principally designed to solve shielding and blanket problems for large toroidal reactors. TRIDENT-CTR is a two-dimensional, x-y and r-z geometry, multigroup, neutral particle transport code. The use of triangular finite elements gives it the geometric flexibilitymore » to cope with the nonorthogonal shapes of many toroidal designs. The code is capable of handling a wide variety of problems having irregular domains in both x-y and r-z geometries.« less
Baryonic torii: Toroidal baryons in a generalized Skyrme model
NASA Astrophysics Data System (ADS)
Gudnason, Sven Bjarke; Nitta, Muneto
2015-02-01
We study a Skyrme-type model with a potential term motivated by Bose-Einstein condensates (BECs), which we call the BEC Skyrme model. We consider two flavors of the model: the first is the Skyrme model, and the second has a sixth-order derivative term instead of the Skyrme term, both with the added BEC-motivated potential. The model contains toroidally shaped Skyrmions, and they are characterized by two integers P and Q , representing the winding numbers of two complex scalar fields along the toroidal and poloidal cycles of the torus, respectively. The baryon number is B =P Q . We find stable Skyrmion solutions for P =1 ,2 ,3 ,4 ,5 with Q =1 , while for P =6 and Q =1 , it is only metastable. We further find that configurations with higher Q >1 are all unstable and split into Q configurations with Q =1 . Finally we discover a phase transition, possibly of first order, in the mass parameter of the potential under study.
Modelling of 3D fields due to ferritic inserts and test blanket modules in toroidal geometry at ITER
NASA Astrophysics Data System (ADS)
Liu, Yueqiang; Äkäslompolo, Simppa; Cavinato, Mario; Koechl, Florian; Kurki-Suonio, Taina; Li, Li; Parail, Vassili; Saibene, Gabriella; Särkimäki, Konsta; Sipilä, Seppo; Varje, Jari
2016-06-01
Computations in toroidal geometry are systematically performed for the plasma response to 3D magnetic perturbations produced by ferritic inserts (FIs) and test blanket modules (TBMs) for four ITER plasma scenarios: the 15 MA baseline, the 12.5 MA hybrid, the 9 MA steady state, and the 7.5 MA half-field helium plasma. Due to the broad toroidal spectrum of the FI and TBM fields, the plasma response for all the n = 1-6 field components are computed and compared. The plasma response is found to be weak for the high-n (n > 4) components. The response is not globally sensitive to the toroidal plasma flow speed, as long as the latter is not reduced by an order of magnitude. This is essentially due to the strong screening effect occurring at a finite flow, as predicted for ITER plasmas. The ITER error field correction coils (EFCC) are used to compensate the n = 1 field errors produced by FIs and TBMs for the baseline scenario for the purpose of avoiding mode locking. It is found that the middle row of the EFCC, with a suitable toroidal phase for the coil current, can provide the best correction of these field errors, according to various optimisation criteria. On the other hand, even without correction, it is predicted that these n = 1 field errors will not cause substantial flow damping for the 15 MA baseline scenario.
NASA Astrophysics Data System (ADS)
Besse, Nicolas; Coulette, David
2016-08-01
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic
Kelleher, W.P.
1987-01-01
In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field.
Fatigue life analysis for traction drives with application to a toroidal type geometry
NASA Technical Reports Server (NTRS)
Coy, J. J.; Loewenthal, S. H.; Zaretsky, E. V.
1976-01-01
A contact fatigue life analysis for traction drives was developed which was based on a modified Lundberg-Palmgren theory. The analysis was used to predict life for a cone-roller toroidal traction drive. A 90-percent probability of survival was assumed for the calculated life. Parametric results were presented for life and Hertz contact stress as a function of load, drive ratio, and size. A design study was also performed. The results were compared to previously published work for the dual cavity toroidal drive as applied to a typical compact passenger vehicle drive train. For a representative duty cycle condition wherein the engine delivers 29 horsepower at 2000 rpm with the vehicle moving at 48.3 km/hr (30 mph) the drive life was calculated to be 19,200 km (11 900 miles).
Velocity-Space Diffusion Coefficients Due to Full-Wave ICRF Fields in Toroidal Geometry
Harvey, R.W.; Jaeger, F.; Berry, L.A.; Batchelor, D.B.; D'Azevedo, E.; Carter, M.D.; Ershov, N.M.; Smirnov, A.P.; Bonoli, P.; Wright, J.C.; Smithe, D.N.
2005-09-26
Jaeger et al. have calculated bounce-averaged QL diffusion coefficients from AORSA full-wave fields, based on non-Maxwellian distributions from CQL3D Fokker-Planck code. A zero banana-width approximation is employed. Complementing this calculation, a fully numerical calculation of ion velocity diffusion coefficients using the full-wave fields in numerical tokamak equilibria has been implemented to determine the finite orbit width effects. The un-approximated Lorentz equation of motion is integrated to obtain the change in velocity after one complete poloidal transit of the tokamak. Averaging velocity changes over initial starting gyro-phase and toroidal angle gives bounce-averaged diffusion coefficients. The coefficients from the full-wave and Lorentz orbit methods are compared for an ITER DT second harmonic tritium ICRF heating case: the diffusion coefficients are similar in magnitude but reveal substantial finite orbit effects.
Electron cyclotron heating and current drive in toroidal geometry. Technical progress report
Kritz, A.H.
1993-03-01
The Principal Investigator has continued to work on problems associated both with the deposition and with the emission of electron cyclotron heating power electron cyclotron heating in toroidal plasmas. Inparticular, the work has focused on the use of electron cyclotron heating to stabilize q = 1 and q = 2 instabilities in tokamaks and on the use of electron cyclotron emission as a plasma diagnostic. The research described in this report has been carried out in collaboration with scientists at Princeton, MIT and Livermore. The Principal Investigator is now employed at Lehigh University, and a small group effort on electron cyclotron heating in plasmas has begun to evolve at Lehigh involving undergraduate and graduate students. Work has also been done in support of the electron cyclotron heating and current drive program at the Center for Research in Plasma Physics in Lausanne, Switzerland.
NASA Astrophysics Data System (ADS)
Fernandez-Nieves, Alberto
We will discuss how nematic liquid crystals organize inside toroidal droplets. When the director is parallel to the bounding surface, we find spontaneous reflection symmetry breaking, which we attribute to the role played by saddle-splay contributions to the Frank free energy. When the director is perpendicular to the bounding surface, we find that the structure is reminiscent of the escape radial configuration seen in cylinders, but with a central doubly-twisted organization, which we attribute to the geometry of the torus. We will end by presenting recent experiments with active nematics on the toroidal surface. In this case, topology and activity both affect the structure and dynamics of the material.
Xiao, Yong; Holod, Ihor; Wang, Zhixuan; Lin, Zhihong; Zhang, Taige
2015-02-15
Developments in gyrokinetic particle simulation enable the gyrokinetic toroidal code (GTC) to simulate turbulent transport in tokamaks with realistic equilibrium profiles and plasma geometry, which is a critical step in the code–experiment validation process. These new developments include numerical equilibrium representation using B-splines, a new Poisson solver based on finite difference using field-aligned mesh and magnetic flux coordinates, a new zonal flow solver for general geometry, and improvements on the conventional four-point gyroaverage with nonuniform background marker loading. The gyrokinetic Poisson equation is solved in the perpendicular plane instead of the poloidal plane. Exploiting these new features, GTC is able to simulate a typical DIII-D discharge with experimental magnetic geometry and profiles. The simulated turbulent heat diffusivity and its radial profile show good agreement with other gyrokinetic codes. The newly developed nonuniform loading method provides a modified radial transport profile to that of the conventional uniform loading method.
NASA Astrophysics Data System (ADS)
Chu, M. S.; Guo, Wenfeng
2016-06-01
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
Tamed symplectic forms and generalized geometry
NASA Astrophysics Data System (ADS)
Enrietti, Nicola; Fino, Anna; Grantcharov, Gueo
2013-09-01
We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized Kähler structures. By considering the commutator Q of the two associated almost complex structures J±, we prove that if either the manifold is 4-dimensional or the distribution Im Q is involutive, then the manifold can be expressed locally as a disjoint union of twisted Poisson leaves.
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Potential for general relativity and its geometry
NASA Astrophysics Data System (ADS)
Gabadadze, Gregory; Hinterbichler, Kurt; Pirtskhalava, David; Shang, Yanwen
2013-10-01
The unique ghost-free mass and nonlinear potential terms for general relativity are presented in a diffeomorphism and local Lorentz invariant vierbein formalism. This construction requires an additional two-index Stückelberg field, beyond the four scalar fields used in the metric formulation, and unveils a new local SL(4) symmetry group of the mass and potential terms, not shared by the Einstein-Hilbert term. The new field is auxiliary but transforms as a vector under two different Lorentz groups, one of them the group of local Lorentz transformations, the other an additional global group. This formulation enables a geometric interpretation of the mass and potential terms for gravity in terms of certain volume forms. Furthermore, we find that the decoupling limit is much simpler to extract in this approach; in particular, we are able to derive expressions for the interactions of the vector modes. We also note that it is possible to extend the theory by promoting the two-index auxiliary field into a Nambu-Goldstone boson nonlinearly realizing a certain spacetime symmetry, and show how it is “eaten up” by the antisymmetric part of the vierbein.
Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.
2014-06-15
An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.
Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.
2007-06-29
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.
Self-dual geometry of generalized Hermitian surfaces
Arsen'eva, O E; Kirichenko, V F
1998-02-28
Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces.
Rotating string in doubled geometry with generalized isometries
NASA Astrophysics Data System (ADS)
Kikuchi, Toru; Okada, Takashi; Sakatani, Yuho
2012-08-01
In this paper, we first construct a globally well-defined nongeometric background which contains several branes in type II string theory compactified on a 7-torus. One of these branes is called 522, which is a codimension-2 object and has a nontrivial monodromy given by a T-duality transformation. The geometry near the 522-brane is shown to approach the nongeometric background constructed in J. de Boer and M. Shigemori, Phys. Rev. Lett. 104, 251603 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.251603. We then construct the solution of a fundamental string rotating along a nontrivial cycle in the 522 background. Although the background is not axisymmetric in the usual sense, we show that it is actually axisymmetric as a doubled geometry by explicitly finding a generalized Killing vector. We also show that a vector on the doubled geometry associated with the winding and momentum charges of the rotating string solution is Lie-transported in the generalized sense along the generalized Killing vector.
Third Elementary Dipole Moment: Toroidal
NASA Astrophysics Data System (ADS)
Cordrey, Vincent; Eshete, Amanuel; Majewski, Walerian
2015-04-01
In this paper we study the generally unknown characteristics of toroids, magnets without magnetic poles. Toroids have never seemed interesting enough to be studied for their physical features in labs due to the fact that they have no magnetic fields on the outside, but rather a very strong magnetic field trapped inside. Toroidal solenoids or magnets (rings magnetized circumferentially) interact with the external magnetic field only through its curl, which can be created either by an electric current, or by a time-dependent electric flux. We confirmed a theoretical prediction, that a toroid would not interact with the curl-less magnetic field of a current-carrying wire running outside of the torus's hole. We used our toroids as magnetic curlmeters, measuring the torque on the toroid, when the current-carrying wire runs through the toroid. From this torque we found the toroidal dipole moment. We are experimenting on detecting the escape of the inner magnetic field of the toroid outside of it, when magnetic toroid rotates or when electric toroid is driven by AC voltage. We also will discuss toroidal (or anapole) moments of fundamental particles, nuclei and atoms, and toroids' applications in metamaterials.
Generalized quantum gravity condensates for homogeneous geometries and cosmology
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Pranzetti, Daniele; Ryan, James P.; Sindoni, Lorenzo
2015-12-01
We construct a generalized class of quantum gravity condensate states that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction also lends itself easily to application to the case of spherically symmetric quantum geometries.
Generalized -deformed correlation functions as spectral functions of hyperbolic geometry
NASA Astrophysics Data System (ADS)
Bonora, L.; Bytsenko, A. A.; Guimarães, M. E. X.
2014-08-01
We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with , is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to . With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry.
Fixed boundary toroidal plasma equilibria with toroidal flows
NASA Astrophysics Data System (ADS)
Hu, Yanqiang; Hu, Yemin; Xiang, Nong
2016-04-01
The fixed boundary toroidal plasma equilibria with toroidal flows are investigated by solving the modified Grad-Shafranov equation numerically in the cylindrical coordinate system. For normal equilibrium configurations with geometry and profiles similar to usual tokamaks with no flow, it is found that the effect of flow is to lead to an outward shift of the magnetic flux surfaces, together with the profiles of pressure, and mass and current densities. The shifts could become significant when the toroidal flow Mach number exceeds 0.5. For non-conventional current profiles, even for the usual tokamak geometry, novel current reversal equilibrium configurations may result, sometimes with changed topology in the poloidal flux function. This change in the topology of plasma equilibrium can be attributed to the large toroidal flow. The computed results may correspond to situations of intense tangential injection during the low toroidal current phase in expected experimental situations.
NASA Astrophysics Data System (ADS)
Nishimura, S.; Sugama, H.; Maaßberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-01
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maaßberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Nishimura, S.; Sugama, H.; Maassberg, H.; Beidler, C. D.; Murakami, S.; Nakamura, Y.; Hirooka, S.
2010-08-15
The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
NASA Astrophysics Data System (ADS)
Harvey, R. W.; Smirnov, A. P.; Ershov, N. M.; Bonoli, P.; Wright, J. C.; Jaeger, F.; Batchelor, D. B.; Berry, L. A.; Carter, M. D.; Smithe, D. N.
2003-10-01
Numerical calculations of bounce-averaged ion velocity-space diffusion coefficients resulting from full-wave code electromagnetic fields in tokamak geometry have been implemented by two methods: (1) appropriate averaging of velocity "kicks" during one transit of the torus cross-section calculated by direct numerical integration of the Lorentz equation of motion in tokamak and full-wave EM fields; and (2) local Fourier analysis of full-wave fields to obtain wavenumbers and polarizations, followed by analysis with a previously implemented ray-tracing/quasilinear-diffusion-coefficient calculation in the CQL3D collisional-quasilinear Fokker-Planck code. Diffusion coefficient results from the two approaches are compared. The diffusion coefficients are used in the FP code for calculation of the RF-driven nonthermal ion distributions.
Lectures on Cohomology, T-Duality, and Generalized Geometry
NASA Astrophysics Data System (ADS)
Bouwknegt, P.
These are notes for lectures, originally entitled "Selected Mathematical Aspects of Modern Quantum Field Theory", presented at the Summer School "New Paths Towards Quantum Gravity", Holbæ k, Denmark, 10-16 May 2008. My aim for these lectures was to introduce a mixture of physics and mathematics postgraduate students into a selection of exciting new developments on the interface of mathematics and quantum field theory. This write-up covers three topics: (1) cohomology and differential characters, (2) T-duality, and (3) generalized geometry. The three chapters can be read, more or less, independent of each other, but there is a common central theme, namely the occurrence of a (local) 2-form gauge field in certain quantum fields theories, the so-called B-field, which plays a role analogous to the electromagnetic gauge field.
Dawson, John M.; Furth, Harold P.; Tenney, Fred H.
1988-12-06
Method for producing fusion power wherein a neutral beam is injected into a toroidal bulk plasma to produce fusion reactions during the time permitted by the slowing down of the particles from the injected beam in the bulk plasma.
Geometry of the generalized Bloch sphere for qutrits
NASA Astrophysics Data System (ADS)
Goyal, Sandeep K.; Neethi Simon, B.; Singh, Rajeev; Simon, Sudhavathani
2016-04-01
The geometry of the generalized Bloch sphere Ω3, the state space of a qutrit, is studied. Closed form expressions for Ω3, its boundary ∂Ω3, and the set of extremals {{{Ω }}}3{{ext}} are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU(3), the symmetry underlying Ω3, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .
Magnetic Properties of 3D Printed Toroids
NASA Astrophysics Data System (ADS)
Bollig, Lindsey; Otto, Austin; Hilpisch, Peter; Mowry, Greg; Nelson-Cheeseman, Brittany; Renewable Energy; Alternatives Lab (REAL) Team
Transformers are ubiquitous in electronics today. Although toroidal geometries perform most efficiently, transformers are traditionally made with rectangular cross-sections due to the lower manufacturing costs. Additive manufacturing techniques (3D printing) can easily achieve toroidal geometries by building up a part through a series of 2D layers. To get strong magnetic properties in a 3D printed transformer, a composite filament is used containing Fe dispersed in a polymer matrix. How the resulting 3D printed toroid responds to a magnetic field depends on two structural factors of the printed 2D layers: fill factor (planar density) and fill pattern. In this work, we investigate how the fill factor and fill pattern affect the magnetic properties of 3D printed toroids. The magnetic properties of the printed toroids are measured by a custom circuit that produces a hysteresis loop for each toroid. Toroids with various fill factors and fill patterns are compared to determine how these two factors can affect the magnetic field the toroid can produce. These 3D printed toroids can be used for numerous applications in order to increase the efficiency of transformers by making it possible for manufacturers to make a toroidal geometry.
NASA Astrophysics Data System (ADS)
Ginzburg, V. B.
1996-09-01
A toroidal spiral field is introduced that propagates around all the objects in the universe. The nature of this field can be either gravitational or electrostatic or magnetic, and it governs the motion of the objects as well as the forces that act upon them. The topology of the toroidal spiral field is obtained when the Bertrami vortex comprised of two helical fluxes of opposite vorticity is curved into a circle. The main parameter that defines the geometry of the toroidal spiral field is the inversion radius of a sphere at which the toroidal fluxes of opposite vorticity meet. The inversion sphere is the border surface at which the matter converts into anti-matter, and at which the law of physics are inverted. The theory covers the problem of two objects orbiting each other with possible sizes ranging from an elementary particle to a black hole and to a galaxy. The equations obtained define the radii of the stationary quantum orbits which can be applied to a structure of the hydrogen atom, including its nucleus, as well as to a structure of a planetary system and a black hole. They also establish the relativistic relationships for the gravitational and inertial masses as well as for the electrical charge which are quite different than those proposed by Lorentz.
Generalization in Place Learning and Geometry Knowledge in Rats
ERIC Educational Resources Information Center
Tommasi, Luca; Thinus-Blanc, Catherine
2004-01-01
Rats were trained to search for a food reward hidden under sawdust in the center of a square-shaped enclosure designed to force orientation on the basis of the overall geometry of the environment. They were then tested in a number of enclosures differing in shape and in size (rectangular-, double-side square-, and equilateral triangle-shaped…
Toroidal Alfven wave stability in ignited tokamaks
Cheng, C.Z.; Fu, G.Y.; Van Dam, J.W.
1989-01-01
The effects of fusion-product alpha particles on the stability of global-type shear Alfven waves in an ignited tokamak plasma are investigated in toroidal geometry. Finite toroidicity can lead to stabilization of the global Alfven eigenmodes, but it induces a new global shear Alfven eigenmodes, which is strongly destabilized via transit resonance with alpha particles. 8 refs., 2 figs.
GASP- General Aviation Synthesis Program. Volume 2: Geometry
NASA Technical Reports Server (NTRS)
Hague, D.
1978-01-01
The gross characteristics of an aircraft under study are specified to the subroutines SIZE. The principal quantities specified are both geometric (lengths and areas) and operational (altitude and Mach number). The sequence of computations carried out by SIZE is controlled by the parameter NPC which is passed into SIZE by COMMON. When NPC-0, the computation is initialized. Subsequently, NPC is set to 2 and the program advances through the geometric computations. Geometry models for the fuselage, wing, empennage, cabin pressurization, and nacelle area are examined.
Cosmology for quadratic gravity in generalized Weyl geometry
NASA Astrophysics Data System (ADS)
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.
2016-04-01
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.
Sketching the General Quadratic Equation Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
J Selvaggi; S Salon; O Kwon CVK Chari
2006-02-14
An alternative method is developed to compute the magnetic field from a circular cylindrical magnetic source. Specifically, a Fourier series expansion whose coefficients are toroidal functions is introduced which yields an alternative to the more familiar spherical harmonic solution or the Elliptic integral solution. This alternate formulation coupled with a method called charge simulation allows one to compute the external magnetic field from an arbitrary magnetic source in terms of a toroidal expansion. This expansion is valid on any finite hypothetical external observation cylinder. In other words, the magnetic scalar potential or the magnetic field intensity is computed on a exterior cylinder which encloses the magnetic source. This method can be used to accurately compute the far field where a finite element formulation is known to be inaccurate.
Bonanos, Peter
1983-01-01
A toroidal magnet for confining a high magnetic field for use in fusion reactor research and nuclear particle detection. The magnet includes a series of conductor elements arranged about and fixed at its small major radius portion to the outer surface of a central cylindrical support each conductor element having a geometry such as to maintain the conductor elements in pure tension when a high current flows therein, and a support assembly which redistributes all or part of the tension which would otherwise arise in the small major radius portion of each coil element to the large major radius portion thereof.
Generalized geometry, calibrations and supersymmetry in diverse dimensions
NASA Astrophysics Data System (ADS)
Lüst, Dieter; Patalong, Peter; Tsimpis, Dimitrios
2011-01-01
We consider type II backgrounds of the form {mathbb{R}^{1,d - 1}} × {mathcal{M}_{10 - d}} for even d, preserving 2 d/2 real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is mathcal{N} = left( {2,0} right) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence had been known to hold in the d = 4 case. Assuming the correspondence to hold for all d, we list the calibration forms for all admissible D-branes, as well as the background supersymmetry equations in pure-spinor form. We find a number of general features, including the following: The pattern of codimensions at which each calibration form appears exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations implies that the internal manifold is generalized Calabi-Yau. Our results are manifestly invariant under generalized mirror symmetry.
Inflatable nested toroid structure
NASA Technical Reports Server (NTRS)
Johnson, Christopher J. (Inventor); Raboin, Jasen L. (Inventor); Spexarth, Gary R. (Inventor)
2011-01-01
An inflatable structure comprises at least two generally toroidal, inflatable modules. When in a deployed mode, the first, inner module has a major diameter less than that of a second, outer module and is positioned within the inner circumference of the outer module such that the first module is nested circumferentially alongside the second module. The inflatable structure, in a non-deployed, non-inflated mode, is of compact configuration and adapted to be transported to a site of deployment. When deployed, the inflatable structure is of substantially increased interior volume. In one embodiment, access between the interior of the first module and the second module is provided by at least one port or structural pass-through. In another embodiment, the inflatable structure includes at least one additional generally toroidal module external of and circumferentially surrounding the second module.
Generalized Particle Swarm Algorithm for HCR Gearing Geometry Optimization
NASA Astrophysics Data System (ADS)
Kuzmanović, Siniša; Vereš, Miroslav; Rackov, Milan
2012-12-01
Logically rectangular mixed methods for Darcy flow on general geometry
Arbogast, T.; Keenan, P.T.; Wheeler, M.F.; Yotov, I.
1995-12-31
The authors consider an expanded mixed finite element formulation (cell centered finite difference) for Darcy flow with a tensor absolute permeability. The reservoir can be geometrically general with internal features, but the computational domain is rectangular. The method is defined on a curvilinear grid that need not be orthogonal, obtained by mapping the rectangular, computational grid. The original flow problem becomes a similar problem with a modified permeability on the computational grid. Quadrature rules turn the mixed method into a cell-centered finite difference method with a 9 point stencil in 2-D and 19 in 3-D. As shown by theory and experiment, if the modified permeability on the computational domain is smooth, then the convergence rate is optimal and both pressure and velocity are superconvergent at certain points. If not, Lagrange multiplier pressures can be introduced on boundaries of elements so that optimal convergence is retained. This modification presents only small changes in the solution process; in fact, the same parallel domain decomposition algorithms can be applied with little or no change to the code if the modified permeability is smooth over the subdomains. This Lagrange multiplier procedure can be used to extend the difference scheme to multi-block domains, and to give a coupling with unstructured grids. In all cases, the mixed formulation is locally conservative. Computational results illustrate the advantage and convergence of this method.
Auluck, S. K. H.
2014-10-15
Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects the shape of the DPF current sheath. Locally unidirectional shock propagation in this coordinate system enables construction of a system of 7 one-dimensional hyperbolic conservation law equations with geometric source terms, taking into account all the components of magnetic field and flow velocity. Rankine-Hugoniot jump conditions for this system lead to expressions for the axial magnetic field and three components of fluid velocity having high ion kinetic energy.
NASA Astrophysics Data System (ADS)
Auluck, S. K. H.
2014-10-01
Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects the shape of the DPF current sheath. Locally unidirectional shock propagation in this coordinate system enables construction of a system of 7 one-dimensional hyperbolic conservation law equations with geometric source terms, taking into account all the components of magnetic field and flow velocity. Rankine-Hugoniot jump conditions for this system lead to expressions for the axial magnetic field and three components of fluid velocity having high ion kinetic energy.
Advancements in generalized-geometry discrete ordinates transport for lattice physics calculations
DeHart, M. D.
2006-07-01
This paper describes the generalized-geometry capabilities of the two-dimensional NEWT transport solver, used within the TRITON depletion sequence of the SCALE code system for lattice physics calculation. With the release of SCALE 5.1 in 2006, NEWT will introduce a new automated grid generation procedure based on simple body specifications, using an input format based on the SCALE Generalized-Geometry Processor. The paper will contrast the discretization techniques against those used in other unstructured grid treatments; illustrate the ease of model development, features, capabilities; and demonstrate the unique adaptability of NEWT for a wide range of fuel configurations. (authors)
Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries
NASA Astrophysics Data System (ADS)
Batle, J.; Bagdasaryan, Armen; Abdel-Aty, M.; Abdalla, S.
2016-06-01
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the S d - 1 -sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.
NASA Astrophysics Data System (ADS)
Raybould, T. A.; Fedotov, V. A.; Papasimakis, N.; Kuprov, I.; Youngs, I. J.; Chen, W. T.; Tsai, D. P.; Zheludev, N. I.
2016-07-01
We demonstrate that the induced toroidal dipole, represented by currents flowing on the surface of a torus, makes a distinct and indispensable contribution to circular dichroism. We show that toroidal circular dichroism supplements the well-known mechanism involving electric dipole and magnetic dipole transitions. We illustrate this with rigorous analysis of the experimentally measured polarization-sensitive transmission spectra of an artificial metamaterial, constructed from elements of toroidal symmetry. We argue that toroidal circular dichroism will be found in large biomolecules with elements of toroidal symmetry and should be taken into account in the interpretation of circular dichroism spectra of organics.
Generalized functional formulation for multi-fractal representation of basin hydraulic geometry
NASA Astrophysics Data System (ADS)
Kim, JongChun; Paik, Kyungrock
2015-04-01
Natural rivers exhibit power-functional variability in their width, depth, and velocity with flow discharge (Leopold and Maddock, 1953). This relation named hydraulic geometry has been empirically supported by many field studies across the world (e.g., Leopold et al., 1964; Stall and Fok, 1968). The relationship appears either at a fixed cross-section, showing temporal variability, or along a downstream direction across an entire basin, showing spatial variability, the latter named downstream or basin hydraulic geometry. Theoretical studies that attempt to explain the power-law phenomenon (fractal), have assumed that the watershed is homogeneous hydrologically and geologically. Nevertheless, real watersheds are often subject to spatially heterogeneous conditions, due to various reasons including partial area storm coverage (Sólyom and Tucker, 2004) and transmission losses on bed and banks (Lane et al., 1997). In this setting, hydraulic geometry relationships are likely to deviate from monotonic power-law relationship and to follow rather more complex multi-fractal characteristics. In fact, deviation from single power-law was reported for at-a-station relationship of midwest rivers in US (Dodov and Foufoula-Georgiou, 2004). In the case of downstream variation, we identify significant multi-fractal characteristics over the Colorado River basin where strong heterogeneity in geological and hydrological settings presents. Conventional power-law hydraulic geometry relationships cannot express the functional variability for these cases. Motivated by this fact, we generalize the hydraulic geometry functional formulation in this study to express multi-fractal relationships. To do so, we couple the formulation of Paik and Kumar (2004), which generalized at-a-station and downstream relationships, with the formulation of Dodov and Foufoula-Georgiou (2004) which was proposed for multi-scaling in at-a-station relationship. The proposed formulation is successfully evaluated with
Lindenmeyer, Carl W.
1981-01-01
A lower support receives a toroid at a winding station with the axis of the toroid aligned with a slot in the support. An upper guide member applies an axial force to hold the toroid against the lower support. A pair of movable jaws carried by an indexing mechanism engage the outer surface of the toroid to apply a radial holding force. While the toroid is thus held, a wire is placed axially through the toroid, assisted by a funnel-shaped surface in the upper guide member, and is drawn tight about the toroid by a pair of cooperating draw rollers. When operated in the "full cycle" mode, the operator then actuates a switch which energizes a power drive to release the axial clamp and to drive the indexing mechanism and the jaws to rotate the toroid about its axis. At the same time, the wire is ejected from the draw rollers beneath the toroid so that the operator may grasp it to form another loop. When the toroid is fully indexed, the jaws release it, and the upper guide member is returned to clamp the toroid axially while the indexing mechanism is returned to its starting position. The apparatus may also be operated in a "momentary contact" mode in which the mechanism is driven only for the time a switch is actuated.
Experimental Investigation of the Natural Frequencies of Liquids in Toroidal Tanks
NASA Technical Reports Server (NTRS)
McCarty, John Locke; Leonard, H. Wayne; Walton, William C., Jr.
1960-01-01
Several toroidal configurations applicable to missile and space-vehicle liquid storage systems were oscillated to study the natural frequencies of the antisymmetric modes of contained liquids over a range of liquid depths and tank sizes. Natural frequencies for tank oscillations parallel to the free surface of both vertical and horizontal tank orientations. Natural frequencies were obtained. The data are presented in terms of dimensionless parameters which are obtained by relating experimentally determined natural liquid frequencies to analytical expressions developed through consideration of the physics of the problem and from existing solutions for liquids in tanks having similar boundaries at the liquid surface. The experimental results obtained for the toroids indicate that these parameters are applicable to the prediction of the natural frequencies of fluids in toroids of general geometry and size.
Huang, Yao-Wei; Chen, Wei Ting; Wu, Pin Chieh; Fedotov, Vassili A.; Zheludev, Nikolay I.; Tsai, Din Ping
2013-01-01
Toroidal shapes are often found in bio-molecules, viruses, proteins and fats, but only recently it was proved experimentally that toroidal structures can support exotic high-frequency electromagnetic excitations that are neither electric or magnetic multipoles. Such excitations, known as toroidal moments, could be playing an important role in enhancing inter-molecular interaction and energy transfer due to its higher electromagnetic energy confinement and weaker coupling to free space. Using a model toroidal metamaterial system, we show that coupling optical gain medium with high Q-factor toroidal resonance mode can enhance the single pass amplification to up to 65 dB. This offers an opportunity of creating the “toroidal” lasing spaser, a source of coherent optical radiation that is fueled by toroidal plasmonic oscillations in the nanostructure. PMID:23393619
NASA Astrophysics Data System (ADS)
Cha, Wan-Gi; Vogel, Sabrina; Bursac, Nikola; Albers, Albert; Volk, Wolfram
2016-08-01
Beads are used in deep drawn sheet metal parts for increasing the part stiffness. Thus, reductions of sheet metal thickness and consequently weight reduction can be reached. Style guides for types and positions of beads exist, which are often applied. However, higher stiffness effects can be realized using numeric optimization. The optimization algorithm considers the two-stepped manufacturing process consisting of deep drawing and bead stamping. The formability in both manufacturing steps represents a limiting factor. Considering nonlinear strain paths using generalized forming limit concept (GFLC), acceptable geometries will be determined in simulation. Among them, the efficient geometry which has higher stiffness effects will be selected in numerical and experimental tests. These will be integrated in the optimization algorithm.
D-branes in generalized geometry and Dirac-Born-Infeld action
NASA Astrophysics Data System (ADS)
Asakawa, T.; Sasa, S.; Watamura, S.
2012-10-01
The purpose of this paper is to formulate the Dirac-Born-Infeld (DBI) action in a framework of generalized geometry and clarify its symmetry. A D-brane is defined as a Dirac structure where scalar fields and gauge field are treated on an equal footing in a static gauge. We derive generalized Lie derivatives corresponding to the diffeomorphism and B- field gauge transformations and show that the DBI action is invariant under non-linearly realized symmetries for all types of diffeomorphisms and B-field gauge transformations. Consequently, we can interpret not only the scalar field but also the gauge field on the D-brane as the generalized Nambu-Goldstone boson.
General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry
NASA Astrophysics Data System (ADS)
Savickas, David
2014-03-01
The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.
Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries
NASA Astrophysics Data System (ADS)
Savickas, David
2015-04-01
General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).
NASA Technical Reports Server (NTRS)
Egolf, T. A.; Landgrebe, A. J.
1983-01-01
An analytic investigation to generalize wake geometry of a helicopter rotor in steady level forward flight and to demonstrate the influence of wake deformation in the prediction of rotor airloads and performance is described. Volume 1 presents a first level generalized wake model based on theoretically predicted tip vortex geometries for a selected representative blade design. The tip vortex distortions are generalized in equation form as displacements from the classical undistorted tip vortex geometry in terms of vortex age, blade azimuth, rotor advance ratio, thrust coefficient, and number of blades. These equations were programmed to provide distorted wake coordinates at very low cost for use in rotor airflow and airloads prediction analyses. The sensitivity of predicted rotor airloads, performance, and blade bending moments to the modeling of the tip vortex distortion are demonstrated for low to moderately high advance ratios for a representative rotor and the H-34 rotor. Comparisons with H-34 rotor test data demonstrate the effects of the classical, predicted distorted, and the newly developed generalized wake models on airloads and blade bending moments. Use of distorted wake models results in the occurrence of numerous blade-vortex interactions on the forward and lateral sides of the rotor disk. The significance of these interactions is related to the number and degree of proximity to the blades of the tip vortices. The correlation obtained with the distorted wake models (generalized and predicted) is encouraging.
A geometry and texture coupled flexible generalization of urban building models
NASA Astrophysics Data System (ADS)
Zhang, Man; Zhang, Liqiang; Takis Mathiopoulos, P.; Xie, Wenqing; Ding, Yusi; Wang, Hao
2012-06-01
In the past, numerous research efforts have focused on generalization of city building models. However, a generic procedure for creating flexible generalization results supporting the fast and efficient update of original building models with various complexities is still an open problem. Moreover, building clusters created in previously published generalization methods are not flexible enough to meet the various requirements for both legible and realistic visualization. Motivated by these observations, this paper proposes a new method for generating a flexible generalization outcome which enables convenient updating of original building models. It also proposes a flexible preprocessing of this generalized information to render a legible and realistic urban scene. This is accomplished by introducing a novel component structure, termed as FEdge, particularly designed for efficiently managing the geometry and texture information in building cluster instances (both original building models and building clusters) during the generalization, visualization and updating processes. Furthermore, a multiple representation structure, referred to as Evolved Buffer-Tree (EBT), is also introduced. The purpose of the EBT is to organize building cluster instances and to employ more flexible LODs for both legible and realistic visualization of urban scenes. FEdge has an intuitive planar shape which can be effectively used in representing rough 3D facade composed by detailed continuous meshes. Each FEdge is given a unique identifier, referred to as FEdge Index. In the proposed generalization scheme, firstly each original building model treated as a building cluster instance is abstracted and presented as FEdge Indices. These FEdge Indices are then used for producing generalized building cluster instances in the EBT portably, and to support convenient model updating and flexible preprocessing of the generalization results for renderable building cluster instances. Secondly, to achieve
Thermodynamic interpretation of the generalized gravity models with geometry-matter coupling
NASA Astrophysics Data System (ADS)
Harko, Tiberiu
2014-08-01
Modified gravity theories with geometry-matter coupling, in which the action is an arbitrary function of the Ricci scalar and the matter Lagrangian [f(R,Lm) gravity], and of the Ricci scalar and of the trace of the matter energy-momentum tensor [f(R,T) gravity], respectively, have the intriguing property that the divergence of the matter energy-momentum tensor is nonzero. In the present paper, by using the formalism of open thermodynamic systems, we interpret the generalized conservation equations in these gravitational theories from a thermodynamic point of view as describing irreversible matter creation processes, which could be validated by fundamental particle physics. Thus particle creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents, with the second law of thermodynamics requiring that space-time transforms into matter. The equivalent particle number creation rates, the creation pressure and the entropy production rates are obtained for both f(R,Lm) and f(R,T) gravity theories. The temperature evolution laws of the newly created particles are also obtained. In the case of the f(R,T) gravity theory the open irreversible thermodynamic interpretation of a simple cosmological model is presented in detail. It is also shown that due to the geometry-matter coupling, during the cosmological evolution a large amount of comoving entropy could be produced.
Unifying the Geometry of General Relativity with the Virtual Particle Nature of Quantum Theory
NASA Astrophysics Data System (ADS)
Laubenstein, John
2007-03-01
General Relativity (GR) and Quantum Electro-Dynamics (QED) utilize different underlying assumptions regarding the nature of vacuum and space-time. GR requires the actual geometry of space-time to change in the presence of mass resulting in gravitation. QED operates within flat space-time and propagates forces through the exchange of virtual photons. Efforts to unify these theories are -- despite their mathematical elegance -- complex, cumbersome and incomplete. The inability to achieve unification may suggest a need to re-think basic conceptual models. The IWPD Research Center has found evidence suggesting that time -- as a unique degree of freedom -- may be illusionary. Our research suggests that time may be ``embedded'' within a spatial dimension through a geometric manipulation of the light cone in Minkowski space-time. This interpretation of space-time provides predictions that are experimentally verifiable and suggests a conceptual path for the unification of GR and QED.
Development of a general method for obtaining the geometry of microfluidic networks
Razavi, Mohammad Sayed Salimpour, M. R.; Shirani, Ebrahim
2014-01-15
In the present study, a general method for geometry of fluidic networks is developed with emphasis on pressure-driven flows in the microfluidic applications. The design method is based on general features of network's geometry such as cross-sectional area and length of channels. Also, the method is applicable to various cross-sectional shapes such as circular, rectangular, triangular, and trapezoidal cross sections. Using constructal theory, the flow resistance, energy loss and performance of the network are optimized. Also, by this method, practical design strategies for the fabrication of microfluidic networks can be improved. The design method enables rapid prediction of fluid flow in the complex network of channels and is very useful for improving proper miniaturization and integration of microfluidic networks. Minimization of flow resistance of the network of channels leads to universal constants for consecutive cross-sectional areas and lengths. For a Y-shaped network, the optimal ratios of consecutive cross-section areas (A{sub i+1}/A{sub i}) and lengths (L{sub i+1}/L{sub i}) are obtained as A{sub i+1}/A{sub i} = 2{sup −2/3} and L{sub i+1}/L{sub i} = 2{sup −1/3}, respectively. It is shown that energy loss in the network is proportional to the volume of network. It is also seen when the number of channels is increased both the hydraulic resistance and the volume occupied by the network are increased in a similar manner. Furthermore, the method offers that fabrication of multi-depth and multi-width microchannels should be considered as an integral part of designing procedures. Finally, numerical simulations for the fluid flow in the network have been performed and results show very good agreement with analytic results.
Potthoff, Clifford M.
1978-01-01
The disclosure is directed to an apparatus for placing wire windings on a toroidal body, such as a transformer core, having an orifice in its center. The apparatus comprises a wire storage spool, a wire loop holding continuous belt maintained in a C-shaped loop by a belt supporting structure and provision for turning the belt to place and tighten loops of wire on a toroidal body, which is disposed within the gap of the C-shaped belt loop.
Living Toroids - Cells on Toroidal Surfaces
NASA Astrophysics Data System (ADS)
Chang, Ya-Wen; Angelini, Thomas; Marquez, Samantha; Kim, Harold; Fernandez-Nieves, Alberto
2014-03-01
Cellular environment influences a multitude of cellular functions by providing chemical and physical signals that modulate cell behavior, dynamics, development, and eventually survival. Substrate mechanics has been recognized as one of the important physical cues that governs cell behavior at single cell level as well as in collective cell motion. Past research has suggested several contact-guided behaviors to be the result of surface curvature. However, studies on the effect of curvature are relatively scarce likely due to the difficulty in generating substrates with well-defined curvature. Here we describe the generation of toroidal droplets, which unlike spherical droplets, have regions of both positive and negative Gaussian curvature. Additionally, the range of curvatures can be controlled by varying the size and aspect ratio of the torus. Cells are either encapsulated inside toroidal droplets or located on toroidal hydrogel surfaces. Preliminary studies use B. Subtilis to study the organization of bacteria biofilms. When confined in droplets surrounded by yield-stress fluid, bacteria self-organize into heterogeneous biofilm at fluid- substrate interface. It is found that the surface curvature in the sub-millimeter scale has little effect on biofilm architecture.
DeHart, M.D.
1992-12-01
A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.
General relativity exactly described in terms of Newton's laws within curved geometries
NASA Astrophysics Data System (ADS)
Savickas, D.
2014-07-01
Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.
CALCULATION OF PARTICLE BOUNCE AND TRANSIT TIMES ON GENERAL GEOMETRY FLUX SURFACES
Swanson, D.; Menard, J.
2007-01-01
A viable nuclear fusion reactor must confi ne energetic plasmas long enough so that the fusion energy produced exceeds the energy consumed to heat the plasma and maintain confi nement. It is well-known that magnetohydrodynamic (MHD) or plasma fl uid instabilities limit confi nement. One such important instability is the resistive wall mode (RWM). Plasma rotation faster than a critical frequency has been observed to stabilize the RWM. Some theories predict that the critical frequency will vary inversely with the characteristic times particles take to orbit the plasma. Previous calculations of these orbit times have assumed high aspect ratio and circular plasma cross-section, approximations unsuitable for the National Spherical Torus Experiment (NSTX). Analytic solutions for the orbit times have been derived as functions of particle energy and magnetic moment for low aspect ratio and elliptical cross-sections. Numeric solutions for arbitrary aspect ratio and cross-sectional geometry were also computed using Mathematica and IDL and agree with the analytic forms. In typical parameter regimes for NSTX, the generalized orbit times can differ from the high aspect ratio, circular approximations by as much as 40%. This result might help to assess how accurately theory describes RWM stabilization in NSTX. If theory and experiment are found to agree, generalized orbit times can be used to predict RWM stabilization in low aspect ratio nuclear fusion reactors.
Heterotic free fermionic and symmetric toroidal orbifold models
NASA Astrophysics Data System (ADS)
Athanasopoulos, P.; Faraggi, A. E.; Nibbelink, S. Groot; Mehta, V. M.
2016-04-01
Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z_2× Z_2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: we give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z_2× Z_2 orbifold geometries in six dimensions.
Toroidal Event Horizons in Binary Black Hole Mergers
NASA Astrophysics Data System (ADS)
Bohn, Andy; Teukolsky, Saul; Kidder, Lawrence; Simulating eXtreme Spacetimes Collaboration
2016-03-01
We find the first binary black hole (BBH) event horizon with a short-lived toroidal topology. The BBH mergers are produced using the Spectral Einstein Code (SpEC). It is expected that a toroidal topology should appear in space-like slicings of these 2 + 1 dimensional event horizons, but this topology has not been found previously. While we do not see a toroidal phase in the generalized harmonic slicing used to simulate the BBHs, we do find a toroidal phase after using a motivated coordinate transformation to another space-like slicing.
A generalization of the Drude-Smith formula for magneto-optical conductivities in Faraday geometry
NASA Astrophysics Data System (ADS)
Han, F. W.; Xu, W.; Li, L. L.; Zhang, C.
2016-06-01
In this study, we generalize the impulse response approach and Poisson statistics proposed by Smith [Phys. Rev. B 64, 155106 (2001)] to evaluate the longitudinal and transverse magneto-optical conductivities in an electron gas system in Faraday geometry. Comparing with the standard Drude model, the coefficients an are introduced in the Drude-Smith formula to describe the backscattering or localization effect for the nth electronic scattering event. Such a formula can also be applied to study the elements of the dielectric function matrix in the presence of magnetic and radiation fields in electron gas systems. This theoretical work is primely motivated by recent experimental activities in measuring the real and imaginary parts of longitudinal and transverse magneto-optical conductivities in condensed matter materials and electronic devices using terahertz time-domain spectroscopy. We believe that the results obtained from this study can provide an appropriate theoretical tool in reproducing the experimental findings and in fitting with experimental data to determine the important sample and material parameters.
Ohkawa, Tihiro; Baker, Charles C.
1981-01-01
In a plasma device having a toroidal plasma containment vessel, a toroidal field-generating coil system includes fixed linking coils each formed of first and second sections with the first section passing through a central opening through the containment vessel and the second section completing the linking coil to link the containment vessel. A plurality of removable unlinked coils are each formed of first and second C-shaped sections joined to each other at their open ends with their bights spaced apart. The second C-shaped section of each movable coil is removably mounted adjacent the second section of a linking coil, with the containment vessel disposed between the open ends of the first and second C-shaped sections. Electric current is passed through the linking and removable coils in opposite sense in the respective adjacent second sections to produce a net toroidal field.
Gerald, II, Rex E.; Sanchez, Jairo; Rathke, Jerome W.
2004-08-10
A video toroid cavity imager for in situ measurement of electrochemical properties of an electrolytic material sample includes a cylindrical toroid cavity resonator containing the sample and employs NMR and video imaging for providing high-resolution spectral and visual information of molecular characteristics of the sample on a real-time basis. A large magnetic field is applied to the sample under controlled temperature and pressure conditions to simultaneously provide NMR spectroscopy and video imaging capabilities for investigating electrochemical transformations of materials or the evolution of long-range molecular aggregation during cooling of hydrocarbon melts. The video toroid cavity imager includes a miniature commercial video camera with an adjustable lens, a modified compression coin cell imager with a fiat circular principal detector element, and a sample mounted on a transparent circular glass disk, and provides NMR information as well as a video image of a sample, such as a polymer film, with micrometer resolution.
Westerly, David C.; Mo Xiaohu; DeLuca, Paul M. Jr.; Tome, Wolfgang A.; Mackie, Thomas R.
2013-06-15
Purpose: Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke ['Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media,' Phys. Med. Biol. 47, 3313-3330 (2002)] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth. Methods: Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Moliere scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam. Results: Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as much as 1.4 mm (21%) at the depth
Westerly, David C.; Mo, Xiaohu; Tomé, Wolfgang A.; Mackie, Thomas R.; DeLuca, Paul M.
2013-01-01
Purpose: Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke [“Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media,” Phys. Med. Biol. 47, 3313–3330 (2002)10.1088/0031-9155/47/18/304] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth. Methods: Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Molière scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam. Results: Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as
Progress in Compact Toroid Experiments
Dolan, Thomas James
2002-09-01
The term "compact toroids" as used here means spherical tokamaks, spheromaks, and field reversed configurations, but not reversed field pinches. There are about 17 compact toroid experiments under construction or operating, with approximate parameters listed in Table 1.
VACUUM calculation in azimuthally symmetric geometry
Chance, M.S.
1996-11-01
A robustly accurate and effective method is presented to solve Laplace`s equation in general azimuthally symmetric geometry for the magnetic scalar potential in the region surrounding a plasma discharge which may or may not contain external conducting shells. These shells can be topologically toroidal or spherical, and may have toroidal gaps in them. The solution is incorporated into the various MHD stability codes either through the volume integrated perturbed magnetic energy in the vacuum region or through the continuity requirements for the normal component of the perturbed magnetic field and the total perturbed pressure across the unperturbed plasma-vacuum boundary. The method is based upon using Green`s second identity and the method of collocation. As useful byproducts, the eddy currents and the simulation of Mirnov loop measurements are calculated.
Appearance of toroidal structure in dissipating laser-generated sparks
NASA Astrophysics Data System (ADS)
Nassif, D.; Hüwel, L.
2000-03-01
We have investigated the temporal and spatial evolution of laser-induced plasmas in pure nitrogen. A 1064 nm, 20 ns pulse from a neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser with pulse energies ranging from 175 to 500 mJ is tightly focused to produce a spark at various, near-atmospheric pressures. Spatially resolved Rayleigh scattered light from a time-delayed, 355 nm Nd:YAG laser pulse traversing the spark at right angles is collected with an image intensifier gated, linear diode array. At a delay time of 30 μs, the laser plasma remnant appears as a nearly spherically symmetric region with a center temperature of about 4500 K. After around 100 μs, the hot gas starts to change into a toroidal shape expanding radially at an average speed of a few meters per second. The final torus size increases with decreasing pressure and increasing laser power. This general behavior of the plasma afterglow can be reconciled with a numerical model, where in the aftermath of the spark shock wave a pair of vortices is produced which in turn moves the residual hot gas into the observed toroidal geometry.
Hall MHD Equilibrium of Accelerated Compact Toroids
NASA Astrophysics Data System (ADS)
Howard, S. J.; Hwang, D. Q.; Horton, R. D.; Evans, R. W.; Brockington, S. J.
2007-11-01
We examine the structure and dynamics of the compact toroid's magnetic field. The compact toroid is dramatically accelerated by a large rail-gun Lorentz force density equal to j xB. We use magnetic data from the Compact Toroid Injection Experiment to answer the question of exactly where in the system j xB has nonzero values, and to what extent we can apply the standard model of force-free equilibrium. In particular we present a method of analysis of the magnetic field probe signals that allows direct comparison to the predictions of the Woltjer-Taylor force-free model and Turner's generalization of magnetic relaxation in the presence of a non-zero Hall term and fluid vorticity.
Influence of toroidal rotation on resistive tearing modes in tokamaks
Wang, S.; Ma, Z. W.
2015-12-15
Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τ{sub R}/τ{sub V} ≫ 1, where τ{sub R} and τ{sub V} represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τ{sub R}/τ{sub V} ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.
Influence of toroidal rotation on resistive tearing modes in tokamaks
NASA Astrophysics Data System (ADS)
Wang, S.; Ma, Z. W.
2015-12-01
Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τR/τV ≫ 1, where τR and τV represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τR/τV ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.
The geometrical structure of quantum theory as a natural generalization of information geometry
Reginatto, Marcel
2015-01-13
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
A General, Synthetic Model for Predicting Biodiversity Gradients from Environmental Geometry.
Gross, Kevin; Snyder-Beattie, Andrew
2016-10-01
Latitudinal and elevational biodiversity gradients fascinate ecologists, and have inspired dozens of explanations. The geometry of the abiotic environment is sometimes thought to contribute to these gradients, yet evaluations of geometric explanations are limited by a fragmented understanding of the diversity patterns they predict. This article presents a mathematical model that synthesizes multiple pathways by which environmental geometry can drive diversity gradients. The model characterizes species ranges by their environmental niches and limits on range sizes and places those ranges onto the simplified geometries of a sphere or cone. The model predicts nuanced and realistic species-richness gradients, including latitudinal diversity gradients with tropical plateaus and mid-latitude inflection points and elevational diversity gradients with low-elevation diversity maxima. The model also illustrates the importance of a mid-environment effect that augments species richness at locations with intermediate environments. Model predictions match multiple empirical biodiversity gradients, depend on ecological traits in a testable fashion, and formally synthesize elements of several geometric models. Together, these results suggest that previous assessments of geometric hypotheses should be reconsidered and that environmental geometry may play a deeper role in driving biodiversity gradients than is currently appreciated.
A General, Synthetic Model for Predicting Biodiversity Gradients from Environmental Geometry.
Gross, Kevin; Snyder-Beattie, Andrew
2016-10-01
Latitudinal and elevational biodiversity gradients fascinate ecologists, and have inspired dozens of explanations. The geometry of the abiotic environment is sometimes thought to contribute to these gradients, yet evaluations of geometric explanations are limited by a fragmented understanding of the diversity patterns they predict. This article presents a mathematical model that synthesizes multiple pathways by which environmental geometry can drive diversity gradients. The model characterizes species ranges by their environmental niches and limits on range sizes and places those ranges onto the simplified geometries of a sphere or cone. The model predicts nuanced and realistic species-richness gradients, including latitudinal diversity gradients with tropical plateaus and mid-latitude inflection points and elevational diversity gradients with low-elevation diversity maxima. The model also illustrates the importance of a mid-environment effect that augments species richness at locations with intermediate environments. Model predictions match multiple empirical biodiversity gradients, depend on ecological traits in a testable fashion, and formally synthesize elements of several geometric models. Together, these results suggest that previous assessments of geometric hypotheses should be reconsidered and that environmental geometry may play a deeper role in driving biodiversity gradients than is currently appreciated. PMID:27622881
Tokamak with liquid metal toroidal field coil
Ohkawa, Tihiro; Schaffer, Michael J.
1981-01-01
Tokamak apparatus includes a pressure vessel for defining a reservoir and confining liquid therein. A toroidal liner disposed within the pressure vessel defines a toroidal space within the liner. Liquid metal fills the reservoir outside said liner. Electric current is passed through the liquid metal over a conductive path linking the toroidal space to produce a toroidal magnetic field within the toroidal space about the major axis thereof. Toroidal plasma is developed within the toroidal space about the major axis thereof.
Advanced toroidal facility vaccuum vessel stress analyses
Hammonds, C.J.; Mayhall, J.A.
1987-01-01
The complex geometry of the Advance Toroidal Facility (ATF) vacuum vessel required special analysis techniques in investigating the structural behavior of the design. The response of a large-scale finite element model was found for transportation and operational loading. Several computer codes and systems, including the National Magnetic Fusion Energy Computer Center Cray machines, were implemented in accomplishing these analyses. The work combined complex methods that taxed the limits of both the codes and the computer systems involved. Using MSC/NASTRAN cyclic-symmetry solutions permitted using only 1/12 of the vessel geometry to mathematically analyze the entire vessel. This allowed the greater detail and accuracy demanded by the complex geometry of the vessel. Critical buckling-pressure analyses were performed with the same model. The development, results, and problems encountered in performing these analyses are described. 5 refs., 3 figs.
Method to integrate full particle orbit in toroidal plasmas
NASA Astrophysics Data System (ADS)
Wei, X. S.; Xiao, Y.; Kuley, A.; Lin, Z.
2015-09-01
It is important to integrate full particle orbit accurately when studying charged particle dynamics in electromagnetic waves with frequency higher than cyclotron frequency. We have derived a form of the Boris scheme using magnetic coordinates, which can be used effectively to integrate the cyclotron orbit in toroidal geometry over a long period of time. The new method has been verified by a full particle orbit simulation in toroidal geometry without high frequency waves. The full particle orbit calculation recovers guiding center banana orbit. This method has better numeric properties than the conventional Runge-Kutta method for conserving particle energy and magnetic moment. The toroidal precession frequency is found to match that from guiding center simulation. Many other important phenomena in the presence of an electric field, such as E × B drift, Ware pinch effect and neoclassical polarization drift are also verified by the full orbit simulation.
Toroidal equilibria in spherical coordinates
Tsui, K. H.
2008-11-15
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low {beta} Solovev and high {beta} plasma equilibria in terms of elementary functions.
Toroidal rotation studies in KSTAR
NASA Astrophysics Data System (ADS)
Lee, S. G.; Lee, H. H.; Yoo, J. W.; Kim, Y. S.; Ko, W. H.; Terzolo, L.; Bitter, M.; Hill, K.; KSTAR Team
2014-10-01
Investigation of the toroidal rotation is one of the most important topics for the magnetically confined fusion plasma researches since it is essential for the stabilization of resistive wall modes and its shear plays an important role to improve plasma confinement by suppressing turbulent transport. The most advantage of KSTAR tokamak for toroidal rotation studies is that it equips two main diagnostics including the high-resolution X-ray imaging crystal spectrometer (XICS) and charge exchange spectroscopy (CES). Simultaneous core toroidal rotation and ion temperature measurements of different impurity species from the XICS and CES have shown in reasonable agreement with various plasma discharges in KSTAR. It has been observed that the toroidal rotation in KSTAR is faster than that of other tokamak devices with similar machine size and momentum input. This may due to an intrinsically low toroidal field ripple and error field of the KSTAR device. A strong braking of the toroidal rotation by the n = 1 non-resonant magnetic perturbations (NRMPs) also indicates these low toroidal field ripple and error field. Recently, it has been found that n = 2 NRMPs can also damp the toroidal rotation in KSTAR. The detail toroidal rotation studies will be presented. Work supported by the Korea Ministry of Science, ICT and Future Planning under the KSTAR project.
Reactors Power Balance Based on Compact Toroid
NASA Astrophysics Data System (ADS)
Romadanov, I.
2013-10-01
The power balance of the plasma source system based on compact toroid with a pulse mode of formation is considered. Developed model takes into account the time dependence of the processes, in a pulsed mode of operation of the system. Also magnetic configuration shape and nuclei energy distribution fluency were considered. Analytical solution of Grad-Shafranov equation was taken to determine the shape of the separatrix and magnetic fields into the configuration. For practical calculation, program was written. Code is able to calculates volume power reactions in the confined plasma, using as input the geometry of the magnetic field, the cross section of reaction rates and energy distribution of the nuclei.
Trapped ion mode in toroidally rotating plasmas
Artun, M.; Tang, W.M.; Rewoldt, G.
1995-04-01
The influence of radially sheared toroidal flows on the Trapped Ion Mode (TIM) is investigated using a two-dimensional eigenmode code. These radially extended toroidal microinstabilities could significantly influence the interpretation of confinement scaling trends and associated fluctuation properties observed in recent tokamak experiments. In the present analysis, the electrostatic drift kinetic equation is obtained from the general nonlinear gyrokinetic equation in rotating plasmas. In the long perpendicular wavelength limit k{sub {tau}}{rho}{sub bi} {much_lt} 1, where {rho}{sub bi} is the average trapped-ion banana width, the resulting eigenmode equation becomes a coupled system of second order differential equations nmo for the poloidal harmonics. These equations are solved using finite element methods. Numerical results from the analysis of low and medium toroidal mode number instabilities are presented using representative TFTR L-mode input parameters. To illustrate the effects of mode coupling, a case is presented where the poloidal mode coupling is suppressed. The influence of toroidal rotation on a TFTR L-mode shot is also analyzed by including a beam species with considerable larger temperature. A discussion of the numerical results is presented.
NASA Astrophysics Data System (ADS)
Chung, Kyung Tae; Lee, Jong Woo
1989-08-01
A connection which is both Einstein and semisymmetric is called an SE connection, and a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by g λμ through an SE connection is called an n-dimensional SE manifold and denoted by SEXn. This paper is a direct continuation of earlier work. In this paper, we derive the generalized fundamental equations for the hypersubmanifold of SEXn, including generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations.
Deformation energy of a toroidal nucleus and plane fragmentation barriers
NASA Astrophysics Data System (ADS)
Fauchard, C.; Royer, G.
1996-02-01
The path leading to pumpkin-like configurations and toroidal shapes is investigated using a one-parameter shape sequence. The deformation energy is determined within the analytical expressions obtained for the various shape-dependent functions and the generalized rotating liquid drop model taking into account the proximity energy and the temperature. With increasing mass and angular momentum, a potential well appears in the toroidal shape path. For the heaviest systems, the pocket is large and locally favourable with respect to the plane fragmentation barriers which might allow the formation of evanescent toroidal systems which would rapidly decay in several fragments to minimize the surface tension.
Formation of magnetic islands due to field perturbations in toroidal stellarator configurations
Lee, D.K.; Harris, J.H.; Lee, G.S.
1990-06-01
An explicit formulation is developed to determine the width of a magnetic island separatrix generated by magnetic field perturbations in a general toroidal stellarator geometry. A conventional method is employed to recast the analysis in a magnetic flux coordinate system without using any simplifying approximations. The island width is seen to be proportional to the square root of the Fourier harmonic of B{sup {rho}}/B{sup {zeta}} that is in resonance with the rational value of the rotational transform, where B{sup {rho}} and B{sup {zeta}} are contravariant normal and toroidal components of the perturbed magnetic field, respectively. The procedure, which is based on a representation of three-dimensional flux surfaces by double Fourier series, allows rapid and fairly accurate calculation of the island widths in real vacuum field configurations, without the need to follow field lines through numerical integration of the field line equations. Numerical results of the island width obtained in the flux coordinate representation for the Advanced Toroidal Facility agree closely with those determined from Poincare puncture points obtained by following field lines. 22 refs., 5 tabs.
Amundsen, Morten; Linder, Jacob
2016-01-01
An extension of quasiclassical Keldysh-Usadel theory to higher spatial dimensions than one is crucial in order to describe physical phenomena like charge/spin Hall effects and topological excitations like vortices and skyrmions, none of which are captured in one-dimensional models. We here present a numerical finite element method which solves the non-linearized 2D and 3D quasiclassical Usadel equation relevant for the diffusive regime. We show the application of this on three model systems with non-trivial geometries: (i) a bottlenecked Josephson junction with external flux, (ii) a nanodisk ferromagnet deposited on top of a superconductor and (iii) superconducting islands in contact with a ferromagnet. In case (i), we demonstrate that one may control externally not only the geometrical array in which superconducting vortices arrange themselves, but also to cause coalescence and tune the number of vortices. In case (iii), we show that the supercurrent path can be tailored by incorporating magnetic elements in planar Josephson junctions which also lead to a strong modulation of the density of states. The finite element method presented herein paves the way for gaining insight in physical phenomena which have remained largely unexplored due to the complexity of solving the full quasiclassical equations in higher dimensions. PMID:26961921
A test of general relativity from the three-dimensional orbital geometry of a binary pulsar.
van Straten, W; Bailes, M; Britton, M; Kulkarni, S R; Anderson, S B; Manchester, R N; Sarkissian, J
2001-07-12
Binary pulsars provide an excellent system for testing general relativity because of their intrinsic rotational stability and the precision with which radio observations can be used to determine their orbital dynamics. Measurements of the rate of orbital decay of two pulsars have been shown to be consistent with the emission of gravitational waves as predicted by general relativity, but independent verification was not possible. Such verification can in principle be obtained by determining the orbital inclination in a binary pulsar system using only classical geometrical constraints. This would permit a measurement of the expected retardation of the pulse signal arising from the general relativistic curvature of space-time in the vicinity of the companion object (the 'Shapiro delay'). Here we report high-precision radio observations of the binary millisecond pulsar PSR J0437-4715, which establish the three-dimensional structure of its orbit. We see the Shapiro delay predicted by general relativity, and we determine the mass of the neutron star and its white dwarf companion. The determination of such masses is necessary in order to understand the origin and evolution of neutron stars. PMID:11449265
ERIC Educational Resources Information Center
Linenberger, Kimberly J.; Cole, Renee S.; Sarkar, Somnath
2011-01-01
We present a guided-inquiry experiment using Spartan Student Version, ready to be adapted and implemented into a general chemistry laboratory course. The experiment provides students an experience with Spartan Molecular Modeling software while discovering the relationships between the structure and properties of molecules. Topics discussed within…
A test of general relativity from the three-dimensional orbital geometry of a binary pulsar.
van Straten, W; Bailes, M; Britton, M; Kulkarni, S R; Anderson, S B; Manchester, R N; Sarkissian, J
2001-07-12
Binary pulsars provide an excellent system for testing general relativity because of their intrinsic rotational stability and the precision with which radio observations can be used to determine their orbital dynamics. Measurements of the rate of orbital decay of two pulsars have been shown to be consistent with the emission of gravitational waves as predicted by general relativity, but independent verification was not possible. Such verification can in principle be obtained by determining the orbital inclination in a binary pulsar system using only classical geometrical constraints. This would permit a measurement of the expected retardation of the pulse signal arising from the general relativistic curvature of space-time in the vicinity of the companion object (the 'Shapiro delay'). Here we report high-precision radio observations of the binary millisecond pulsar PSR J0437-4715, which establish the three-dimensional structure of its orbit. We see the Shapiro delay predicted by general relativity, and we determine the mass of the neutron star and its white dwarf companion. The determination of such masses is necessary in order to understand the origin and evolution of neutron stars.
Dynamics of the Disruption Halo Current Toroidal Asymmetry in NSTX
S.P. Gerhardt
2012-09-27
This paper describes the dynamics of disruption halo current non-axisymmetries in the lower divertor of the National Spherical Torus Experiment [M. Ono, et al. Nuclear Fusion 40, 557 (2000)]. While. The halo currents typically have a strongly asymmetric structure where they enter the divertor floor, and this asymmetry has been observed to complete up to 7 toroidal revolutions over the duration of the halo current pulse. However, the rotation speed and toroidal extend of the asymmetry can vary significantly during the pulse. The rotation speed, halo current pulse duration, and total number of revolutions tend to be smaller in cases with large halo currents. The halo current pattern is observed to become toroidally symmetric at the end of the halo current pulse. It is proposed that this symmeterization is due to the loss of most or all of the closed field line geometry in the final phase of the vertical displacement event.
Visualizing the Formation and Collapse of DNA Toroids
van den Broek, Bram; Noom, Maarten C.; van Mameren, Joost; Battle, Christopher; MacKintosh, Fred C.; Wuite, Gijs J.L.
2010-01-01
Abstract In living organisms, DNA is generally confined into very small volumes. In most viruses, positively charged multivalent ions assist the condensation of DNA into tightly packed toroidal structures. Interestingly, such cations can also induce the spontaneous formation of DNA toroids in vitro. To resolve the condensation dynamics and stability of DNA toroids, we use a combination of optical tweezers and fluorescence imaging to visualize in real-time spermine-induced (de)condensation in single DNA molecules. By actively controlling the DNA extension, we are able to follow (de)condensation under tension with high temporal and spatial resolution. We show that both processes occur in a quantized manner, caused by individual DNA loops added onto or removed from a toroidal condensate that is much smaller than previously observed in similar experiments. Finally, we present an analytical model that qualitatively captures the experimentally observed features, including an apparent force plateau. PMID:20441754
NASA Astrophysics Data System (ADS)
Bloshanskiĭ, I. L.
1984-02-01
The precise geometry is found of measurable sets in N-dimensional Euclidean space on which generalized localization almost everywhere holds for multiple Fourier series which are rectangularly summable.Bibliography: 14 titles.
Grey-body surface radiation coupled with conduction and convection for general geometries
NASA Astrophysics Data System (ADS)
Engelman, Michael; Jamnia, Mohammad-Ali
1991-11-01
This paper presents a numerical technique for the simulation of the effects of grey-diffuse surface radiation on the temperature field of fluid flows using FIDAP, a general purpose incompressible, viscous fluid code. The radiating surface relationships assume a non-participating medium, constant surface temperature and heat fluxes at the discretized elemental level. The technique involves the decoupling of energy and radiation exchange equations. A concept of macrosurfaces, each containing a number of radiating boundary surfaces, is introduced. These boundary macroelements then carry the information from the radiating boundary into the fluid regime. A number of simulations illustrating the algorithm are presented.
Instability of Toroidal Magnetic Field in Jets and Plerions
NASA Astrophysics Data System (ADS)
Begelman, Mitchell C.
1998-01-01
Astrophysical jets and pulsar-fed supernova remnants (plerions) are expected to develop highly organized magnetic structures dominated by concentric loops of toroidal field, Bφ. It has been argued that such structures could explain the polarization properties of some jets and contribute to their lateral confinement through magnetic tension forces. A concentric toroidal field geometry is also central to the Rees-Gunn model for the Crab Nebula, the archetypal plerion, and leads to the deduction that the Crab pulsar's wind must have a weak magnetic field. Yet this kind of equilibrium between magnetic and gas pressure forces, the ``equilibrium Z-pinch'' of the controlled fusion literature, is well known to be susceptible to disruptive localized instabilities, even when the magnetic field is weak and/or boundary conditions (e.g., a dense external medium) slow or suppress global modes. Thus, the magnetic field structures imputed to the interiors of jets and plerions are unlikely to persist for very long. To determine the growth rates of Z-pinch instabilities under astrophysical conditions, I derive a dispersion relation that is valid for the relativistic fluids of which jets and plerions may be composed, in the ideal magnetohydrodynamics (MHD) limit. The dominant instabilities are kink (m = 1) and pinch (m = 0) modes. The former generally dominate, destroying the concentric field structure and probably driving the system toward a more chaotic state in which the mean field strength is independent of radius (and in which resistive dissipation of the field may be enhanced). I estimate the timescales over which the field structure is likely to be rearranged and relate these to distances along relativistic jets and radii from the central pulsar in a plerion. I conclude that the central tenet of the Rees-Gunn model for the Crab Nebula, the existence of a concentric toroidal field well outside the pulsar wind's termination shock, is physically unrealistic. With this assumption
NASA Astrophysics Data System (ADS)
Im, Wonpil; Roux, Benoît
2001-09-01
A general method has been developed to include the electrostatic reaction field in Brownian dynamics (BD) simulations of ions diffusing through complex molecular channels of arbitrary geometry. Assuming that the solvent is represented as a featureless continuum dielectric medium, a multipolar basis-set expansion is developed to express the reaction field Green's function. A reaction field matrix, which provides the coupling between generalized multipoles, is calculated only once and stored before the BD simulations. The electrostatic energy and forces are calculated at each time step by updating the generalized multipole moments. The method is closely related to the generalized solvent boundary potential [Im et al., J. Chem. Phys. 114, 2924 (2001)] which was recently developed to include the influence of distant atoms on a small region part of a large macromolecular system in molecular dynamics simulations. It is shown that the basis-set expansion is accurate and computationally inexpensive for three simple models such as a spherical ionic system, an impermeable membrane system, and a cylindrical pore system as well as a realistic system such as OmpF porin with all atomic details. The influence of the static field and the reaction field on the ion distribution and conductance in the OmpF channel is studied and discussed.
PARTICLE-HOLE NATURE OF THE LIGHT HIGH-SPIN TOROIDAL ISOMERS
Staszczak, A.; Wong, Cheuk-Yin
2015-01-01
Nuclei under non-collective rotation with a large angular momentum above some threshold can assume a toroidal shape. In our previous work, we showed by using cranked Skyrme Hartree Fock approach that even even, N = Z, high-K, toroidal isomeric states may have general occurrences for light nuclei with 28 < A < 52. We present here some additional results and systematics on the particle-hole nature of these high-spin toroidal isomers.
Mirror theory applied to toroidal systems
Cohen, R.H.
1987-08-25
Central features of a mirror plasma are strong departures from Maxwellian distribution functions, ambipolar potentials and densities which vary along a field line, and losses, and the mirror field itself. To examine these features, mirror theorists have developed analytical and numerical techniques to solve the Fokker-Planck equation, evaluate the potentials consistent with the resulting distribution functions, and assess the microstability of these distributions. Various combinations of mirror-plasma fetures are present and important in toroidal plasmas as well, particularly in the edge region and in plasmas with strong r.f. heating. In this paper we survey problems in toroidal plasmas where mirror theory and computational techniques are applicable, and discuss in more detail three specific examples: calculation of the toroidal generalization of the Spitzer-Haerm distribution function (from which trapped-particle effects on current drive can be calculated), evaluation of the nonuniform potential and density set up by pulsed electron-cyclotron heating, and calculation of steady-state distribution functions in the presence of strong r.f. heating and collisions. 37 refs., 3 figs.
Toroidal plasma enhanced CVD of diamond films
Zvanya, John Cullen, Christopher Morris, Thomas Krchnavek, Robert R.; Holber, William Basnett, Andrew Basnett, Robert; Hettinger, Jeffrey
2014-09-01
An inductively coupled toroidal plasma source is used as an alternative to microwave plasmas for chemical vapor deposition of diamond films. The source, operating at a frequency of 400 kHz, synthesizes diamond films from a mixture of argon, methane, and hydrogen. The toroidal design has been adapted to create a highly efficient environment for diamond film deposition: high gas temperature and a short distance from the sample to the plasma core. Using a toroidal plasma geometry operating in the medium frequency band allows for efficient (≈90%) coupling of AC line power to the plasma and a scalable path to high-power and large-area operation. In test runs, the source generates a high flux of atomic hydrogen over a large area, which is favorable for diamond film growth. Using a deposition temperature of 900–1050 °C and a source to sample distance of 0.1–2.0 cm, diamond films are deposited onto silicon substrates. The results showed that the deposition rate of the diamond films could be controlled using the sample temperature and source to sample spacing. The results also show the films exhibit good-quality polycrystalline diamond as verified by Raman spectroscopy, x-ray diffraction, and scanning electron microscopy. The scanning electron microscopy and x-ray diffraction results show that the samples exhibit diamond (111) and diamond (022) crystallites. The Raman results show that the sp{sup 3} peak has a narrow spectral width (FWHM 12 ± 0.5 cm{sup −1}) and that negligible amounts of the sp{sup 2} band are present, indicating good-quality diamond films.
NASA Astrophysics Data System (ADS)
Rong, Y. M.; Chang, Y.; Huang, Y.; Zhang, G. J.; Shao, X. Y.
2015-12-01
There are few researches that concentrate on the prediction of the bead geometry for laser brazing with crimping butt. This paper addressed the accurate prediction of the bead profile by developing a generalized regression neural network (GRNN) algorithm. Firstly GRNN model was developed and trained to decrease the prediction error that may be influenced by the sample size. Then the prediction accuracy was demonstrated by comparing with other articles and back propagation artificial neural network (BPNN) algorithm. Eventually the reliability and stability of GRNN model were discussed from the points of average relative error (ARE), mean square error (MSE) and root mean square error (RMSE), while the maximum ARE and MSE were 6.94% and 0.0303 that were clearly less than those (14.28% and 0.0832) predicted by BPNN. Obviously, it was proved that the prediction accuracy was improved at least 2 times, and the stability was also increased much more.
Toroidal Flow Shear Driven turbulence and Transport
NASA Astrophysics Data System (ADS)
Wang, Weixing; Ethier, S.; Hinton, F. L.; Hahm, T. S.; Tang, W. M.
2012-10-01
New results from global nonlinear gyrokinetic simulations with the GTS code show that strong flow shear can drive a negative compressibility mode [1-3] unstable in tokamak geometry in some experimentally relevant parameter regimes. The modes reside in a low-k range, similar to that of ITG mode, with smaller but almost constant growth rate over a wider kθ range, while the mode frequency increases strongly with kθ. More interestingly, the flow shear modes show significantly finite k//, unlike ITG and TEM. The nonlinear energy transfer to longer wavelength via toroidal mode coupling and corresponding strong zonal flow and geodestic acoustic mode (GAM) generation are shown to play a critical role in the nonlinear saturation of the instability. The associated turbulence fluctuations can produce significant momentum and energy transport, including an intrinsic torque in the co-current direction. Remarkably, strong ``resonance'' in the fluctuations and associated transport peaks at the lowest order rational surfaces with integer q-number (rather than fractional), consistent with theoretical calculation. As a consequence, local ``corrugations'' are generated in all plasma profiles (temperatures, density and toroidal rotation), potentially impacting transport barrier formation near the rational surface. Discussions on flow optimization for minimizing plasma transport will be reported.[4pt] [1] N. Mattor and P. H. Diamond, Phys. Fluids 31, 1180 (1988).[0pt] [2] P. J. Catto et al., Phys. Fluids 16, 1719 (1973).[0pt] [3] M. Artun and W. M. Tang, Phys. Fluids B4, 1102 (1992).
Kinetic resonance damping rate of the toroidal ion temperature gradient mode
Kim, J.Y.; Kishimoto, Y.; Horton, W.; Tajima, T.
1993-09-01
The linear damping rates of the toroidal ion temperature gradient ({eta}{sub i}) mode due to the toroidal resonance are calculated in the local kinetic limit. The well-known Landau contour method is generalized to treat the analytic continuation problem of the guiding center dispersion function in the toroidal resonance system where the resonance occurs from both the magnetic {Delta}B-curvature drift and the parallel ion transit drift. A detailed numerical analysis is presented for the dependence of the damping rate of the toroidal {eta}{sub i} mode on various parameters such as {var_epsilon}{sub n}, {kappa}{sub y}, and the trapped electron fraction. In addition, a consideration is presented on the decay problem of the ballistic response by the phase mixing in the toroidal system, which is directly related to the present damping problem of the wave normal modes by the toroidal resonance.
NASA Astrophysics Data System (ADS)
Pfeifer, Christian
2016-01-01
We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian geometries and obtain Finslerian geodesic coordinates. They generalize normal coordinates known from metric geometry to Finsler geometric manifolds and it turns out that they are identical to the Douglas-Thomas normal coordinates introduced earlier. We expand the Finsler Lagrangian of a Finsler spacetime in these new coordinates and find that it is constant to quadratic order. The quadratic order term comes with the nonlinear curvature of the manifold. From physics these coordinates may be interpreted as the realisation of an Einstein elevator in Finslerian spacetime geometries.
Reduced-magnetohydrodynamic simulations of toroidally and poloidally localized edge localized modes
Hoelzl, M.; Guenter, S.; Mueller, W.-C.; Lackner, K.; Krebs, I.; Wenninger, R. P.; Huysmans, G. T. A.; Collaboration: ASDEX Upgrade Team
2012-08-15
We use the non-linear reduced-magnetohydrodynamic code JOREK to study edge localized modes (ELMs) in the geometry of the ASDEX Upgrade tokamak. Toroidal mode numbers, poloidal filament sizes, and radial propagation speeds of filaments into the scrape-off layer are in good agreement with observations for type-I ELMs in ASDEX Upgrade. The observed instabilities exhibit a toroidal and poloidal localization of perturbations which is compatible with the 'solitary magnetic perturbations' recently discovered in ASDEX Upgrade [R. Wenninger et al., 'Solitary magnetic perturbations at the ELM onset,' Nucl. Fusion (accepted)]. This localization can only be described in numerical simulations with high toroidal resolution.
Progress in toroidal confinement and fusion research
Furth, H.P.
1987-10-01
During the past 30 years, the characteristic T/sub i/n tau/sub E/-value of toroidal-confinement experiments has advanced by more than seven orders of magnitude. Part of this advance has been due to an increase of gross machine parameters. Most of this advance has been due to an increase of gross machine parameters. Most of the advance is associated with improvements in the ''quality of plasma confinement.'' The combined evidence of spherator and tokamak research clarifies the role of magnetic-field geometry in determining confinement and points to the importance of shielding out plasma edge effects. A true physical understanding of anomalous transport remains to be achieved. 39 refs., 11 figs., 1 tab.
Report for collisional and chaotic transport of energetic particles in toroidal plasma
Cary, J.R.; Shasharina, S.G.
1995-04-01
The authors have made progress in two general areas of confinement plasma physics. (1) We studies a new loss mechanism of the toroidally trapped particles related to the up-down asymmetry of ripple in a tokamak. (2) We estimated the bootstrap current of the particles making transitions between the toroidally and locally states in non-axisymmetric tori, stellarators and tokamaks.
Concentric Nested Toroidal Inflatable Structures
NASA Technical Reports Server (NTRS)
Johnson, Christopher J.; Raboin, Jasen L.; Spexarth, Gary R.
2010-01-01
Assemblies comprising multiple limited- height toroidal inflatable structures nested in a concentric arrangement have been invented to obtain more design flexibility than can be obtained in single taller, wider toroidal inflatable structures (see figure). Originally intended for use as containers for habitats for humans in outer space or on remote planets, these and related prior inflatable structures could also be useful on Earth as lightweight, compactly stowable, portable special-purpose buildings that could be transported to remote locations and there inflated to full size and shape. In the case of a single inflatable toroidal structure, one important source of lack of design flexibility is the fact that an increase in outer diameter (which is sometimes desired) is necessarily accompanied by an increase in height (which is sometimes undesired). Increases in diameter and height can also cause difficulty in utilization of the resulting larger volume, in that it can become necessary to partition the volume by means of walls and floors, and features (e.g., stairs or ladders) must be added to enable vertical movement between floors. Moreover, ascending and descending between floors in a gravitational environment could pose unacceptable difficulty for the inhabitants under some circumstances. Another source of lack of design flexibility in a single toroidal inflatable structure is that for a given inflation pressure, an increase in the outer diameter of the structure necessarily entails an increase in the maximum stress in the structure. Because it is necessary to keep the maximum stress within the load-bearing capability of the structural materials, consistent with other aspects of the design, this may translate to a limit on the outer diameter. In an assembly comprising concentric nested toroidal structures, an increase in outer diameter does not necessarily entail an increase in height or a maximum stress in excess of the load-bearing capability of the structural
Bellucci, S.; Saharian, A. A.; Bardeghyan, V. M.
2010-09-15
The vacuum expectation value of fermionic current is evaluated for a massive spinor field in spacetimes with an arbitrary number of toroidally compactified spatial dimensions in the presence of a constant gauge field. By using the Abel-Plana type summation formula and the zeta-function technique we present the fermionic current in two different forms. Nontrivial topology of the background spacetime leads to the Aharonov-Bohm effect for the fermionic current induced by the gauge field. The current is a periodic function of the magnetic flux with the period equal to the flux quantum. In the absence of gauge field it vanishes for special cases of untwisted and twisted fields. Applications of general formulas to Kaluza-Klein type models and to cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic flux the total fermionic current in carbon nanotubes vanishes, due to the cancellation of contributions from two different sublattices of the hexagonal lattice of graphene.
Material equations for electromagnetism with toroidal polarizations.
Dubovik, V M; Martsenyuk, M A; Saha, B
2000-06-01
With regard to the toroid contributions, a modified system of equations of electrodynamics moving continuous media has been obtained. Alternative formalisms to introduce the toroid moment contributions in the equations of electromagnetism has been worked out. The two four-potential formalism has been developed. Lorentz transformation laws for the toroid polarizations has been given. Covariant form of equations of electrodynamics of continuous media with toroid polarizations has been written. PMID:11088406
Induced geometry from disformal transformation
NASA Astrophysics Data System (ADS)
Yuan, Fang-Fang; Huang, Peng
2015-05-01
In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these results, we further propose a geometry which is naturally a generalization of Weyl geometry.
NASA Astrophysics Data System (ADS)
Bergmann, Ryan
general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP ha
Physics models in the toroidal transport code PROCTR
Howe, H.C.
1990-08-01
The physics models that are contained in the toroidal transport code PROCTR are described in detail. Time- and space-dependent models are included for the plasma hydrogenic-ion, helium, and impurity densities, the electron and ion temperatures, the toroidal rotation velocity, and the toroidal current profile. Time- and depth-dependent models for the trapped and mobile hydrogenic particle concentrations in the wall and a time-dependent point model for the number of particles in the limiter are also included. Time-dependent models for neutral particle transport, neutral beam deposition and thermalization, fusion heating, impurity radiation, pellet injection, and the radial electric potential are included and recalculated periodically as the time-dependent models evolve. The plasma solution is obtained either in simple flux coordinates, where the radial shift of each elliptical, toroidal flux surface is included to maintain an approximate pressure equilibrium, or in general three-dimensional torsatron coordinates represented by series of helical harmonics. The detailed coupling of the plasma, scrape-off layer, limiter, and wall models through the neutral transport model makes PROCTR especially suited for modeling of recycling and particle control in toroidal plasmas. The model may also be used in a steady-state profile analysis mode for studying energy and particle balances starting with measured plasma profiles.
Topology of tokamak plasma equilibria with toroidal current reversal
Rodrigues, Paulo; Bizarro, Joao P. S.
2012-01-15
Some general principles about scalar functions with critical points are used to rigorously ascertain that magnetic equilibria with both toroidal current reversal and nested magnetic surfaces are atypical solutions and highly unstable to arbitrary perturbations of boundary conditions and other parameters. The cause for such is shown to lie in the condition of nested magnetic surfaces and not in the possibility of current reversal and consequent vanishing of the poloidal field inside the plasma. Rather than supporting the claim that instability against experimentally driven perturbations forbids configurations with toroidal current reversal, it is argued that these can be attained if an axisymmetric island system is allowed for in order to break the condition of nested magnetic surfaces. A number of results previously reported in the literature are discussed and reinterpreted under the proposed framework, providing some physical insight on the nature of equilibria with toroidal current reversal.
Perturbing macroscopic magnetohydrodynamic stability for toroidal plasmas
NASA Astrophysics Data System (ADS)
Comer, Kathryn J.
We have introduced a new perturbative technique to rapidly explore the dependence of long wavelength ideal magnetohydrodynamic (MHD) instabilities on equilibrium profiles, shaping properties, and wall parameters. Traditionally, these relations are studied with numerical parameter scans using computationally intensive stability codes. Our perturbative technique first finds the equilibrium and stability using traditional methods. Subsequent small changes in the original equilibrium parameters change the stability. We quickly find the new stability with an expansion of the energy principle, rather than with another run of the stability codes. We first semi-analytically apply the technique to the screw pinch after eliminating compressional Alfven wave effects. The screw pinch results validate the approach, but also indicate that allowable perturbations to equilibria with certain features may be restricted. Next, we extend the approach to toroidal geometry using experimental equilibria and a simple constructed equilibrium, with the ideal MHD stability code GATO. Stability properties are successfully predicted from perturbed toroidal equilibria when only the vacuum beyond the plasma is perturbed (through wall parameter variations), rather than the plasma itself. Small plasma equilibrium perturbations to both experimental and simple equilibria result in very large errors to the predicted stability, and valid results are found only over a narrow range of most perturbations. Despite the large errors produced when changing plasma parameters, the wall perturbations revealed two useful applications of this technique. Because the calculations are non-iterative matrix multiplications, the convergence issues that can disrupt a full MHD stability code are absent. Marginal stability, therefore, is much easier to find with the perturbative technique. Also, the perturbed results can be input as the initial guess for the eigenvalue for a full stability code, and improve subsequent
Electromagnetic Torque in Tokamaks with Toroidal Asymmetries
NASA Astrophysics Data System (ADS)
Logan, Nikolas Christopher
Toroidal rotation and rotation shear strongly influences stability and confinement in tokamaks. Breaking of the toroidal symmetry by fields orders of magnitude smaller than the axisymmetric field can, however, produce electromagnetic torques that significantly affect the plasma rotation, stability and confinement. These electromagnetic torques are the study of this thesis. There are two typical types of electromagnetic torques in tokamaks: 1) "resonant torques" for which a plasma current defined by a single toroidal and single poloidal harmonic interact with external currents and 2) "nonresonant torques" for which the global plasma response to nonaxisymmetric fields is phase shifted by kinetic effects that drive the rotation towards a neoclassical offset. This work describes the diagnostics and analysis necessary to evaluate the torque by measuring the rate of momentum transfer per unit area in the vacuum region between the plasma and external currents using localized magnetic sensors to measure the Maxwell stress. These measurements provide model independent quantification of both the resonant and nonresonant electromagnetic torques, enabling direct verification of theoretical models. Measured values of the nonresonant torque are shown to agree well with the perturbed equilibrium nonambipolar transport (PENT) code calculation of torque from cross field transport in nonaxisymmetric equilibria. A combined neoclassical toroidal viscosity (NTV) theory, valid across a wide range of kinetic regimes, is fully implemented for the first time in general aspect ratio and shaped plasmas. The code captures pitch angle resonances, reproducing previously inaccessible collisionality limits in the model. The complete treatment of the model enables benchmarking to the hybrid kinetic MHD stability codes MARS-K and MISK, confirming the energy-torque equivalency principle in perturbed equilibria. Experimental validations of PENT results confirm the torque applied by nonaxisymmetric
NASA Astrophysics Data System (ADS)
Yazgan, Efe; Taşci, Emre; Erkoç, Şakir
An algorithm to generate toroidal or helical cage structures has been developed. Any toroidal or helical structure can be generated following four stages. In the first stage a Fonseca type unit cell and its symmetrical counterpart is formed which represents one-fifth of a toroid. In the second stage one-fifth fragment of the torus is fully obtained by applying geometry optimization to the structure obtained in the first stage. In the third stage the torus fragment obtained in the second stage is reproduced five times and connected to each other to generate either toroidal or helical structure. In the last stage a final optimization process is reapplied to get the complete structure desired.
Toroidal momentum transport in a tokamak due to profile shearing
Buchholz, R.; Grosshauser, S. R.; Hornsby, W. A.; Migliano, P.; Peeters, A. G.; Camenen, Y.; Casson, F. J.
2014-06-15
The effect of profile shearing on toroidal momentum transport is studied in linear and non-linear gyro-kinetic simulations. Retaining the radial dependence of both plasma and geometry parameters leads to a momentum flux that has contributions both linear in the logarithmic gradients of density and temperature, as well as contributions linear in the derivatives of the logarithmic gradients. The effect of the turbulence intensity gradient on momentum transport is found to be small for the studied parameters. Linear simulations at fixed normalized toroidal wave number predict a weak dependence of the momentum flux on the normalized Larmor radius ρ{sub *}=ρ/R. Non-linear simulations, however, at sufficiently small ρ{sub *} show a linear scaling of the momentum flux with ρ{sub *}. The obtained stationary rotation gradients are in the range of, although perhaps smaller than, current experiments. For a reactor plasma, however, a rather small rotation gradient should result from profile shearing.
Prospects for toroidal fusion reactors
Sheffield, J.; Galambos, J.D.
1994-06-01
Work on the International Thermonuclear Experimental Reactor (ITER) tokamak has refined understanding of the realities of a deuterium-tritium (D-T) burning magnetic fusion reactor. An ITER-like tokamak reactor using ITER costs and performance would lead to a cost of electricity (COE) of about 130 mills/kWh. Advanced tokamak physics to be tested in the Toroidal Physics Experiment (TPX), coupled with moderate components in engineering, technology, and unit costs, should lead to a COE comparable with best existing fission systems around 60 mills/kWh. However, a larger unit size, {approximately}2000 MW(e), is favored for the fusion system. Alternative toroidal configurations to the conventional tokamak, such as the stellarator, reversed-field pinch, and field-reversed configuration, offer some potential advantage, but are less well developed, and have their own challenges.
Experimental studies of compact toroids
Not Available
1991-01-01
The Berkeley Compact Toroid Experiment (BCTX) device is a plasma device with a Marshall-gun generated, low aspect ratio toroidal plasma. The device is capable of producing spheromak-type discharges and may, with some modification, produce low-aspect ratio tokamak configurations. A unique aspect of this experimenal devie is its large lower hybrid (LH) heating system, which consists of two 450MHz klystron tubes generating 20 megawatts each into a brambilla-type launching structure. Successful operation with one klystron at virtually full power (18 MW) has been accomplished with 110 {mu}s pulse length. A second klystron is currently installed in its socket and magnet but has not been added to the RF drive system. This report describes current activities and accomplishments and describes the anticipated results of next year's activity.
Bounds on the local energy density of holographic CFTs from bulk geometry
NASA Astrophysics Data System (ADS)
Fischetti, Sebastian; Hickling, Andrew; Wiseman, Toby
2016-11-01
The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the local energy density in static states of holographic (2+1)-dimensional CFTs living on a closed (but otherwise generally curved) spatial geometry. We allow for the presence of a marginal scalar deformation, dual to a massless scalar field in the bulk. For certain vacuum states in which the bulk geometry is well-behaved at zero temperature, we find that the bulk equations of motion imply that the local energy density integrated over specific boundary domains is negative. In the absence of scalar deformations, we use the inverse mean curvature flow to show that if the CFT spatial geometry has spherical topology but non-constant curvature, the local energy density must be positive somewhere. This result extends to other topologies, but only for certain types of vacuum; in particular, for a generic toroidal boundary, the vacuum’s bulk dual must be the zero-temperature limit of a toroidal black hole.
Toroidal Flow in Tokamak Plasmas
NASA Astrophysics Data System (ADS)
Callen, J. D.; Cole, A. J.; Hegna, C. C.
2007-11-01
Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial diffusion due to axisymmetric neoclassical, paleoclassical and anomalous transport are usually considered. In addition, the toroidal flow can be affected by field errors. Small, non-axisymmetric field errors arise from coil irregularities, active control coils and collective plasma magnetic distortions (e.g., NTMs, RWMs). Resonant field errors cause localized electromagnetic torques near rational surfaces in the plasma, which can lock the plasma to the wall leading to magnetic islands and reduced confinement or disruptions. Their penetration into the plasma is limited by flow-shielding effects; but they can be amplified by the plasma response at high beta. Non-resonant field errors cause magnetic pumping and radial banana drifts, and lead to toroidal flow damping over the entire plasma. Many of these processes can also produce momentum pinch and intrinsic flow effects. This poster will seek to present a coherent picture of all these effects and suggest ways they could be tested and distinguished experimentally.
NASA Astrophysics Data System (ADS)
Bergmann, Ryan
general 3D geometries on GPUs, but compared to production codes like Serpent and MCNP, WARP has limited capabilities. Despite WARP's lack of features, its novel algorithm implementations show that high performance can be achieved on a GPU despite the inherently divergent program flow and sparse data access patterns. WARP is not ready for everyday nuclear reactor calculations, but is a good platform for further development of GPU-accelerated Monte Carlo neutron transport. In it's current state, it may be a useful tool for multiplication factor searches, i.e. determining reactivity coefficients by perturbing material densities or temperatures, since these types of calculations typically do not require many flux tallies. (Abstract shortened by UMI.)
Toroidal midplane neutral beam armor and plasma limiter
Kugel, H.W.; Hand, S.W. Jr.; Ksayian, H.
1985-05-31
This invention contemplates an armor shield/plasma limiter positioned upon the inner wall of a toroidal vacuum chamber within which is magnetically confined an energetic plasma in a tokamak nuclear fusion reactor. The armor shield/plasma limiter is thus of a general semi-toroidal shape and is comprised of a plurality of adjacent graphite plates positioned immediately adjacent to each other so as to form a continuous ring upon and around the toroidal chamber's inner wall and the reactor's midplane coil. Each plate has a generally semi-circular outer circumference and a recessed inner portion and is comprised of upper and lower half sections positioned immediately adjacent to one another along the midplane of the plate. With the upper and lower half sections thus joined, a channel or duct is provided within the midplane of the plate in which a magnetic flux loop is positioned. The magnetic flux loop is thus positioned immediately adjacent to the fusing toroidal plasma and serves as a diagnostic sensor with the armor shield/plasma limiter minimizing the amount of power from the energetic plasma as well as from the neutral particle beams heating the plasma incident upon the flux loop.
ERIC Educational Resources Information Center
Fahlgren, Maria; Brunström, Mats
2014-01-01
The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…
Toroidal cell and battery. [Patent application
Nagle, W.J.
1981-04-01
A toroidal storage battery designed to handle relatively high amp-hour loads is described. The cell includes a wound core disposed within a pair of toroidal channel shaped electrodes spaced apart by nylon insulator. The shape of the case electrodes of this toroidal cell allows a first planar doughnut shaped surface and the inner cylindrical case wall to be used as a first electrode and a second planar doughnut shaped surface and the outer cylindrical case wall to be used as a second electrode. Connectors may be used to stack two or more toroidal cells together by connecting substantially the entire surface area of the first electrode of a first cell to substantially the entire surface area of the second electrode of a second cell. The central cavity of each toroidal cell may be used as a conduit for pumping a fluid through the toroidal cell to thereby cool the cell. Official Gazette of the U.S. Patent and Trademark Office
Transport and Dynamics in Toroidal Fusion Systems
Schnack, Dalton D
2006-05-16
This document reports the successful completion of the OFES Theory Milestone for FY2005, namely, Perform parametric studies to better understand the edge physics regimes of laboratory experiments. Simulate at increased resolution (up to 20 toroidal modes), with density evolution, late into the nonlinear phase and compare results from different types of edge modes. Simulate a single case including a study of heat deposition on nearby material walls. The linear stability properties and nonlinear evolution of Edge Localized Modes (ELMs) in tokamak plasmas are investigated through numerical computation. Data from the DIII-D device at General Atomics (http://fusion.gat.com/diii-d/) is used for the magnetohydrodynamic (MHD) equilibria, but edge parameters are varied to reveal important physical effects. The equilibrium with very low magnetic shear produces an unstable spectrum that is somewhat insensitive to dissipation coefficient values. Here, linear growth rates from the non-ideal NIMROD code (http://nimrodteam.org) agree reasonably well with ideal, i.e. non-dissipative, results from the GATO global linear stability code at low toroidal mode number (n) and with ideal results from the ELITE edge linear stability code at moderate to high toroidal mode number. Linear studies with a more realistic sequence of MHD equilibria (based on DIII-D discharge 86166) produce more significant discrepancies between the ideal and non-ideal calculations. The maximum growth rate for the ideal computations occurs at toroidal mode index n=10, whereas growth rates in the non-ideal computations continue to increase with n unless strong anisotropic thermal conduction is included. Recent modeling advances allow drift effects associated with the Hall electric field and gyroviscosity to be considered. A stabilizing effect can be observed in the preliminary results, but while the distortion in mode structure is readily apparent at n=40, the growth rate is only 13% less than the non-ideal MHD
Anomalous toroidal field penetration in Tormac V
Feinberg, B.; Vaucher, B.G.; Shaw, R.S.; Vella, M.C.
1981-07-01
Magnetic field penetration into a cool, collisional, magnetized plasma has been investigated in Tormac V. Magnetic probe and laser interferometer studies reveal anomalous penetration of the applied toroidal field into a plasma with an initial parallel bias toroidal field. The applied poloidal field, however, formed a well-defined magnetic front which was effective at sweeping up particles. Strong shear in the vacuum magnetic field does not inhibit the apparent decoupling of the applied toroidal field from the applied poloidal field.
Anomalous toroidal field penetration in Tormac V
Feinberg, B.; Vaucher, B. G.; Shaw, R. S.; Vella, M. C.
1981-07-01
We investigate magnetic field penetration into a cool, collisional, magnetized plasma in Tormac V. Magnetic probe and laser interferometer studies reveal anomalous penetration of the applied toroidal field into a plasma with an initial parallel bias toroidal field. The applied poloidal field, however, formed a well-defined magnetic front which was effective at sweeping up particles. Lastly, strong shear in the vacuum magnetic field does not inhibit the apparent decoupling of the applied toroidal field from the applied poloidal field.
ATF (Advanced Toroidal Facility) data management
Kannan, K.L.; Baylor, L.R.
1988-01-01
Data management for the Advanced Toroidal Facility (ATF), a stellarator located at Oak Ridge National Laboratory (ORNL), is provided by DMG, a locally developed, VAX-based software system. DMG is a data storage and retrieval software system that provides the user interface to ATF raw and analyzed data. Data are described in terms of data models and data types and are organized as signals into files, which are internally documented. The system was designed with user accessibility, software maintainability, and extensibility as primary goals. Extensibility features include compatibility with ATF as it moves from pulsed to steady-state operation and capability for use of the DMG system with experiments other than ATF. DMG is implemented as a run-time library of routines available as a shareable image. General-purpose and specialized data acquisition and analysis applications have been developed using the DMG system. This paper describes the DMG system and the interfaces to it. 4 refs., 2 figs.
NASA Astrophysics Data System (ADS)
Pfefferlé, D.; Graves, J. P.; Cooper, W. A.
2015-05-01
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).
Toroidal transformer design program with application to inverter circuitry
NASA Technical Reports Server (NTRS)
Dayton, J. A., Jr.
1972-01-01
Estimates of temperature, weight, efficiency, regulation, and final dimensions are included in the output of the computer program for the design of transformers for use in the basic parallel inverter. The program, written in FORTRAN 4, selects a tape wound toroidal magnetic core and, taking temperature, materials, core geometry, skin depth, and ohmic losses into account, chooses the appropriate wire sizes and number of turns for the center tapped primary and single secondary coils. Using the program, 2- and 4-kilovolt-ampere transformers are designed for frequencies from 200 to 3200 Hz and the efficiency of a basic transistor inverter is estimated.
Ideal MHD stability calculations in axisymmetric toroidal coordinate systems
Grimm, R.C.; Dewar, R.L.; Manickam, J.
1982-03-01
A scalar form of the ideal MHD energy principle is shown to provide a more accurate and efficient numerical method for determining the stability of an axisymmetric toroidal equilibrium than the usual vector form. Additional improvement is obtained by employing a class of straight magnetic field line flux coordinates which allow for an optimal choice of the poloidal angle in the minor cross section of the torus. The usefulness of these techniques is illustrated by a study (using a new code, PEST 2) of the convergence properties of the finite element Galerkin representation in tokamak and spheromak geometries, and by the accurate determination of critical ..beta.. values for ballooning modes.
Fabrication of toroidal composite pressure vessels. Final report
Dodge, W.G.; Escalona, A.
1996-11-24
A method for fabricating composite pressure vessels having toroidal geometry was evaluated. Eight units were fabricated using fibrous graphite material wrapped over a thin-walled aluminum liner. The material was wrapped using a machine designed for wrapping, the graphite material was impregnated with an epoxy resin that was subsequently thermally cured. The units were fabricated using various winding patterns. They were hydrostatically tested to determine their performance. The method of fabrication was demonstrated. However, the improvement in performance to weight ratio over that obtainable by an all metal vessel probably does not justify the extra cost of fabrication.
Plastic Finite Element Analysis of D0 Toroid Iron Welds
Wands, R.; /Fermilab
1987-11-23
The assembly of the DO toroid iron involves the use of large groove welds to connect massive blocks of steel. These welds are very heavily constrained, and large thermal strains develop which have produced large cracks in the base metal near the weld. The effort to solve these problems has involved investigations of weld geometry, weld preparation, and the metallurgy of both the base metal and the welding rod. The purpose of this analysis was to compare the effects of two welding rods with markedly different yield strengths and post-yieding behaviour on the plastic strains developed in the base metal near the weld.
Turbulent equipartition theory of toroidal momentum pinch
Hahm, T. S.; Rewoldt, G.; Diamond, P. H.; Gurcan, O. D.
2008-05-15
The mode-independent part of the magnetic curvature driven turbulent convective (TurCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14, 072302 (2007)], which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of 'magnetically weighted angular momentum density', nm{sub i}U{sub parallel}R/B{sup 2}, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustrated that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms that exist in a simpler geometry.
Turbulent Equipartition Theory of Toroidal Momentum Pinch
T.S. Hahm, P.H. Diamond, O.D. Gurcan, and G. Rewaldt
2008-01-31
The mode-independet part of magnetic curvature driven turbulent convective (TuroCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14,072302 (2007)] which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of "magnetically weighted angular momentum density," nmi U|| R/B2, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustratd that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms which exist in a simpler geometry.
Point vortex interactions on a toroidal surface
NASA Astrophysics Data System (ADS)
Sakajo, Takashi; Shimizu, Yuuki
2016-07-01
Owing to non-constant curvature and a handle structure, it is not easy to imagine intuitively how flows with vortex structures evolve on a toroidal surface compared with those in a plane, on a sphere and a flat torus. In order to cultivate an insight into vortex interactions on this manifold, we derive the evolution equation for N-point vortices from Green's function associated with the Laplace-Beltrami operator there, and we then formulate it as a Hamiltonian dynamical system with the help of the symplectic geometry and the uniformization theorem. Based on this Hamiltonian formulation, we show that the 2-vortex problem is integrable. We also investigate the point vortex equilibria and the motion of two-point vortices with the strengths of the same magnitude as one of the fundamental vortex interactions. As a result, we find some characteristic interactions between point vortices on the torus. In particular, two identical point vortices can be locally repulsive under a certain circumstance.
Toroidal plasma equilibrium with gravity
Yoshikawa, S.
1980-09-01
Toroidal magnetic field configuration in a gravitational field is calculated both from a simple force-balance and from the calculation using magnetic surfaces. The configuration is found which is positionally stable in a star. The vibrational frequency near the equilibrium point is proportional to the hydrostatic frequency of a star multiplied by the ratio (W/sub B//W/sub M/)/sup 1/2/ where W/sub B/ is the magnetic field energy density, and W/sub M/ is the material pressure at the equilibrium point. It is proposed that this frequency may account for the observed solar spot cycles.
Toroidal current asymmetry in tokamak disruptions
Strauss, H. R.
2014-10-15
It was discovered on JET that disruptions were accompanied by toroidal asymmetry of the toroidal plasma current I{sub ϕ}. It was found that the toroidal current asymmetry was proportional to the vertical current moment asymmetry with positive sign for an upward vertical displacement event (VDE) and negative sign for a downward VDE. It was observed that greater displacement leads to greater measured I{sub ϕ} asymmetry. Here, it is shown that this is essentially a kinematic effect produced by a VDE interacting with three dimensional MHD perturbations. The relation of toroidal current asymmetry and vertical current moment is calculated analytically and is verified by numerical simulations. It is shown analytically that the toroidal variation of the toroidal plasma current is accompanied by an equal and opposite variation of the toroidal current flowing in a thin wall surrounding the plasma. These currents are connected by 3D halo current, which is π/2 radians out of phase with the n = 1 toroidal current variations.
Toroidal dipolar response in a metamaterial.
Kaelberer, T; Fedotov, V A; Papasimakis, N; Tsai, D P; Zheludev, N I
2010-12-10
Toroidal multipoles are fundamental electromagnetic excitations different from those associated with the familiar charge and magnetic multipoles. They have been held responsible for parity violation in nuclear and particle physics, but direct evidence of their existence in classical electrodynamics has remained elusive. We report on the observation of a resonant electromagnetic response in an artificially engineered medium, or metamaterial, that cannot be attributed to magnetic or charge multipoles and can only be explained by the existence of a toroidal dipole. Our direct experimental evidence of the toroidal response brings attention to the often ignored electromagnetic interactions involving toroidal multipoles, which could be present in naturally occurring systems, especially at the macromolecule level, where toroidal symmetry is ubiquitous.
Asymmetric Magnon Excitation by Spontaneous Toroidal Ordering
NASA Astrophysics Data System (ADS)
Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi
2016-05-01
The effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from the antisymmetric spin-orbit coupling and the multiorbital correlation effect. We show that the model exhibits a Néel-type antiferromagnetic order, which simultaneously accompanies a ferroic toroidal order. We find that the occurrence of toroidal order modulates the magnon dispersion in an asymmetric way with respect to the wave number: a toroidal dipole order on the zigzag chain leads to a band-bottom shift, while a toroidal octupole order on the honeycomb lattice gives rise to a valley splitting. These asymmetric magnon excitations could be a source of unusual magnetic responses, such as nonreciprocal magnon transport. A variety of modulations are discussed while changing the lattice and magnetic symmetries. The implications regarding candidate materials for asymmetric magnon excitations are presented.
Cutoff frequency of toroidal plasma waveguide
Zakeri-Khatir, H.; Aghamir, F. M.
2015-02-15
The cutoff frequencies of E and H-modes of empty and plasma filled toroidal waveguides are evaluated. The effects of space curvature and plasma density on cutoff frequencies for both modes are investigated. Using a suitable variable change, a scalar wave equation in the direction of propagation was obtained. The study indicates that the curvature in the direction of wave propagation in toroidal waveguide has an analogous effect as a straight waveguide filled with anisotropic media. The Rayleigh-Schrodinger perturbation method was employed to solve for cutoff frequencies in the first order of approximation. In the limit of small space curvature, the toroidal waveguide cutoff frequencies for both E and H-modes approach those of TM and TE modes of empty cylindrical waveguide with a radius equal to toroidal waveguide minor radius. The analysis shows that the curvature in the direction of propagation in toroidal waveguides leads to the removal of the degeneracy between E and H-modes.
Tokamak with mechanical compression of toroidal magnetic field
Ohkawa, Tihiro
1981-01-01
A tokamak apparatus includes a pressure vessel for defining a reservoir and confining liquid therein. A collapsible toroidal liner disposed within the pressure vessel defines a toroidal space within the liner. Liquid metal fills the reservoir outside said liner. A toroidal magnetic field is developed within the toroidal space about the major axis thereof. A toroidal plasma is developed within the toroidal space about the major axis thereof. Pressure is applied to the liquid metal to collapse the liner and reduce the volume of the toroidal space, thereby increasing the toroidal magnetic flux density therein.
Closed expressions for the magnetic field of toroidal multipole configurations
Sheffield, G.V.
1983-04-01
Closed analytic expressions for the vector potential and the magnetic field for the lower order toroidal multipoles are presented. These expressions can be applied in the study of tokamak plasma cross section shaping. An example of such an application is included. These expressions also allow the vacuum fields required for plasma equilibrium to be specified in a general form independent of a particular coil configuration.
Radial Eigenmodes for a Toroidal Waveguide with Rectangular Cross Section
Rui Li
2012-07-01
In applying mode expansion to solve the CSR impedance for a section of toroidal vacuum chamber with rectangular cross section, we identify the eigenvalue problem for the radial eigenmodes which is different from that for cylindrical structures. In this paper, we present the general expressions of the radial eigenmodes, and discuss the properties of the eigenvalues on the basis of the Sturm-Liouville theory.
Antenna excitation of drift wave in a toroidal plasma
Diallo, A.; Ricci, P.; Fasoli, A.; Furno, I.; Labit, B.; Mueller, S. H.; Podesta, M.; Poli, F. M.; Skiff, F.
2007-10-15
In a magnetized toroidal plasma, an antenna tunable in vertical wave number is used to excite density perturbations. Coherent detection is performed by means of Langmuir probes to directly determine both the wave vector and the plasma response induced by the antenna. Comparison between the theoretical density response predicted by the generalized Hasegawa-Wakatani model, and the experimentally determined density response enables us the identification of one peak of the plasma response as a drift wave.
Development of Toroidal Core Transformers
Leon, Francisco
2014-05-31
The original objective of this project was to design, build and test a few prototypes of singlephase dry-type distribution transformers of 25 kVA, 2.4 kV primary to 120 V transformers using cores made of a continuous steel strip shaped like a doughnut (toroid). At different points during the development of the project, the scope was enhanced to include the more practical case of a 25 kVA transformer for a 13.8 kV primary system voltage. Later, the scope was further expanded to design and build a 50 kVA unit to transformer voltage from 7.62 kV to 2x120 V. This is a common transformer used by Con Edison of New York and they are willing to test it in the field. The project officially started in September 2009 and ended in May 2014. The progress was reported periodically to DOE in eighteen quarterly reports. A Continuation Application was submitted to DOE in June 2010. In May 2011 we have requested a non-cost extension of the project. In December 2011, the Statement of Project Objectives (SOPO) was updated to reflect the real conditions and situation of the project as of 2011. A second Continuation Application was made and funding was approved in 2013 by DOE and the end date was extended to May 2014.The technical challenges that were overcome in this project include: the development of the technology to pass the impulse tests, derive a model for the thermal performance, produce a sound mechanical design, and estimate the inrush current. However, the greatest challenge that we faced during the development of the project was the complications of procuring the necessary parts and materials to build the transformers. The actual manufacturing process is relatively fast, but getting all parts together is a very lengthy process. The main products of this project are two prototypes of toroidal distribution transformers of 7.62 kV (to be used in a 13.8 kV system) to 2x120 V secondary (standard utilization voltage); one is rated at 25 kVA and the other at 50 kVA. The 25 k
Gyrokinetic analysis of shear flow instability in torodial geometry
NASA Astrophysics Data System (ADS)
Yoon, Eisung; Hahm, T. S.
2008-11-01
Motivated by recent observation of intrinsic rotation in tokamak plasmas, we study linear stability of ion gyroradius scale short wavelength fluctuations in the presence of sheared parallel flow, ion temperature gradient, and toroidal mode coupling. Our gyrokinetic approach in toroidal geometry is an extension of previous studies including those by Catto et al., [Phys. Fluids 16 1719 (1973)] Mattor and Diamond [Phys. Fluids 31 1180 (1988)], and Artun and Tang [Phys. Fluids B 4 1102 (1992)].
NCSX Toroidal Field Coil Design
Kalish, M.; Rushinski, J.; Myatt, L.; Brooks, A.; Dahlgren, F.; Chrzanowski, J.; Reiersen, W.; Freudenberg, K.
2005-10-07
The National Compact Stellarator Experiment (NCSX) is an experimental device whose design and construction is underway at the Department of Energy's Princeton Plasma Physics Laboratory (PPPL). The primary coil systems for the NCSX device consist of the twisted plasma-shaping Modular Coils, the Poloidal Field Coils, and the Toroidal Field (TF) Coils. The TF Coils are D-shaped coils wound from hollow copper conductor, and vacuum impregnated with a glass-epoxy resin system. There are 18 identical, equally spaced TF coils providing 1/R field at the plasma. They operate within a cryostat, and are cooled by LN2, nominally, to 80K. Wedge shaped castings are assembled to the inboard face of these coils, so that inward radial loads are reacted via the nesting of each of the coils against their adjacent partners. This paper outlines the TF Coil design methodology, reviews the analysis results, and summarizes how the design and analysis support the design requirements.
Dual-band toroidal-dipole-induced transparency in optical regime
NASA Astrophysics Data System (ADS)
Li, Jie; Dong, Zheng-Gao; Zhu, Ming-Jie; Shao, Jian; Wang, Ying-Hua; Li, Jia-Qi
2016-09-01
The interference between toroidal and electric dipoles in the optical regime is investigated in a metallic composite metastructure composed of a 12-fold double-bar and an upright rod. It shows that toroidal and electric dipoles can be simultaneously excited, exhibiting a plasmon analog of electromagnetically induced transparency (EIT) and suppressing the far-field radiation. By shifting the upright rod transversally, another transparency window emerges due to the asymmetry of the geometry, resulting in dual-band EIT-like behavior. The result not only contributes to the understanding of optical toroidal dipoles, but also creates the possibility of designing optical devices based on the dual-band EIT-like effect.
Li, Hai-ming; Liu, Shao-bin Liu, Si-yuan; Ding, Guo-wen; Yang, Hua; Yu, Zhi-yang; Zhang, Hai-feng; Wang, Shen-yun
2015-02-23
In this paper, a low-loss and high transmission analogy of electromagnetically induced transparency based on electric toroidal dipolar response is numerically and experimentally demonstrated. It is obtained by the excitation of the low-loss electric toroidal dipolar response, which confines the magnetic field inside a dielectric substrate with toroidal geometry. The metamaterial electromagnetically induced transparency (EIT) structure is composed of the cut wire and asymmetric split-ring resonators. The transmission level is as high as 0.88, and the radiation loss is greatly suppressed, which can be proved by the surface currents distributions, the magnetic field distributions, and the imaginary parts of the effective permeability and permittivity. It offers an effective way to produce low-loss and high transmission metamaterial EIT.
Poloidal field amplification in a coaxial compact toroid accelerator
NASA Astrophysics Data System (ADS)
Horton, R. D.; Hwang, D. Q.; Howard, S.; Brockington, S. J.; Evans, R. W.
2008-09-01
The Compact Toroid Injection Experiment (CTIX) produces spheromak-like compact toroids (SCTs) without external power switching, initiating a discharge by pulsed gas injection into a formation region containing a seed magnetic field generated by a solenoidal coil. After formation, the plasma is driven by an inductively delayed capacitor bank into an acceleration region, where surface axial and toroidal magnetic fields are measured at several axial positions. Due to strong eddy-current effects, formation-region magnetic field cannot be simply computed; instead, it is measured using the response of axial and radial test coils in the formation region to short solenoid test current pulses. A temporal and spatial reconstruction method is developed allowing formation-region field to be computed from the test-coil data for any CTIX discharge of identical solenoid geometry. By varying the peak value and timing of solenoidal current, curves of peak accelerator-region field as a function of initial formation-region field are developed. Curves of peak accelerator-region axial magnetic field are thereby found to be highly nonlinear functions of formation-region field, showing a threshold value for the formation-region field of approximately 5 G, above which acceleration-region field saturates at values between 2 and 12 kG. The direction of acceleration-region axial field reverses sign when the direction of solenoid current is reversed. Saturated accelerator-region axial field is a function of axial position and accelerator voltage, and is typically comparable to toroidal field at the same location. The ratio of accelerator-region to formation-region axial field commonly exceeds 1000 near the onset of saturation. This large amplification is of practical advantage for delayed plasma breakdown on CTIX, allowing a modest seed field to produce high poloidal fields, which are necessary for intense SCT acceleration. The results may also provide a useful benchmark for numerical
Johnson-Kendall-Roberts adhesive contact for a toroidal indenter
NASA Astrophysics Data System (ADS)
Argatov, Ivan; Li, Qiang; Pohrt, Roman; Popov, Valentin L.
2016-07-01
The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson-Kendall-Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber's concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.
MINERVA: Ideal MHD stability code for toroidally rotating tokamak plasmas
NASA Astrophysics Data System (ADS)
Aiba, N.; Tokuda, S.; Furukawa, M.; Snyder, P. B.; Chu, M. S.
2009-08-01
A new linear MHD stability code MINERVA is developed for investigating a toroidal rotation effect on the stability of ideal MHD modes in tokamak plasmas. This code solves the Frieman-Rotenberg equation as not only the generalized eigenvalue problem but also the initial value problem. The parallel computing method used in this code realizes the stability analysis of both long and short wavelength MHD modes in short time. The results of some benchmarking tests show the validity of this MINERVA code. The numerical study with MINERVA about the toroidal rotation effect on the edge MHD stability shows that the rotation shear destabilizes the intermediate wavelength modes but stabilizes the short wavelength edge localized MHD modes, though the rotation frequency destabilizes both the long and the short wavelength MHD modes.
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A; Plecháč, Petr
2015-08-28
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Plecháč, Petr
2015-08-28
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
Zonal Toroidal Harmonic Expansions of External Gravitational Fields for Ring-like Objects
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2016-08-01
We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace’s equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000–10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.
Zonal Toroidal Harmonic Expansions of External Gravitational Fields for Ring-like Objects
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2016-08-01
We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace’s equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000-10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.
NASA Astrophysics Data System (ADS)
Lee, H. H.; Seol, J.; Ko, W. H.; Terzolo, L.; Aydemir, A. Y.; In, Y.; Ghim, Y.-c.; Lee, S. G.
2016-08-01
Effects of neoclassical toroidal viscosity (NTV) induced by intrinsic error fields and toroidal field ripple on cocurrent toroidal rotation in H-mode tokamak plasmas are investigated. It is expected that large NTV torque can be localized at the edge region through the 1/ν-regime in the vicinity of E r ˜ 0 in the cocurrent rotating H-mode plasma. Numerical simulation on toroidal rotation demonstrates that the edge localized NTV torque determined by the intrinsic error fields and toroidal field ripples in the level of most tokamaks can damp the toroidal rotation velocity over the whole region while reducing the toroidal rotation pedestal which is clearly observed in Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak. It is found that the NTV torque changes the toroidal rotation gradient in the pedestal region dramatically, but the toroidal rotation profile in the core region responds rigidly without a change in the gradient. On the other hand, it shows that the NTV torque induced by the intrinsic error fields and toroidal field ripple in the level of the KSTAR tokamak, which are expected to be smaller than most tokamaks by at least one order of magnitude, is negligible in determining the toroidal rotation velocity profile. Experimental observation on the toroidal rotation change by the externally applied nonaxisymmetric magnetic fields on KSTAR also suggests that NTV torque arising from nonaxisymmetric magnetic fields can damp the toroidal rotation over the whole region while diminishing the toroidal rotation pedestal.
Tokamak with in situ magnetohydrodynamic generation of toroidal magnetic field
Schaffer, Michael J.
1986-01-01
A tokamak apparatus includes an electrically conductive metal pressure vessel for defining a chamber and confining liquid therein. A liner disposed within said chamber defines a toroidal space within the liner and confines gas therein. The metal vessel provides an electrically conductive path linking the toroidal space. Liquid metal is forced outwardly through the chamber outside of the toroidal space to generate electric current in the conductive path and thereby generate a toroidal magnetic field within the toroidal space. Toroidal plasma is developed within the toroidal space about the major axis thereof.
Steady state compact toroidal plasma production
Turner, William C.
1986-01-01
Apparatus and method for maintaining steady state compact toroidal plasmas. A compact toroidal plasma is formed by a magnetized coaxial plasma gun and held in close proximity to the gun electrodes by applied magnetic fields or magnetic fields produced by image currents in conducting walls. Voltage supply means maintains a constant potential across the electrodes producing an increasing magnetic helicity which drives the plasma away from a minimum energy state. The plasma globally relaxes to a new minimum energy state, conserving helicity according to Taylor's relaxation hypothesis, and injecting net helicity into the core of the compact toroidal plasma. Controlling the voltage so as to inject net helicity at a predetermined rate based on dissipative processes maintains or increases the compact toroidal plasma in a time averaged steady state mode.
Dielectric Metamaterials with Toroidal Dipolar Response
NASA Astrophysics Data System (ADS)
Basharin, Alexey A.; Kafesaki, Maria; Economou, Eleftherios N.; Soukoulis, Costas M.; Fedotov, Vassili A.; Savinov, Vassili; Zheludev, Nikolay I.
2015-01-01
Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here, we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. We show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials' macroscopic response. Because of the unique field configuration of the toroidal mode, the proposed metamaterials could serve as a platform for sensing or enhancement of light absorption and optical nonlinearities.
Toroidal horizons in binary black hole mergers
NASA Astrophysics Data System (ADS)
Bohn, Andy; Kidder, Lawrence E.; Teukolsky, Saul A.
2016-09-01
We find the first binary black hole event horizon with a toroidal topology. It has been predicted that generically the event horizons of merging black holes should briefly have a toroidal topology. However, such a phase has never been seen in numerical simulations. Instead, in all previous simulations, the topology of the event horizon transitions directly from two spheres during the inspiral to a single sphere as the black holes merge. We find a coordinate transformation to a foliation of spacelike hypersurfaces that "cut a hole" through the event horizon surface, resulting in a toroidal event horizon, thus reconciling the numerical work with theoretical expectations. The demonstration requires extremely high numerical precision, which is made possible by a new event horizon code described in a companion paper. A torus could potentially provide a mechanism for violating topological censorship. However, these toroidal event horizons satisfy topological censorship by construction, because we can always trivially apply the inverse coordinate transformation to remove the topological feature.
Bow-shaped toroidal field coils
Bonanos, P.
1981-05-01
Design features of Bow-Shaped Toroidal Field Coils are described and compared with circular and D shaped coils. The results indicate that bow coils can produce higher field strengths, store more energy and be made demountable. The design offers the potential for the production of ultrahigh toroidal fields. Included are representative coil shapes and their engineering properties, a suggested structural design and an analysis of a specific case.
Low-n shear Alfven spectra in axisymmetric toroidal plasmas
Cheng, C.Z.; Chance, M.S.
1985-11-01
In toroidal plasmas, the toroidal magnetic field is nonuniform over a magnetic surface and causes coupling of different poloidal harmonics. It is shown both analytically and numerically that the toroidicity not only breaks up the shear Alfven continuous spectrum, but also creates new, discrete, toroidicity-induced shear Alfven eigenmodes with frequencies inside the continuum gaps. Potential applications of the low-n toroidicity-induced shear Alfven eigenmodes on plasma heating and instabilities are addressed. 17 refs., 4 figs.
NASA Technical Reports Server (NTRS)
Yee, H. C.; Kutler, P.
1983-01-01
A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.
Generation of rotational flows in toroidally confined visco-resistive magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Morales, Jorge; Bos, Wouter; Schneider, Kai; Montgomery, David
2015-11-01
We investigate by numerical simulation the generation of rotational flows in a toroid confining a conducting magnetofluid. A current is driven by the application of externally supported electric and magnetic fields. We show how the properties and intensity of the rotations are regulated by dimensionless numbers (Lundquist and viscous Lundquist) that contain the resistivity and viscosity of the magnetofluid. At the magnetohydrodynamic level (uniform mass density and incompressible magnetofluids), rotational flows appear in toroidal, driven MHD. The evolution of these flows with the transport coefficients, geometry, and safety factor are described. Two different toroidal geometries are considered, one with an up-down symmetric and the other with an asymmetric cross section. We show that there exists a fundamental difference between both studied cases: the volume-averaged angular momentum is zero for the symmetric case, while for the asymmetric cross section a finite volume-averaged angular momentum appears. We observe a breaking in the up-down symmetry of the flow and a toroidal preferred direction emerges.
A toroidal trap for cold {}^{87}{Rb} atoms using an rf-dressed quadrupole trap
NASA Astrophysics Data System (ADS)
Chakraborty, A.; Mishra, S. R.; Ram, S. P.; Tiwari, S. K.; Rawat, H. S.
2016-04-01
We demonstrate the trapping of cold {}87{Rb} atoms in a toroidal geometry using a radio frequency (rf) dressed quadrupole magnetic trap formed by superposing a strong rf-field on a quadrupole trap. This rf-dressed quadrupole trap has the minimum potential away from the quadrupole trap centre on a circular path which facilitates trapping in toroidal geometry. In these experiments, the laser cooled atoms were first trapped in a quadrupole trap, then cooled evaporatively using a weak rf-field, and finally trapped in an rf-dressed quadrupole trap. The radius of the toroid could be varied by varying the frequency of the dressing rf-field. It has also been demonstrated that a single rf source and an antenna can be used for the rf-evaporative cooling as well as for the rf-dressing of atoms. The atoms trapped in the toroidal trap may have applications in the realization of an atom gyroscope as well as in studying the quantum gases in low dimensions.
Finite beta plasma equilibrium in toroidally linked mirrors
Ilgisonis, V.I.; Berk, H.L.; Pastukhov, V.P.
1993-07-01
The problem of finite pressure plasma equilibrium in a system with closed magnetic field lines consisting of quadrupole mirrors linked by simple toroidal cells with elliptical cross-sections is analyzed. An appropriate analytical procedure is developed, that uses conformal mapping techniques, which enables one to obtain the magnetic field structure for the free boundary equilibrium problem. This method has general applicability for finding analytic solutions of the two-dimensional Dirichlet problem outside of an arbitrary closed contour. Using this method, the deformations of the plasma equilibrium configuration due to finite plasma pressure in the toroidal cell are calculated analytically to the second order in {lambda}-expansion, where {lambda} {approximately} {beta}/{epsilon}E, {beta} is the ratio of plasma pressure to the magnetic field pressure, {epsilon} is the inverse aspect ratio and E is the ellipticity of the plasma cross-section. The outer displacement of the plasma column is shown to depend nonlinearly on the increase of plasma pressure, and does not prevent the achievement of substantial {beta} {approximately} 10% in the toroidal cells.
Toroid cavities as NMR detectors in high pressure probes
Woelk, K.; Rathke, J.W.; Klingler, R.J.
1993-03-01
A cylindrical toroid cavity has been developed for application as an NMR detector for high sensitivity and high resolution spectroscopy in metal vessel probes. Those probes are used for in situ investigations at high temperature and pressure. Since the transmitted r.f. field is completely confined within the torus, the cavity can be placed inside the pressurized system without magnetic coupling to the metal vessel. Resonance frequencies up to 400 MHz make the toroid cavity detector especially suited for use in {sup 1}H and {sup 19}F spectroscopy. Typically achieved static {sup 1}H linewidths, measured on CHCl{sub 3} using cavities in Be-Cu pressure vessels, are 2.0 Hz. On the basis of theoretical considerations that include the radial dependence of the r.f. field within cylindrical or circular toroid detectors, equations were evolved to predict the signal intensity as a function of the pulse width. The equations precisely describe the deviations from the sinusoidal approximation, which is generally used for signal intensities derived from Helmholtz or solenoid coils.
Axisymmetric toroidal equilibrium with flow and anisotropic pressure
NASA Astrophysics Data System (ADS)
Iacono, R.; Bondeson, A.; Troyon, F.; Gruber, R.
1990-08-01
Axisymmetric toroidal plasma equilibria with mass flows and anisotropic pressure are investigated. The equilibrium system is derived for a general functional form of the pressures, which includes both fluid models, such as the magnetohydrodynamic (MHD) and the double-adiabatic models, and Grad's guiding center model [Proceedings of the Symposium on Electromagnetics and Fluid Dynamics of Gaseous Plasmas, edited by J. Fox (Polytechnic Inst. of Brooklyn, New York, 1961), p. 37]. This allows for detailed comparisons between the models and clarifies how the ``first hyperbolic region,'' occurring in fluid theory when the poloidal flow is of the order of the poloidal sound speed, can be eliminated in guiding center theory. In the case of a pure toroidal rotation, macroscopic equations of state are derived from the guiding center model, characterized by a parallel temperature that is constant on each magnetic surface and a perpendicular temperature that varies with the magnetic field. The outward centrifugal shifts of the magnetic axis and of the mass density profile, caused by toroidal rotation, are increased by anisotropy if p∥
p⊥. In the guiding center model poloidal flow produces an inward shift of the density profile, in contrast with the MHD result.
Axisymmetric curvature-driven instability in a model divertor geometry
Farmer, W. A.; Ryutov, D. D.
2013-09-15
A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.
Linear Instability Analysis for Toroidal Plasma Flow Equilibria
NASA Astrophysics Data System (ADS)
Varadarajan, V.; Miley, G. H.
1996-02-01
The non-self-adjoint Frieman-Rotenberg equation for the linear ideal magnetohydrodynamic modes in flow equilibria is numerically solved in shaped finite-aspect ratio axisymmetric tokamak geometry. A quadratic form is derived from this equation, and, in particular, the self-adjoint force operator with finite toroidal rotation is cast into a manifestly self-adjoint form. The toroidal rotational velocities in the subsonic regime are considered. The quadratic form is discretized by a mixed finite-element procedure in the radial direction and by Fourier modes in the periodic directions. The mode frequency of the unstable mode is located by root searching, and the final root refinement is obtained by a rapid inverse iteration procedure for complex roots. The real part of then= 1 internal kink mode scales linearly with the plasma rotation, and the imaginary part of the unstable mode is at least an order of magnitude higher in the presence of high plasma rotation velocities. The kink mode is also found to be unstable at high rotation velocities, even when the axis safety factor is above unity. The instability characterized by these features is termed here as the "centrifugal" instability. The centrifugal kink instability would have finite real parts, as shown by the plasma rotation observed in plasma devices such as tokamaks. To explain the features of this mode, the plasma rotation should be taken into account. Therein lies the usefulness of the computational analysis presented here.
Rotation shear induced fluctuation decorrelation in a toroidal plasma
Hahm, T.S.
1994-06-01
The enhanced decorrelation of fluctuations by the combined effects of the E {times} B flow (V{sub E}) shear, the parallel flow (V{sub {parallel}}) shear, and the magnetic shear is studied in toroidal geometry. A two-point nonlinear analysis previously utilized in a cylindrical model shows that the reduction of the radial correlation length below its ambient turbulence value ({Delta}r{sub 0}) is characterized by the ratio between the shearing rate {omega}{sub s} and the ambient turbulence scattering rate {Delta}{omega}{sub T}. The derived shearing rate is given by {omega}{sub s}{sup 2} = ({Delta}r{sub 0}){sup 2}[1/{Delta}{phi}{sup 2}{l_brace}{partial_derivative}/{partial_derivative}r(qV{sub E}/r){r_brace}{sup 2} + 1/{Delta}{eta}{sup 2}{l_brace}{partial_derivative}/{partial_derivative}r(V{parallel}/qR){r_brace}{sup 2}], where {Delta}{phi} and {Delta}{eta} are the correlation angles of the ambient turbulence along the toroidal and parallel directions. This result deviates significantly from the cylindrical result for high magnetic shear or for ballooning-like fluctuations. For suppression of flute-like fluctuations, only the radial shear of qV{sub E}/r contributes, and the radial shear of V{parallel}/qR is irrelevant regardless of the plasma rotation direction.
Saturation of single toroidal number Alfvén modes
NASA Astrophysics Data System (ADS)
Wang, X.; Briguglio, S.
2016-08-01
The results of numerical simulations are presented to illustrate the saturation mechanism of a single toroidal number Alfvén mode, driven unstable, in a tokamak plasma, by the resonant interaction with energetic ions. The effects of equilibrium geometry non-uniformities and finite mode radial width on the wave-particle nonlinear dynamics are discussed. Saturation occurs as the fast-ion density flattening produced by the radial flux associated to the resonant particles captured in the potential well of the Alfvén wave extends over the whole region where mode-particle power exchange can take place. The occurrence of two different saturation regimes is shown. In the first regime, dubbed resonance detuning, that region is limited by the resonance radial width (that is, the width of the region where the fast-ion resonance frequency matches the mode frequency). In the second regime, called radial decoupling, the power exchange region is limited by the mode radial width. In the former regime, the mode saturation amplitude scales quadratically with the growth rate; in the latter, it scales linearly. The occurrence of one or the other regime can be predicted on the basis of linear dynamics: in particular, the radial profile of the fast-ion resonance frequency and the mode structure. Here, we discuss how such properties can depend on the considered toroidal number and compare simulation results with the predictions obtained from a simplified nonlinear pendulum model.
1991-05-01
Version 00 MORSE-CGA was developed to add the capability of modelling rectangular lattices for nuclear reactor cores or for multipartitioned structures. It thus enhances the capability of the MORSE code system. The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. It has been designed as a tool for solving most shielding problems. Through the use of multigroup cross sections, the solution of neutron, gamma-ray, or coupled neutron-gamma-ray problems may be obtainedmore » in either the forward or adjoint mode. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry may be used with an albedo option available at any material surface. Isotropic or anisotropic scattering up to a P16 expansion of the angular distribution is allowed.« less
Optical force on toroidal nanostructures: Toroidal dipole versus renormalized electric dipole
NASA Astrophysics Data System (ADS)
Zhang, Xu-Lin; Wang, S. B.; Lin, Zhifang; Sun, Hong-Bo; Chan, C. T.
2015-10-01
We study the optical forces acting on toroidal nanostructures. A great enhancement of optical force is unambiguously identified as originating from the toroidal dipole resonance based on the source representation, where the distribution of the induced charges and currents is characterized by the three families of electric, magnetic, and toroidal multipoles. On the other hand, the resonant optical force can also be completely attributed to an electric dipole resonance in the alternative field representation, where the electromagnetic fields in the source-free region are expressed by two sets of electric and magnetic multipole fields based on symmetry. The confusion is resolved by conceptually introducing the irreducible electric dipole, toroidal dipole, and renormalized electric dipole. We demonstrate that the optical force is a powerful tool to identify toroidal response even when its scattering intensity is dwarfed by the conventional electric and magnetic multipoles.
Compact toroidal ion-trap design and optimization
Madsen, M. J.; Gorman, C. H.
2010-10-15
We present the design of a type of compact toroidal, or 'halo', ion trap. Such traps may be useful for mass spectrometry, studying small Coulomb cluster rings, quantum-information applications, or other quantum simulations where a ring topology is of interest. We present results from a Monte Carlo optimization of the trap design parameters using finite-element analysis simulations that minimize higher-order anharmonic terms in the trapping pseudopotential, while maintaining complete control over ion placement at the pseudopotential node in three dimensions using static bias fields. These simulations are based on a practical electrode design using readily available parts, yet can be easily scaled to any size trap with similar electrode spacings. We also derive the conditions for a crystal structure transition for two ions in the compact halo trap, the first nontrivial transition for Coulomb crystals in this geometry.
Neoclassical transport in toroidal plasmas with nonaxisymmetric flux surfaces
NASA Astrophysics Data System (ADS)
Belli, E. A.; Candy, J.
2015-05-01
The capability to treat nonaxisymmetric flux surface geometry has been added to the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010). Geometric quantities (i.e. metric elements) are supplied by a recently-developed local 3D equilibrium solver, allowing neoclassical transport coefficients to be systematically computed while varying the 3D plasma shape in a simple and intuitive manner. Code verification is accomplished via detailed comparison with 3D Pfirsch-Schlüter theory. A discussion of the various collisionality regimes associated with 3D transport is given, with an emphasis on non-ambipolar particle flux, neoclassical toroidal viscosity, energy flux and bootstrap current. Finally, we compute the transport in the presence of ripple-type perturbations in a DIII-D-like H-mode edge plasma.
Asymmetric magnon excitation by spontaneous toroidal ordering
Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi
2016-04-12
The effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky–Moriya interaction and anisotropic exchange interactions, which arise from the antisymmetric spin–orbit coupling and the multiorbital correlation effect. We show that the model exhibits a Néel-type antiferromagnetic order, which simultaneously accompanies a ferroic toroidal order. We find that the occurrence of toroidal order modulates the magnon dispersion in an asymmetric way with respect to the wave number: a toroidal dipole order on the zigzag chain leads to a band-bottom shift, while a toroidal octupole order on the honeycomb latticemore » gives rise to a valley splitting. These asymmetric magnon excitations could be a source of unusual magnetic responses, such as nonreciprocal magnon transport. A variety of modulations are discussed while changing the lattice and magnetic symmetries. Furthermore, the implications regarding candidate materials for asymmetric magnon excitations are presented.« less
Long-wavelength microinstabilities in toroidal plasmas
Tang, W.W.; Rewoldt, G.
1993-01-01
Realistic kinetic toroidal eigenmode calculations have been carried out to support a proper assessment of the influence of long-wavelength microturbulence on transport in tokamak plasmas. In order to efficiently evaluate large-scale kinetic behavior extending over many rational surfaces, significant improvements have been made to a toroidal finite element code used to analyze the fully two-dimensional (r,{theta}) mode structures of trapped-ion and toroidal ion temperature gradient (ITG) instabilities. It is found that even at very long wavelengths, these eigenmodes exhibit a strong ballooning character with the associated radial structure relatively insensitive to ion Landau damping at the rational surfaces. In contrast to the long-accepted picture that the radial extent of trapped-ion instabilities is characterized by the ion-gyroradius-scale associated with strong localization between adjacent rational surfaces, present results demonstrate that under realistic conditions, the actual scale is governed by the large-scale variations in the equilibrium gradients. Applications to recent measurements of fluctuation properties in TFTR L-mode plasmas indicate that the theoretical trends appear consistent with spectral characteristics as well as rough heuristic estimates of the transport level. Benchmarking calculations in support of the development of a three-dimensional toroidal gyrokinetic code indicate reasonable agreement with respect to both the properties of the eigenfunctions and the magnitude of the eigenvalues during the linear phase of the simulations of toroidal ITG instabilities.
Long-wavelength microinstabilities in toroidal plasmas
Tang, W.W.; Rewoldt, G.
1993-01-01
Realistic kinetic toroidal eigenmode calculations have been carried out to support a proper assessment of the influence of long-wavelength microturbulence on transport in tokamak plasmas. In order to efficiently evaluate large-scale kinetic behavior extending over many rational surfaces, significant improvements have been made to a toroidal finite element code used to analyze the fully two-dimensional (r,[theta]) mode structures of trapped-ion and toroidal ion temperature gradient (ITG) instabilities. It is found that even at very long wavelengths, these eigenmodes exhibit a strong ballooning character with the associated radial structure relatively insensitive to ion Landau damping at the rational surfaces. In contrast to the long-accepted picture that the radial extent of trapped-ion instabilities is characterized by the ion-gyroradius-scale associated with strong localization between adjacent rational surfaces, present results demonstrate that under realistic conditions, the actual scale is governed by the large-scale variations in the equilibrium gradients. Applications to recent measurements of fluctuation properties in TFTR L-mode plasmas indicate that the theoretical trends appear consistent with spectral characteristics as well as rough heuristic estimates of the transport level. Benchmarking calculations in support of the development of a three-dimensional toroidal gyrokinetic code indicate reasonable agreement with respect to both the properties of the eigenfunctions and the magnitude of the eigenvalues during the linear phase of the simulations of toroidal ITG instabilities.
Antimicrobial Peptides in Toroidal and Cylindrical Pores
Mihajlovic, Maja
2010-01-01
Antimicrobial peptides (AMPs) are small, usually cationic peptides, which permeabilize biological membranes. Their mechanism of action is still not well understood. Here we investigate the preference of alamethicin and melittin for pores of different shapes, using molecular dynamics (MD) simulations of the peptides in pre-formed toroidal and cylindrical pores. When an alamethicin hexamer is initially embedded in a cylindrical pore, at the end of the simulation the pore remains cylindrical or closes if glutamines in the N-termini are not located within the pore. On the other hand, when a melittin tetramer is embedded in toroidal pore or in a cylindrical pore, at the end of the simulation the pore is lined both with peptides and lipid headgroups, and, thus, can be classified as a toroidal pore. These observations agree with the prevailing views that alamethicin forms barrel-stave pores whereas melittin forms toroidal pores. Both alamethicin and melittin form amphiphilic helices in the presence of membranes, but their net charge differs; at pH ~7, the net charge of alamethicin is −1 whereas that of melittin is +5. This gives rise to stronger electrostatic interactions of melittin with membranes than those of alamethicin. The melittin tetramer interacts more strongly with lipids in the toroidal pore than in the cylindrical one, due to more favorable electrostatic interactions. PMID:20403332
Tokamak with liquid metal for inducing toroidal electrical field
Ohkawa, Tihiro
1981-01-01
A tokamak apparatus includes a vessel for defining a reservoir and confining liquid therein. A toroidal liner disposed within said vessel defines a toroidal space within the liner confines gas therein. Liquid metal fills the reservoir outside the liner. A magnetic field is established in the liquid metal to develop magnetic flux linking the toroidal space. The gas is ionized. The liquid metal and the toroidal space are moved relative to one another transversely of the space to generate electric current in the ionized gas in the toroidal space about its major axis and thereby heat plasma developed in the toroidal space.
Kinetic extensions of magnetohydrodynamic models for axisymmetric toroidal plasmas
Cheng, C.Z.
1989-04-01
A nonvariational kinetic-MHD stability code (NOVA-K) has been developed to integrate a set of non-Hermitian integro-differential eigenmode equations due to energetic particles for axisymmetric toroidal plasmas in a general flux coordinate system with an arbitrary Jacobian. The NOVA-K code employs the Galerkin method involving Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /Psi/ direction. Extensive comparisons with the existing variational ideal MHD codes show that the ideal MHD version of the NOVA-K code converges faster and gives more accurate results. The NOVA-K code is employed to study the effects of energetic particles on MHD-type modes: the stabilization of ideal MHD internal kink modes and the excitation of ''fishbone'' internal kink modes; and the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are also presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n = 1 internal kink mode in the hot particle beta space exists even in the absence of the core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to have negligible effects on the stability of the n = 1 internal kink mode, but the circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 60 refs., 24 figs., 1 tab.
Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V
2015-01-01
Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes. PMID:25062896
Bose-Einstein condensates in toroidal traps: Instabilities, swallow-tail loops, and self-trapping
NASA Astrophysics Data System (ADS)
Baharian, Soheil; Baym, Gordon
2013-01-01
We study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a “disorder” potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.
Quasisymmetric toroidal plasmas with large mean flows
Sugama, H.; Watanabe, T.-H.; Nunami, M.; Nishimura, S.
2011-08-15
Geometric conditions for quasisymmetric toroidal plasmas with large mean flows on the order of the ion thermal speed are investigated. Equilibrium momentum balance equations including the inertia term due to the large flow velocity are used to show that, for rotating quasisymmetric plasmas with no local currents crossing flux surfaces, all components of the metric tensor should be independent of the toroidal angle in the Boozer coordinates, and consequently these systems need to be rigorously axisymmetric. Unless the local radial currents vanish, the Boozer coordinates do not exist and the toroidal flow velocity cannot take any value other than a very limited class of eigenvalues corresponding to very rapid rotation especially for low beta plasmas.
Ferroic nature of magnetic toroidal order.
Zimmermann, Anne S; Meier, Dennis; Fiebig, Manfred
2014-09-05
Electric dipoles and ferroelectricity violate spatial inversion symmetry, and magnetic dipoles and ferromagnetism break time-inversion symmetry. Breaking both symmetries favours magnetoelectric charge-spin coupling effects of enormous interest, such as multiferroics, skyrmions, polar superconductors, topological insulators or dynamic phenomena such as electromagnons. Extending the rationale, a novel type of ferroic order violating space- and time-inversion symmetry with a single order parameter should exist. This existence is fundamental and the inherent magnetoelectric coupling is technologically interesting. A uniform alignment of magnetic vortices, called ferrotoroidicity, was proposed to represent this state. Here we demonstrate that the magnetic vortex pattern identified in LiCoPO4 exhibits the indispensable hallmark of such a ferroic state, namely hysteretic poling of ferrotoroidic domains in the conjugate toroidal field, along with a distinction of toroidal from non-toroidal poling effects. This consolidates ferrotoroidicity as fourth form of ferroic order.
Toroidal Precession as a Geometric Phase
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Noncommutative Geometry and Physics
Connes, Alain
2006-11-03
In this very short essay we shall describe a 'spectral' point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a 'sum over geometries' on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of 'observables' in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.
The effect of sheared toroidal rotation on pressure driven magnetic islands in toroidal plasmas
NASA Astrophysics Data System (ADS)
Hegna, C. C.
2016-05-01
The impact of sheared toroidal rotation on the evolution of pressure driven magnetic islands in tokamak plasmas is investigated using a resistive magnetohydrodynamics model augmented by a neoclassical Ohm's law. Particular attention is paid to the asymptotic matching data as the Mercier indices are altered in the presence of sheared flow. Analysis of the nonlinear island Grad-Shafranov equation shows that sheared flows tend to amplify the stabilizing pressure/curvature contribution to pressure driven islands in toroidal tokamaks relative to the island bootstrap current contribution. As such, sheared toroidal rotation tends to reduce saturated magnetic island widths.
Electromagnetic toroidal excitations in matter and free space
NASA Astrophysics Data System (ADS)
Papasimakis, N.; Fedotov, V. A.; Savinov, V.; Raybould, T. A.; Zheludev, N. I.
2016-03-01
The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information.
Dynamics of a toroidal magnetic cloud in the solar wind
NASA Astrophysics Data System (ADS)
Romashets, E. P.; Vandas, M.
2001-06-01
Knowledge about the behavior of compact toroidal magnetic force-free objects in ambient magnetic field may help to better understand dynamical processes in association with coronal mass ejections and their interplanetary counterparts. The problem to find the diamagnetic force acting on a toroidal object in an inhomogeneous magnetic field is solved analytically. At first the drapery of the inhomogeneous magnetic field caused by an insertion of a toroid was found, and then the force acting on the toroid by this disturbed magnetic field was obtained. The problem is considered in purely toroidal coordinates. The obtained solution can be used for calculations of the repulsing diamagnetic force acting on isolated objects in the solar corona such as magnetic clouds of a toroidal shape and for the determination of their velocity profiles. Deformations of toroidal transients due to this melon seed force are not investigated here. Only the force acting on the toroid as a whole is taken in consideration.
Electromagnetic toroidal excitations in matter and free space.
Papasimakis, N; Fedotov, V A; Savinov, V; Raybould, T A; Zheludev, N I
2016-03-01
The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information.
Electromagnetic toroidal excitations in matter and free space.
Papasimakis, N; Fedotov, V A; Savinov, V; Raybould, T A; Zheludev, N I
2016-03-01
The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information. PMID:26906961
Escape of magnetic toroids from the Sun
NASA Technical Reports Server (NTRS)
Bieber, John W.; Rust, David M.
1995-01-01
Analysis of heliospheric magnetic fields at 1 AU shows that 10(exp 24) Mx of net azimuthal flux escapes from the Sun per solar cycle. This rate is consistent with rates derived from other indicators of flux escape, including coronal mass ejections and filament eruptions. The toroidal flux escape rate is compared with the apparent rate of flux emergence at the solar surface, and it is concluded that escaping toroids will remove at least 20% of the emerging flux, and may remove as much as 100% of emerging flux if multiple eruptions occur on the toroids. The data imply that flux escapes the Sun with an efficiency far exceeding Parker's upper limit estimate of 3%. Toroidal flux escape is almost certainly the source of the observed overwinding of the interplanetary magnetic field spiral. Two mechanisms to facilitate net flux escape are discussed: helicity charging to push open the fields and flux transport with reconnection to close them off. We estimate the Sun will shed approximately 2 x 10(exp 45) of magnetic helicity per solar cycle, leading to a mean helicity density of 100 Mx(exp 2)cm(exp -3) at 1 AU, which agrees well with observations.
PULSAR WIND NEBULAE WITH THICK TOROIDAL STRUCTURE
Chevalier, Roger A.; Reynolds, Stephen P. E-mail: reynolds@ncsu.edu
2011-10-10
We investigate a class of pulsar wind nebulae that show synchrotron emission from a thick toroidal structure. The best studied such object is the small radio and X-ray nebula around the Vela pulsar, which can be interpreted as the result of interaction of a mildly supersonic inward flow with the recent pulsar wind. Such a flow near the center of a supernova remnant can be produced in a transient phase when the reverse shock reaches the center of the remnant. Other nebulae with a thick toroidal structure are G106.6+2.9 and G76.9+1.0. Their structure contrasts with young pulsar nebulae like the Crab Nebula and 3C 38, which show a more chaotic, filamentary structure in the synchrotron emission. In both situations, a torus-jet structure is present where the pulsar wind passes through a termination shock, indicating the flow is initially toroidal. We suggest that the difference is due to the Rayleigh-Taylor instability that operates when the outer boundary of the nebula is accelerating into freely expanding supernova ejecta. The instability gives rise to mixing in the Crab and related objects, but is not present in the nebulae with thick toroidal regions.
Toroidal surfaces compared with spherocylindrical surfaces
NASA Astrophysics Data System (ADS)
Malacara-Doblado, Daniel; Malacara-Hernandez, Daniel; Garcia-Marquez, Jorge L.
1995-08-01
Toroidal and sphero-cylindrical optical surfaces are two different kinds of surfaces (Menchaca and Malacara, 1986), but they are almost identical in the vicinity of the optical axis. The separation between these two surfaces increases when the distance to the optical axis increases. In this work the separation between these two surfaces outside of the central region is analytically studied.
Ideal magnetohydrodynamic theory for localized interchange modes in toroidal anisotropic plasmas
NASA Astrophysics Data System (ADS)
Shi, Tonghui; Zheng, L. J.; Wan, B. N.; Sun, Y.; Shen, B.; Qian, J. P.
2016-08-01
Ideal magnetohydrodynamic theory for localized interchange modes is developed for toroidal plasmas with anisotropic pressure. The work extends the existing theories of Johnson and Hastie [Phys. Fluids 31, 1609 (1988)], etc., to the low n mode case, where n is the toroidal mode number. Also, the plasma compressibility is included, so that the coupling of the parallel motion to perpendicular one, i.e., the so-called apparent mass effect, is investigated in the anisotropic pressure case. The singular layer equation is obtained, and the generalized Mercier's criterion is derived.
Dynamical Model for the Toroidal Sporadic Meteors
NASA Astrophysics Data System (ADS)
Pokorný, Petr; Vokrouhlický, David; Nesvorný, David; Campbell-Brown, Margaret; Brown, Peter
2014-07-01
More than a decade of radar operations by the Canadian Meteor Orbit Radar have allowed both young and moderately old streams to be distinguished from the dispersed sporadic background component. The latter has been categorized according to broad radiant regions visible to Earth-based observers into three broad classes: the helion and anti-helion source, the north and south apex sources, and the north and south toroidal sources (and a related arc structure). The first two are populated mainly by dust released from Jupiter-family comets and new comets. Proper modeling of the toroidal sources has not to date been accomplished. Here, we develop a steady-state model for the toroidal source of the sporadic meteoroid complex, compare our model with the available radar measurements, and investigate a contribution of dust particles from our model to the whole population of sporadic meteoroids. We find that the long-term stable part of the toroidal particles is mainly fed by dust released by Halley type (long period) comets (HTCs). Our synthetic model reproduces most of the observed features of the toroidal particles, including the most troublesome low-eccentricity component, which is due to a combination of two effects: particles' ability to decouple from Jupiter and circularize by the Poynting-Robertson effect, and large collision probability for orbits similar to that of the Earth. Our calibrated model also allows us to estimate the total mass of the HTC-released dust in space and check the flux necessary to maintain the cloud in a steady state.
Dynamical model for the toroidal sporadic meteors
Pokorný, Petr; Vokrouhlický, David; Nesvorný, David; Campbell-Brown, Margaret; Brown, Peter E-mail: vokrouhl@cesnet.cz E-mail: margaret.campbell@uwo.ca
2014-07-01
More than a decade of radar operations by the Canadian Meteor Orbit Radar have allowed both young and moderately old streams to be distinguished from the dispersed sporadic background component. The latter has been categorized according to broad radiant regions visible to Earth-based observers into three broad classes: the helion and anti-helion source, the north and south apex sources, and the north and south toroidal sources (and a related arc structure). The first two are populated mainly by dust released from Jupiter-family comets and new comets. Proper modeling of the toroidal sources has not to date been accomplished. Here, we develop a steady-state model for the toroidal source of the sporadic meteoroid complex, compare our model with the available radar measurements, and investigate a contribution of dust particles from our model to the whole population of sporadic meteoroids. We find that the long-term stable part of the toroidal particles is mainly fed by dust released by Halley type (long period) comets (HTCs). Our synthetic model reproduces most of the observed features of the toroidal particles, including the most troublesome low-eccentricity component, which is due to a combination of two effects: particles' ability to decouple from Jupiter and circularize by the Poynting-Robertson effect, and large collision probability for orbits similar to that of the Earth. Our calibrated model also allows us to estimate the total mass of the HTC-released dust in space and check the flux necessary to maintain the cloud in a steady state.
Neoclassical Drift of Circulating Orbits Due toToroidal Electric Field in Tokamaks
Hong, Qin; Guan, Xiaoyin; Fisch, Nathaniel J.
2011-07-19
In tokamaks, Ware pinch is a well known neoclassical effect for trapped particles in response to a toroidal electric field. It is generally believed that there exists no similar neoclassical effect for circulating particles without collisions. However, this belief is erroneous, and misses an important effect. We show both analytically and numerically that under the influence of a toroidal electric field parallel to the current, the circulating orbits drift outward toward the outer wall with a characteristic velocity O ({var_epsilon}{sup -1}) larger than the E x B velocity, where {var_epsilon} is the inverse aspect-ratio of a tokamak. During a RF overdrive, the toroidal electric field is anti-parallel to the current. As a consequence, all charged particles, including backward runaway electrons, will drift inward towards the inner wall.
On steady poloidal and toroidal flows in tokamak plasmas
McClements, K. G.
2010-08-15
The effects of poloidal and toroidal flows on tokamak plasma equilibria are examined in the magnetohydrodynamic limit. ''Transonic'' poloidal flows of the order of the sound speed multiplied by the ratio of poloidal magnetic field to total field B{sub {theta}/}B can cause the (normally elliptic) Grad-Shafranov (GS) equation to become hyperbolic in part of the solution domain. It is pointed out that the range of poloidal flows for which the GS equation is hyperbolic increases with plasma beta and B{sub {theta}/}B, thereby complicating the problem of determining spherical tokamak plasma equilibria with transonic poloidal flows. It is demonstrated that the calculation of the hyperbolicity criterion can be easily modified when the assumption of isentropic flux surfaces is replaced with the more tokamak-relevant one of isothermal flux surfaces. On the basis of the latter assumption, a simple expression is obtained for the variation of density on a flux surface when poloidal and toroidal flows are simultaneously present. Combined with Thomson scattering measurements of density and temperature, this expression could be used to infer information on poloidal and toroidal flows on the high field side of a tokamak plasma, where direct measurements of flows are not generally possible. It is demonstrated that there are four possible solutions of the Bernoulli relation for the plasma density when the flux surfaces are assumed to be isothermal, corresponding to four distinct poloidal flow regimes. Finally, observations and first principles-based theoretical modeling of poloidal flows in tokamak plasmas are briefly reviewed and it is concluded that there is no clear evidence for the occurrence of supersonic poloidal flows.
The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations
Hornsby, W. A. Migliano, P.; Buchholz, R.; Kroenert, L.; Weikl, A.; Peeters, A. G.; Zarzoso, D.; Poli, E.; Casson, F. J.
2015-02-15
Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η{sup 1∕7} scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.
Tokamak equilibria with strong toroidal current density reversal
NASA Astrophysics Data System (ADS)
Ludwig, G. O.; Rodrigues, Paulo; Bizarro, João P. S.
2013-05-01
The equilibrium of large magnetic islands in the core of a tokamak under conditions of strong toroidal current density reversal is investigated by a new method. The method uses distinct spectral representations to describe each simply connected region as well as the containing shell geometry. This ideal conducting shell may substitute for the plasma edge region or take a virtual character representing the external equilibrium field effect. The internal equilibrium of the islands is solved within the framework of the variational moment method. Equivalent surface current densities are defined on the boundaries of the islands and on the thin containing shell, giving a straightforward formulation to the interaction between regions. The equilibrium of the island-shell system is determined by matching moments of the Dirichlet boundary conditions. Finally, the macroscopic stability against a class of tilting displacements is examined by means of an energy principle. It is found out that the up-down symmetric islands are stable to this particular perturbation and geometry but the asymmetric system presents a bifurcation in the equilibrium.
Software Geometry in Simulations
NASA Astrophysics Data System (ADS)
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Toroidal modeling of penetration of the resonant magnetic perturbation field
Liu Yueqiang; Kirk, A.
2013-04-15
A toroidal, quasi-linear model is proposed to study the penetration dynamics of the resonant magnetic perturbation (RMP) field into the plasma. The model couples the linear, fluid plasma response to a toroidal momentum balance equation, which includes torques induced by both fluid electromagnetic force and by (kinetic) neoclassical toroidal viscous (NTV) force. The numerical results for a test toroidal equilibrium quantify the effects of various physical parameters on the field penetration and on the plasma rotation braking. The neoclassical toroidal viscous torque plays a dominant role in certain region of the plasma, for the RMP penetration problem considered in this work.
NASA Astrophysics Data System (ADS)
Zhang, Wenlu; Holod, Ihor; Lin, Zhihong; Xiao, Yong
2012-02-01
Linear properties of toroidal Alfvén eigenmode (TAE) is studied in global gyrokinetic particle simulations using both fast ion and antenna excitations. A synthetic antenna provides a precise measurement of the Alfvén continuum gap width and the TAE eigenmode frequency, damping rate, and mode structures. The measured gap width exhibits a linear dependence on the aspect ratio, in agreement to a local analytic theory. The TAE frequency and mode structure excited by fast ions show a significant radial symmetry breaking relative to the ideal magnetohydrodynamic theory due to the non-perturbative contributions from the fast ions. The electromagnetic capability of the global gyrokinetic toroidal code (GTC) is verified through these global gyrokinetic simulations of Alfvén eigenmode in cylindrical and toroidal geometries.
Matter in the form of toroidal electromagnetic vortices
NASA Astrophysics Data System (ADS)
Hagen, Wilhelm F.
2015-09-01
The creation of charged elementary particles from neutral photons is explained as a conversion process of electromagnetic (EM) energy from linear to circular motion at the speed of light into two localized, toroidal shaped vortices of trapped EM energy that resist change of motion, perceptible as particles with inertia and hence mass. The photon can be represented as a superposition of left and right circular polarized transverse electric fields of opposite polarity originating from a common zero potential axis, the optical axis of the photon. If these components are separated by interaction with a strong field (nucleon) they would curl up into two electromagnetic vortices (EMV) due to longitudinal magnetic field components forming toroids. These vortices are perceptible as opposite charged elementary particles e+/- . These spinning toroids generate extended oscillating fields that interact with stationary field oscillations. The velocity-dependent frequency differences cause beat signals equivalent to matter waves, leading to interference. The extended fields entangled with every particle explain wave particle duality issues. Spin and magnetic moment are the natural outcome of these gyrating particles. As the energy and hence mass of the electron increases with acceleration so does its size shrink proportional to its reduced wavelength. The artificial weak and strong nuclear forces can be easily explained as different manifestations of the intermediate EM forces. The unstable neutron consists of a proton surrounded by a contracted and captured electron. The associated radial EM forces represent the weak nuclear force. The deuteron consists of two axially separated protons held together by a centrally captured electron. The axial EM forces represent the strong nuclear force, providing stability for "neutrons" only within nucleons. The same principles were applied to determine the geometries of force-balanced nuclei. The alpha-particle emerges as a very compact
Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials
NASA Astrophysics Data System (ADS)
Savinov, V.; Fedotov, V. A.; Zheludev, N. I.
2014-05-01
The toroidal dipole is a peculiar electromagnetic excitation that can not be presented in terms of standard electric and magnetic multipoles. A static toroidal dipole has been shown to lead to violation of parity in atomic spectra and many other unusual electromagnetic phenomena. The existence of electromagnetic resonances of toroidal nature was experimentally demonstrated only recently, first in the microwave metamaterials, and then at optical frequencies, where they could be important in spectroscopy analysis of a wide class of media with constituents of toroidal symmetry, such as complex organic molecules, fullerenes, bacteriophages, etc. Despite the experimental progress in studying toroidal resonances, no direct link has yet been established between microscopic toroidal excitations and macroscopic scattering characteristics of the medium. To address this essential gap in the electromagnetic theory, we have developed an analytical approach for calculating the transmissivity and reflectivity of thin slabs of materials that exhibit toroidal dipolar excitations.
ERIC Educational Resources Information Center
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
NASA Astrophysics Data System (ADS)
Albert, Christopher G.; Heyn, Martin F.; Kapper, Gernot; Kasilov, Sergei V.; Kernbichler, Winfried; Martitsch, Andreas F.
2016-08-01
Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant neoclassical toroidal viscosity regimes including superbanana-plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match the existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.
Solar concentrator with a toroidal relay module.
Lin, Jhe-Syuan; Liang, Chao-Wen
2015-10-01
III-V multijunction solar cells require solar concentrators with a high concentration ratio to reduce per watt cost and to increase solar energy transforming efficiency. This paper discusses a novel solar concentrator design that features a high concentration ratio, high transfer efficiency, thin profile design, and a high solar acceptance angle. The optical design of the concentrator utilizes a toroidal relay module, which includes both the off-axis relay lens and field lens design in a single concentric toroidal lens shape. The optical design concept of the concentrator is discussed and the simulation results are shown. The given exemplary design has an aspect ratio of 0.24, a high averaged optical concentration ratio 1230×, a maximum efficiency of 76.8%, and the solar acceptance angle of ±0.9°.
Magnetohydrodynamic stability of structurally stable toroidal plasmas
NASA Astrophysics Data System (ADS)
Rock, F. C.
1981-11-01
The MHD stability of sharp boundary axisymmetric toroidal plasmas with the poloidal field and 'kidney bean' shape implied by the requirements of structural stability (immunity of the magnetic field topology to small perturbations) is investigated. High values of marginal beta (up to 36 percent for R/a = 2) are found. Results are presented for the four magnetic field topologies on the sharp boundary surface with this shape and as a function of elongation.
Toroidal Dipole Moment of a Massless Neutrino
Cabral-Rosetti, L. G.; Mondragon, M.; Perez, E. Reyes
2009-04-20
We obtain the toroidal dipole moment of a massless neutrino {tau}{sub v{sub I}}{sup M} using the results for the anapole moment of a massless Dirac neutrino a{sub v{sub I}}{sup D}, which was obtained in the context of the Standard Model of the electroweak interactions (SM)SU(2){sub L} x U(1){sub Y}.
Neoclassical transport in enhanced confinement toroidal plasmas
Lin, Z.; Tang, W.M.; Lee, W.W.
1996-11-01
It has recently been reported that ion thermal transport levels in enhanced confinement tokamak plasmas have been observed to fall below the irreducible minimum level predicted by standard neoclassical theory. This apparent contradiction is resolved in the present analysis by relaxing the basic neoclassical assumption that the ions orbital excursions are much smaller than the local toroidal minor radius and the equilibrium scale lengths of the system.
Stellarator approach to toroidal plasma confinement
Johnson, J.L.
1981-12-01
An overview is presented of the development and current status of the stellarator approach to controlled thermonuclear confinement. Recent experimental, theoretical, and systems developments have made this concept a viable option for the evolution of the toroidal confinement program. Some experimental study of specific problems associated with departure from two-dimensional symmetry must be undertaken before the full advantages and opportunities of steady-state, net-current-free operation can be realized.
Finite toroidal flow generated by unstable tearing mode in a toroidal plasma
Hao, G. Z. Wang, A. K.; Xu, Y. H.; He, H. D.; Xu, M.; Qu, H. P.; Peng, X. D.; Xu, J. Q.; Qiu, X. M.; Liu, Y. Q.; Sun, Y.; Cui, S. Y.
2014-12-15
The neoclassical toroidal plasma viscosity torque and electromagnetic torque, generated by tearing mode (TM) in a toroidal plasma, are numerically investigated using the MARS-Q code [Liu et al., Phys. Plasmas 20, 042503 (2013)]. It is found that an initially unstable tearing mode can intrinsically drive a toroidal plasma flow resulting in a steady state solution, in the absence of the external momentum input and external magnetic field perturbation. The saturated flow is in the order of 0.5%ω{sub A} at the q=2 rational surface in the considered case, with q and ω{sub A} being the safety factor and the Alfven frequency at the magnetic axis, respectively. The generation of the toroidal flow is robust, being insensitive to the given amplitude of the perturbation at initial state. On the other hand, the flow amplitude increases with increasing the plasma resistivity. Furthermore, the initially unstable tearing mode is fully stabilized by non-linear interaction with the self-generated toroidal flow.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
Toroidal rotation and halo current produced by disruptions
NASA Astrophysics Data System (ADS)
Strauss, Henry; Sugiyama, Linda; Paccagnella, Roberto; Breslau, Joshua; Jardin, Stephen
2013-10-01
In several experiments including JET, it was observed that disruptions were accompanied by toroidal rotation. There is a concern that there may be a resonance between rotating toroidal perturbations and the resonant frequencies of the ITER vacuum vessel, causing enhanced damage. MHD simulations with M3D demonstrate that disruptions produce toroidal rotation. The toroidal velocity can produce several rotations of the sideways force during a disruption. Edge localized modes (ELMs) also produce poloidal and toroidal rotation. A theory of rotation produced by MHD activity will be presented. In the case of ELMs, the theory gives toroidal rotation Alfven Mach number, Mϕ ~10-2βN . This is consistent with a scaling for intrinsic toroidal rotation in H mode tokamaks. It was also discovered on JET that disruptions were accompanied by toroidal variation of the plasma current Iϕ. From ∇ . j = 0 , the toroidal current variation ΔIϕ is proportional to the 3D halo current, ∮Jn Rdl , where Jn is the normal current density at the wall. The 3D halo current is calculated analytically and computationally. A bound on ΔIϕ /Iϕ is found, proportional to the halo current fraction and toroidal peaking factor. Supported by USDOE and ITER.
Multiple toroidal Alfven eigenmodes with a single toroidal mode number in KSTAR plasmas
NASA Astrophysics Data System (ADS)
Rizvi, H.; Ryu, C. M.; Lin, Z.
2016-11-01
Simultaneous excitation of multiple discrete toroidal Alfven eigenmodes (TAEs) for a single toroidal mode number have been observed in KSTAR plasmas. Excitation and characteristics of these modes are studied by using a global gyrokinetic particle-in-cell simulation code. It is shown that compared to a single core-localized mode, excitation of two modes is difficult. The frequency difference between the double TAEs studied from simulation seems to agree well with the experimental value. Details of studies on the frequency, growth rate, mode structures, etc, using the GTC simulation are presented.
Toroid cavity/coil NMR multi-detector
Gerald, II, Rex E.; Meadows, Alexander D.; Gregar, Joseph S.; Rathke, Jerome W.
2007-09-18
An analytical device for rapid, non-invasive nuclear magnetic resonance (NMR) spectroscopy of multiple samples using a single spectrometer is provided. A modified toroid cavity/coil detector (TCD), and methods for conducting the simultaneous acquisition of NMR data for multiple samples including a protocol for testing NMR multi-detectors are provided. One embodiment includes a plurality of LC resonant circuits including spatially separated toroid coil inductors, each toroid coil inductor enveloping its corresponding sample volume, and tuned to resonate at a predefined frequency using a variable capacitor. The toroid coil is formed into a loop, where both ends of the toroid coil are brought into coincidence. Another embodiment includes multiple micro Helmholtz coils arranged on a circular perimeter concentric with a central conductor of the toroid cavity.
Landau damping of geodesic acoustic mode in toroidally rotating tokamaks
Ren, Haijun; Cao, Jintao
2015-06-15
Geodesic acoustic mode (GAM) is analyzed by using modified gyro-kinetic (MGK) equation applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Dispersion relation of GAM in the presence of arbitrary toroidal Mach number is analytically derived. The effects of toroidal rotation on the GAM frequency and damping rate do not depend on the orientation of equilibrium flow. It is shown that the toroidal Mach number M increases the GAM frequency and dramatically decreases the Landau damping rate.
Multiplicity of low-shear toroidal Alfven eigenmodes
Candy, J.; Breizman, B.N. |; Van Dam, J.W.; Ozeki, T.
1996-01-01
An enlarged spectrum of ideal toroidal Alfven eigenmodes is demonstrated to exist within a toroidicity-induced Alfven gap when the inverse aspect ratio is comparable to or larger than the value of the magnetic shear. This limit is appropriate for the low-shear region in most tokamaks, especially those with low aspect ratio. The new modes may be destabilized by fusion-product alpha particles more easily than the standard toroidal Alfven eigenmodes.
NASA Astrophysics Data System (ADS)
Almansa, Julio; Salvat-Pujol, Francesc; Díaz-Londoño, Gloria; Carnicer, Artur; Lallena, Antonio M.; Salvat, Francesc
2016-02-01
The Fortran subroutine package PENGEOM provides a complete set of tools to handle quadric geometries in Monte Carlo simulations of radiation transport. The material structure where radiation propagates is assumed to consist of homogeneous bodies limited by quadric surfaces. The PENGEOM subroutines (a subset of the PENELOPE code) track particles through the material structure, independently of the details of the physics models adopted to describe the interactions. Although these subroutines are designed for detailed simulations of photon and electron transport, where all individual interactions are simulated sequentially, they can also be used in mixed (class II) schemes for simulating the transport of high-energy charged particles, where the effect of soft interactions is described by the random-hinge method. The definition of the geometry and the details of the tracking algorithm are tailored to optimize simulation speed. The use of fuzzy quadric surfaces minimizes the impact of round-off errors. The provided software includes a Java graphical user interface for editing and debugging the geometry definition file and for visualizing the material structure. Images of the structure are generated by using the tracking subroutines and, hence, they describe the geometry actually passed to the simulation code.
Toroidal magnetic detector for high resolution measurement of muon momenta
Bonanos, P.
1992-01-07
A muon detector system including central and end air-core superconducting toroids and muon detectors enclosing a central calorimeter/detector. Muon detectors are positioned outside of toroids and all muon trajectory measurements are made in a nonmagnetic environment. Internal support for each magnet structure is provided by sheets, located at frequent and regularly spaced azimuthal planes, which interconnect the structural walls of the toroidal magnets. In a preferred embodiment, the shape of the toroidal magnet volume is adjusted to provide constant resolution over a wide range of rapidity. 4 figs.
Toroidal magnetic detector for high resolution measurement of muon momenta
Bonanos, Peter
1992-01-01
A muon detector system including central and end air-core superconducting toroids and muon detectors enclosing a central calorimeter/detector. Muon detectors are positioned outside of toroids and all muon trajectory measurements are made in a nonmagnetic environment. Internal support for each magnet structure is provided by sheets, located at frequent and regularly spaced azimuthal planes, which interconnect the structural walls of the toroidal magnets. In a preferred embodiment, the shape of the toroidal magnet volume is adjusted to provide constant resolution over a wide range of rapidity.
Design and implementation of a Thomson scattering diagnostic for the Compact Toroidal Hybrid
NASA Astrophysics Data System (ADS)
Traverso, Peter; Maurer, David; Hartwell, Gregory; Knowlton, Stephen; Miller, Matthew
2012-10-01
The Compact Toroidal Hybrid (CTH) experiment is investigating the avoidance of disruptions in ohmically driven torsaton plasmas in which the ratio of vacuum or external coil transform to the total transform generated by the plasma current and external coils can be lower than 10%. To aid in the characterization and equilibrium reconstruction of these current-carrying CTH plasmas a new Thomson scattering system is under development. Details of the Thomson scattering system design and implementation will be discussed including choice of laser scattering geometry, laser wavelength, stray laser light rejection strategy, collections optics, and spectrometer design.
Edge ambipolar potential in toroidal fusion plasmas
Spizzo, G. Vianello, N.; Agostini, M.; Puiatti, M. E.; Scarin, P.; Spolaore, M.; Terranova, D.; White, R. B.; Abdullaev, S. S.; Schmitz, O.; Cavazzana, R.; Ciaccio, G.
2014-05-15
A series of issues with toroidally confined fusion plasmas are related to the generation of 3D flow patterns by means of edge magnetic islands, embedded in a chaotic field and interacting with the wall. These issues include the Greenwald limit in Tokamaks and reversed-field pinches, the collisionality window for ELM mitigation with the resonant magnetic perturbations (RMPs) in Tokamaks, and edge islands interacting with the bootstrap current in stellarators. Measurements of the 2D map of the edge electric field E{sup r}(r=a,θ,ϕ) in the RFX reversed-field pinch show that E{sup r} has the same helicity of the magnetic islands generated by a m/n perturbation: in fact, defining the helical angle u=mθ−nϕ+ωt, maps show a sinusoidal dependence as a function of u, E{sup r}=E{sup ~r}sin u. The associated E × B flow displays a huge convective cell with v(a)≠0 which, in RFX and near the Greenwald limit, determines a stagnation point for density and a reversal of the sign of E{sup r}. From a theoretical point of view, the question is how a perturbed toroidal flux of symmetry m/n gives rise to an ambipolar potential Φ=Φ{sup ~}sin u. On the basis of a model developed with the guiding center code ORBIT and applied to RFX and the TEXTOR tokamak, we will show that the presence of an m/n perturbation in any kind of device breaks the toroidal symmetry with a drift proportional to the gyroradius ρ, thus larger for ions (ρ{sub i} ≫ ρ{sub e}). Immediately, an ambipolar potential arises to balance the drifts, with the same symmetry as the original perturbation.
Study on splitting of a toroidal bubble near a rigid boundary
NASA Astrophysics Data System (ADS)
Zhang, A. M.; Li, S.; Cui, J.
2015-06-01
The splitting of a toroidal bubble near a rigid boundary is commonly observed in experiments, which is a quite complex phenomenon in bubble dynamics and still not yet well understood. In present study, the bubble splitting phenomenon is studied using the boundary integral method. The vortex ring model is extended to multiple vortex rings to simulate the interaction between two toroidal bubbles after splitting. Buoyancy and non-buoyancy cases are investigated numerically in this study. Numerical results with buoyancy effects show favorable agreement with the experimental observations, which validates the present model. Generally, the first split of the toroidal bubble occurs when an annular "sideways jet" collides with the other side of the bubble. After the toroidal bubble splitting, some new phenomena are found as follows: (i) An annular high pressure region is generated at the splitting location, and the maximum pressure is associated with the velocity differences between the two sides therein just before splitting. (ii) The total volume varies continuously, while the two sub-bubbles vary differently in volume after splitting. (iii) The sideways jet continues propagating on a sub-bubble surface, which would cause more splits or partial breakup of the splash film into droplets. This may be an important reason for the formation of bubble cloud and the rough bubble surface in the rebounding process.
Toroidal membrane vesicles in spherical confinement.
Bouzar, Lila; Menas, Ferhat; Müller, Martin Michael
2015-09-01
We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically.
Plasma current resonance in asymmetric toroidal systems
Hazeltine, R. D.; Catto, Peter J.
2015-09-15
The well-known singularity in the magnetic differential equation for plasma current in an asymmetric toroidal confinement system is resolved by including in the pressure tensor corrections stemming from finite Larmor radius. The result provides an estimate of the amplitude of spikes in the parallel current that occur on rational magnetic surfaces. Resolution of the singularity is shown to depend on both the ambipolarity condition—the requirement of zero surface-averaged radial current—and the form of the magnetic differential equation near the rational surface.
Polar interface phonons in ionic toroidal systems
NASA Astrophysics Data System (ADS)
Nguyen, N. D.; Evrard, R.; Stroscio, Michael A.
2016-09-01
We use the dielectric continuum model to obtain the polar (Fuchs–Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus.
Toroidal membrane vesicles in spherical confinement
NASA Astrophysics Data System (ADS)
Bouzar, Lila; Menas, Ferhat; Müller, Martin Michael
2015-09-01
We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically.
Polar interface phonons in ionic toroidal systems.
Nguyen, N D; Evrard, R; Stroscio, Michael A
2016-09-01
We use the dielectric continuum model to obtain the polar (Fuchs-Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus.
Polar interface phonons in ionic toroidal systems
NASA Astrophysics Data System (ADS)
Nguyen, N. D.; Evrard, R.; Stroscio, Michael A.
2016-09-01
We use the dielectric continuum model to obtain the polar (Fuchs-Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus.
Polar interface phonons in ionic toroidal systems.
Nguyen, N D; Evrard, R; Stroscio, Michael A
2016-09-01
We use the dielectric continuum model to obtain the polar (Fuchs-Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus. PMID:27357246
Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows
Garcia de Andrade, L.C.
2006-02-15
Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of the penetration depth used in superconductors. The ratio between poloidal and toroidal components of the magnetic field depends on the torsion and curvature of the magnetic flux tube. It is shown that the rotation of the almost helical plasma flow contributes to the twist of the magnetic flux tube through the total Frenet torsion along the tube.
Propulsion using the electron spiral toroid
Seward, Clint
1998-01-15
A new propulsion method is proposed which could potentially reduce propellant needed for space travel by three orders of magnitude. It uses the newly patented electron spiral toroid (EST), which stores energy as magnetic field energy. The EST is a hollow toroid of electrons, all spiraling in parallel paths in a thin outer shell. The electrons satisfy the coupling condition, forming an electron matrix. Stability is assured as long as the coupling condition is satisfied. The EST is held in place with a small external electric field; without an external magnetic field. The EST system is contained in a vacuum chamber. The EST can be thought of as an energetic entity, with electrons at 10,000 electron volts. Propulsion would not use combustion, but would heat propellant through elastic collisions with the EST surface and eject them for thrust. Chemical rocket combustion heats propellant to 4000 deg. C; an EST will potentially heat the propellant 29,000 times as much, reducing propellant needs accordingly. The thrust can be turned ON and OFF. The EST can be recharged as needed.
Variable control of neutron albedo in toroidal fusion devices
Jassby, D.L.; Micklich, B.J.
1983-06-01
This invention pertains to methods of controlling in the steady state, neutron albedo in toroidal fusion devices, and in particular, to methods of controlling the flux and energy distribution of collided neutrons which are incident on an outboard wall of a toroidal fusion device.
2-D skin-current toroidal-MHD-equilibrium code
Feinberg, B.; Niland, R.A.; Coonrod, J.; Levine, M.A.
1982-09-01
A two-dimensional, toroidal, ideal MHD skin-current equilibrium computer code is described. The code is suitable for interactive implementation on a minicomptuer. Some examples of the use of the code for design and interpretation of toroidal cusp experiments are presented.
Segmented saddle-shaped passive stabilization conductors for toroidal plasmas
Leuer, James A.
1990-05-01
A large toroidal vacuum chamber for plasma generation and confinement is lined with a toroidal blanket for shielding using modules segmented in the toroidal direction. To provide passive stabilization in the same manner as a conductive vacuum chamber wall, saddle-shaped conductor loops are provided on blanket modules centered on a midplane of the toroidal chamber with horizontal conductive bars above and below the midplane, and vertical conductive legs on opposite sides of each module to provide return current paths between the upper and lower horizontal conductive bars. The close proximity of the vertical legs provided on adjacent modules without making physical contact cancel the electromagnetic field of adjacent vertical legs. The conductive bars spaced equally above and below the midplane simulate toroidal conductive loops or hoops that are continuous, for vertical stabilization of the plasma even though they are actually segmented.
Segmented saddle-shaped passive stabilization conductors for toroidal plasmas
Leuer, J.A.
1990-05-01
A large toroidal vacuum chamber for plasma generation and confinement is lined with a toroidal blanket for shielding using modules segmented in the toroidal direction. To provide passive stabilization in the same manner as a conductive vacuum chamber wall, saddle-shaped conductor loops are provided on blanket modules centered on a midplane of the toroidal chamber with horizontal conductive bars above and below the midplane, and vertical conductive legs on opposite sides of each module to provide return current paths between the upper and lower horizontal conductive bars. The close proximity of the vertical legs provided on adjacent modules without making physical contact cancel the electromagnetic field of adjacent vertical legs. The conductive bars spaced equally above and below the midplane simulate toroidal conductive loops or hoops that are continuous, for vertical stabilization of the plasma even though they are actually segmented. 5 figs.
Plasmonic Toroidal Dipolar Response under Radially Polarized Excitation
Bao, Yanjun; Zhu, Xing; Fang, Zheyu
2015-01-01
Plasmonic toroidal resonance has attracted growing interests because of its low loss electromagnetic properties and potential high sensitive nanophotonic applications. However, the realization in a metamaterial requires three-dimensional complicated structural design so far. In this paper, we design a simple metal-dielectric-metal (MIM) sandwich nanostructure, which exhibits a strong toroidal dipolar resonance under radially polarized excitation. The toroidal dipole moment as the dominant contribution for the scattering is demonstrated by the mirror-image method and further analyzed by Lagrangian hybridization model. The proposed toroidal configuration also shows a highly tolerant for misalignment between the structure center and the incident light focus. Our study proves the way for the toroidal plasmonic application with the cylindrical vector beams. PMID:26114966
Formation of a compact toroid for enhanced efficiency
Mozgovoy, A. G.; Romadanov, I. V.; Ryzhkov, S. V.
2014-02-15
We report here our results on the formation of a plasma configuration with the generic name of compact toroid (CT). A method of compact toroid formation to confine, heat and compress a plasma is investigated. Formation of a compact torus using an additional toroidal magnetic field helps to increase the plasma current to a maintainable level of the original magnetic field. We design the Compact Toroid Challenge (CTC) experiment in order to improve the magnetic flux trapping during field reversal in the formation of a compact toroid. The level of the magnetic field immersed in the plasma about 70% of the primary field is achieved. The CTC device and scheme of high level capturing of magnetic flux are presented.
NASA Technical Reports Server (NTRS)
Jordan, T. M.
1970-01-01
A description of the FASTER-III program for Monte Carlo Carlo calculation of photon and neutron transport in complex geometries is presented. Major revisions include the capability of calculating minimum weight shield configurations for primary and secondary radiation and optimal importance sampling parameters. The program description includes a users manual describing the preparation of input data cards, the printout from a sample problem including the data card images, definitions of Fortran variables, the program logic, and the control cards required to run on the IBM 7094, IBM 360, UNIVAC 1108 and CDC 6600 computers.
NASA Technical Reports Server (NTRS)
Jordan, T. M.
1970-01-01
The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.
Turbulent Equipartition Theory of Toroidal Momentum Pinch
NASA Astrophysics Data System (ADS)
Hahm, T. S.
2007-11-01
The turbulent convective flux (pinch) of the toroidal angular momentum density is derived using the nonlinear toroidal gyrokinetic equation which conserves phase space density and energy[1], and a novel pinch mechanism which originates from the symmetry breaking due to the magnetic field curvature is identified. A net parallel momentum transfer from the waves to the ion guiding centers is possible when the fluctuation intensity varies on the flux surface, resulting in imperfect cancellation of the curvature drift contribution to the parallel acceleration. This pinch velocity of the angular momentum density can also be understood as a manifestation of a tendency to homogenize the profile of ``magnetically weighted angular momentum density,'' nmiRU/B^2. This part of the pinch flux is mode-independent (whether it's TEM driven or ITG driven), and radially inward for fluctuations peaked at the low-B-field side, with a pinch velocity typically, V^TEPAng˜- 2 χφ/R0. We compare and contrast the pinch of toroidal angular momentum with the now familiar ``turbulent equipartition'' (TEP) mechanism for the particle pinch[2] which exhibit some relevance in various L-mode plasmas in tokamaks. In our theoretical model[3], the TEP momentum pinch is shown to arise from the fact that, in a low-β tokamak equilibrium, B^2uE= cB x∇ δφ is approximately incompressible, so that the magnetically weighted angular momentum density (minU/B^3 minUR/B^2) is locally advected by fluctuating E xB velocities, to the lowest order in O(a/R). As a consequence minUR/B^2 is mixed or homogenized, so that ψ minUR/B^2 ->0. [1] T.S. Hahm, Phys. Fluids 31, 2670 (1988) [2] V.V. Yankov, JETP Lett. 60, 171 (1994); M.B. Isichenko et al., Phys. Rev. Lett. 74, 4436 (1995); X. Garbet et al., Phys. Plasmas 12, 082511 (2005). [3] T.S. Hahm, P.H. Diamond, O. Gurcan, and G. Rewoldt, Phys. Plasmas 14, 072302 (2007).
Epithelial Proliferation on Curved Toroidal Surfaces
NASA Astrophysics Data System (ADS)
Chang, Ya-Wen; Cruz, Ricardo; Fragkopoulos, Alexandros; Marquez, Samantha; Garcia, Andres; Fernandez-Nieves, Alberto
Cellular environment influences a multitude of cellular functions by providing chemical and physical signals that modulate cell behavior, dynamics, development, and eventually survival. In strongly interacting epithelial cells, cells coordinate their behavior to respond to mechanical constraints in 2D. Local differences in tissue tension has also been shown to impact cell reproduction within an epithelial-cell sheet. Much less is known about how cells respond to out-of-plane curvatures. Here, we describe the proliferation of MDCK on toroidal hydrogel substrates, which unlike spheres or planes, have regions of both positive and negative Gaussian curvature. Additionally, the range of curvatures can be controlled by varying the size and aspect ratio of the torus, allowing us to quantify the relation between substrate curvature and cell proliferation.
Isomorphic routing on a toroidal mesh
NASA Technical Reports Server (NTRS)
Mao, Weizhen; Nicol, David M.
1993-01-01
We study a routing problem that arises on SIMD parallel architectures whose communication network forms a toroidal mesh. We assume there exists a set of k message descriptors (xi, yi), where (xi, yi) indicates that the ith message's recipient is offset from its sender by xi hops in one mesh dimension, and yi hops in the other. Every processor has k messages to send, and all processors use the same set of message routing descriptors. The SIMD constraint implies that at any routing step, every processor is actively routing messages with the same descriptors as any other processor. We call this isomorphic routing. Our objective is to find the isomorphic routing schedule with least makespan. We consider a number of variations on the problem, yielding complexity results from O(k) to NP-complete. Most of our results follow after we transform the problem into a scheduling problem, where it is related to other well-known scheduling problems.
Wall conditioning in ATF (Advanced Toroidal Facility)
Langley, R.A.; Clark, T.L.; Glowienka, J.C.; Goulding, R.H.; Mioduszewski, P.K.; Rasmussen, D.A.; Rayburn, T.F.; Schaich, C.R.; Shepard, T.D.; Simpkins, J.E.
1989-01-01
Techniques for cleaning and conditioning the vacuum vessel of the Advanced Toroidal Facility (ATF) and its internal components are described. The vacuum vessel cleaning technique combines baking to 150/degree/C and glow discharges with hydrogen gas. Chromium gettering is used to further condition the system. The major internal components are the anodized aluminium baffles in the Thomson scattering system, a graphite-shielded ICRF antenna, two graphite limiters, and a diagnostic graphite plate. Three independent heating systems are used to bake some of the major components of the system. The major characteristics used for assessing cleanliness and conditioning progress are the maximum pressure attained during bakeout, the result of gas analysis, and relevant plasma parameters (e.g., time to radiative decay). Details of the various cleaning and conditioning procedures and results are presented. 5 refs., 8 figs., 3 tabs.
Toroid Joining Gun For Fittings And Couplings
NASA Technical Reports Server (NTRS)
Fox, Robert L.; Swaim, Robert J.; Johnson, Samuel D.; Buckley, John D.; Copeland, Carl E.; Coultrip, Robert H.; Johnston, David F.; Phillips, William M.
1992-01-01
Hand-held gun used to join metal heat-to-shrink couplings. Uses magnetic induction (eddy currents) to produce heat in metal coupling, and thermocouple to measure temperature and signals end of process. Gun, called "toroid joining gun" concentrates high levels of heat in localized areas. Reconfigured for use on metal heat-to-shrink fitting and coupling applications. Provides rapid heating, operates on low power, lightweight and portable. Safe for use around aircraft fuel and has no detrimental effects on surrounding surfaces or objects. Reliable in any environment and under all weather conditions. Gun logical device for taking full advantage of capabilities of new metal heat-to-shrink couplings and fittings.
Unstable-stable resonators with toroidal mirrors.
Borghese, A; Canevari, R; Donati, V; Garifo, L
1981-10-15
A resonator with toroidal mirrors is described. This resonator behaves like an off-axis unstable confocal resonator in one transverse dimension and like an on-axis concave-convex stable resonator in the other orthogonal dimension. Some experimental results are reported for a fast flow high power cw-CO(2) laser whose transverse cross section is restricted in the stable-resonator direction. These cavities allow an output laser beam with a fully illuminated cross section which is well suited for focusing. Moreover, the fraction of the available laser power which may be concentrated in the central lobe of the focal plane intensity distribution is 2.5-4.5 times higher than other unstable resonators with similarly restricted modal volumes. Finally the alignment requirements are examined. PMID:20372215
Recent Progress in Compact Toroidal Hybrid Research
NASA Astrophysics Data System (ADS)
Maurer, D. A.; Cianciosa, M.; Hanson, J. D.; Hartwell, G. J.; Hebert, J. D.; Herfindal, J. L.; Knowlton, S. F.; Archmiller, M. C.; Traverso, P.; Pandya, M.; Ma, X.
2013-10-01
The Compact Toroidal Hybrid (CTH) experiment is investigating the passive avoidance of disruptions with the addition of a small amount of vacuum transform provided by external coils. In ohmically-driven stellarator plasmas, disruption suppression depends upon the particular disruption scenario. Recent progress on the suppression of low edge q, density limit, and vertically unstable plasma disruptions is overviewed. Interpretation of these results makes use of 3D equilibrium reconstructions using the V3FIT code. Several new diagnostic tools, including new magnetic sensors for MHD fluctuation studies, a multipoint Thomson scattering system, and a 2D soft x-ray two-color camera system are under development to further enable our understanding of CTH disruption dynamics. Future research directions, including plans for an island divertor, will be discussed. This work is supported by U. S. Department of Energy Grant No. DE-FG02- 00ER54610.
Helicity of a toroidal vortex with swirl
NASA Astrophysics Data System (ADS)
Bannikova, E. Yu.; Kontorovich, V. M.; Poslavsky, S. A.
2016-04-01
Based on the solutions of the Bragg-Hawthorne equation, we discuss the helicity of a thin toroidal vortex in the presence of swirl, orbital motion along the torus directrix. The relation between the helicity and circulations along the small and large linked circumferences (the torus directrix and generatrix) is shown to depend on the azimuthal velocity distribution in the core of the swirling ring vortex. In the case of nonuniform swirl, this relation differs from the well-known Moffat relation, viz., twice the product of such circulations multiplied by the number of linkages. The results can find applications in investigating the vortices in planetary atmospheres and the motions in the vicinity of active galactic nuclei.
Nonideal magnetohydrodynamic instabilities and toroidal magnetic confinement
Furth, H.P.
1985-05-01
The marked divergence of experimentally observed plasma instability phenomena from the predictions of ideal magnetohydrodynamics led in the early 1960s to the formulations of finite-resistivity stability theory. Beginning in the 1970s, advanced plasma diagnostics have served to establish a detailed correspondence between the predictions of the finite-resistivity theory and experimental plasma behavior - particularly in the case of the resistive kink mode and the tokamak plasma. Nonlinear resistive-kink phenomena have been found to govern the transport of magnetic flux and plasma energy in the reversed-field pinch. The other predicted finite-resistivity instability modes have been more difficult to identify directly and their implications for toroidal magnetic confinement are still unresolved.
Petascale Parallelization of the Gyrokinetic Toroidal Code
Ethier, Stephane; Adams, Mark; Carter, Jonathan; Oliker, Leonid
2010-05-01
The Gyrokinetic Toroidal Code (GTC) is a global, three-dimensional particle-in-cell application developed to study microturbulence in tokamak fusion devices. The global capability of GTC is unique, allowing researchers to systematically analyze important dynamics such as turbulence spreading. In this work we examine a new radial domain decomposition approach to allow scalability onto the latest generation of petascale systems. Extensive performance evaluation is conducted on three high performance computing systems: the IBM BG/P, the Cray XT4, and an Intel Xeon Cluster. Overall results show that the radial decomposition approach dramatically increases scalability, while reducing the memory footprint - allowing for fusion device simulations at an unprecedented scale. After a decade where high-end computing (HEC) was dominated by the rapid pace of improvements to processor frequencies, the performance of next-generation supercomputers is increasingly differentiated by varying interconnect designs and levels of integration. Understanding the tradeoffs of these system designs is a key step towards making effective petascale computing a reality. In this work, we examine a new parallelization scheme for the Gyrokinetic Toroidal Code (GTC) [?] micro-turbulence fusion application. Extensive scalability results and analysis are presented on three HEC systems: the IBM BlueGene/P (BG/P) at Argonne National Laboratory, the Cray XT4 at Lawrence Berkeley National Laboratory, and an Intel Xeon cluster at Lawrence Livermore National Laboratory. Overall results indicate that the new radial decomposition approach successfully attains unprecedented scalability to 131,072 BG/P cores by overcoming the memory limitations of the previous approach. The new version is well suited to utilize emerging petascale resources to access new regimes of physical phenomena.
Rodrigues, Paulo; Bizarro, Joao P. S.
2013-04-15
The axisymmetry condition and two of Maxwell's equations are used to show that, in general, there are no nested magnetic surfaces around a poloidal-magnetic-field null for a sufficiently small value of the toroidal current density flowing there. Hence, the toroidal current density at the axis of a magnetic configuration with extreme shear reversal cannot continuously approach zero unless nested surfaces are first broken or particular values are assigned to boundary conditions and other plasma parameters. The threshold of the toroidal current-density at which the topology changes is shown to be set by such parameters, and some examples of the predicted topology transition are presented using analytical solutions of the Grad-Shafranov equation.
Nuclear resonance tomography with a toroid cavity detector
Woelk, K.; Rathke, J.W.; Klingler, R.J.
1996-11-12
A toroid cavity detection system is described for determining the spectral properties and distance from a fixed point for a sample using Nuclear Magnetic Resonance. The detection system consists of a toroid with a central conductor oriented along the main axis of the toroidal cylinder and perpendicular to a static uniform magnetic field oriented along the main axis of the toroid. An rf signal is input to the central conductor to produce a magnetic field perpendicular to the central axis of the toroid and whose field strength varies as the inverse of the radius of the toroid. The toroid cavity detection system can be used to encapsulate a sample, or the detection system can be perforated to allow a sample to flow into the detection device or to place the samples in specified sample tubes. The central conductor can also be coated to determine the spectral property of the coating and the coating thickness. The sample is then subjected to the respective magnetic fields and the responses measured to determine the desired properties. 4 figs.
Nuclear resonance tomography with a toroid cavity detector
Woelk, Klaus; Rathke, Jerome W.; Klingler, Robert J.
1996-01-01
A toroid cavity detection system for determining the spectral properties and distance from a fixed point for a sample using Nuclear Magnetic Resonance. The detection system consists of a toroid with a central conductor oriented along the main axis of the toroidal cylinder and perpendicular to a static uniform magnetic field oriented along the main axis of the toroid. An rf signal is inputted to the central conductor to produce a magnetic field perpendicular to the central axis of the toroid and whose field strength varies as the inverse of the radius of the toroid. The toroid cavity detection system can be used to encapsulate a sample, or the detection system can be perforated to allow a sample to flow into the detection device or to place the samples in specified sample tubes. The central conductor can also be coated to determine the spectral property of the coating and the coating thickness. The sample is then subjected to the respective magnetic fields and the responses measured to determine the desired properties.
NASA Astrophysics Data System (ADS)
Prástaro, Agostino
2008-02-01
Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.
Toroidal flow and radial particle flux in tokamak plasmas
NASA Astrophysics Data System (ADS)
Callen, J. D.; Cole, A. J.; Hegna, C. C.
2009-08-01
Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial plasma transport due to collisional processes and microturbulence-induced anomalous transport are usually considered. In addition, toroidal flow can be affected by nonaxisymmetric magnetic fields; resonant components cause localized electromagnetic toroidal torques near rational surfaces in flowing plasmas and nonresonant components induce "global" toroidal flow damping torque throughout the plasma. Also, poloidal magnetic field transients on the magnetic field diffusion time scale can influence plasma transport. Many of these processes can also produce momentum pinch and intrinsic flow effects. This paper presents a comprehensive and self-consistent description of all these effects within a fluid moment context. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfvén waves (Grad-Shafranov equilibrium and ion radial force balance), sound waves (pressure constant along a field line and incompressible flows within a flux surface), and ion collisions (damping of poloidal flow). Finally, plasma transport across magnetic flux surfaces is induced by the many second order (in the small gyroradius expansion) toroidal torque effects indicated above. Nonambipolar components of the induced particle transport fluxes produce radial plasma currents. Setting the flux surface average of the net radial current induced by all these effects to zero yields the transport-time-scale equation for evolution of the plasma toroidal flow. It includes a combination of global toroidal flow damping and resonant torques induced by nonaxisymmetric magnetic field components, poloidal magnetic field transients, and momentum source effects, as well as the usual collision- and microturbulence-induced transport. On the transport time scale, the plasma toroidal rotation determines the radial electric field for net ambipolar particle transport
The residual zonal flow in tokamak plasmas toroidally rotating at arbitrary velocity
Zhou, Deng
2014-08-15
Zonal flows, initially driven by ion-temperature-gradient turbulence, may evolve due to the neoclassic polarization in a collisionless tokamak plasma. In our previous work [D. Zhou, Nucl. Fusion 54, 042002 (2014)], the residual zonal flow in a tokamak plasma rotating toroidally at sonic speed is found to have the same form as that of a static plasma. In the present work, the form of the residual zonal flow is presented for tokamak plasmas rotating toroidally at arbitrary velocity. The gyro-kinetic equation is analytically solved for low speed rotation to give the expression of residual zonal flows, and the expression is then generalized for cases with arbitrary rotating velocity through interpolation. The zonal flow level decreases as the rotating velocity increases. The numerical evaluation is in good agreement with the former simulation result for high aspect ratio tokamaks.
Kinetic effect of toroidal rotation on the geodesic acoustic mode
Guo, W. Ye, L.; Zhou, D.; Xiao, X.; Wang, S.
2015-01-15
Kinetic effects of the toroidal rotation on the geodesic acoustic mode are theoretically investigated. It is found that when the toroidal rotation increases, the damping rate increases in the weak rotation regime due to the rotation enhancement of wave-particle interaction, and it decreases in the strong rotation regime due to the reduction of the number of resonant particles. Theoretical results are consistent with the behaviors of the geodesic acoustic mode recently observed in DIII-D and ASDEX-Upgrade. The kinetic damping effect of the rotation on the geodesic acoustic mode may shed light on the regulation of turbulence through the controlling the toroidal rotation.
Toroidal Single Wall Carbon Nanotubes in Fullerene Crop Circles
NASA Technical Reports Server (NTRS)
Han, Jie; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
We investigate energetics and structure of circular and polygonal single wall carbon nanotubes (SWNTs) using large scale molecular simulations on NAS SP2, motivated by their unusual electronic and magnetic properties. The circular tori are formed by bending tube (no net whereas the polygonal tori are constructed by turning the joint of two tubes of (n, n), (n+1, n-1) and (n+2, n-2) with topological pentagon-heptagon defect, in which n =5, 8 and 10. The strain energy of circular tori relative to straight tube decreases by I/D(sup 2) where D is torus diameter. As D increases, these tori change from buckling to an energetically stable state. The stable tori are perfect circular in both toroidal and tubular geometry with strain less than 0. 03 eV/atom when D greater than 10, 20 and 40 nm for torus (5,5), (8,8) and (10, 10). Polygonal tori, whose strain is proportional to the number of defects and I/D are energetically stable even for D less than 10 nm. However, their strain is higher than that of perfect circular tori. In addition, the local maximum strain of polygonal tori is much higher than that of perfect circular tori. It is approx. 0.03 eV/atom or less for perfect circular torus (5,5), but 0.13 and 0.21 eV/atom for polygonal tori (6,4)/(5,5) and (7,3)/(5,5). Therefore, we conclude that the circular tori with no topological defects are more energetically stable and kinetically accessible than the polygonal tori containing the pentagon-heptagon defects for the laser-grown SWNTs and Fullerene crop circles.
Conventionalism and integrable Weyl geometry
NASA Astrophysics Data System (ADS)
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Toroidal transducer with two large focal zones for increasing the coagulated volume
NASA Astrophysics Data System (ADS)
Vincenot, J.; Melodelima, D.; Kocot, A.; Chavrier, F.; Chapelon, J. Y.
2012-11-01
Toroidal HIFU transducers have been shown to generate large conical ablations (7 cm3 in 40 seconds). The focal zone is composed of a first ring-shaped focal zone and an overlap of ultrasound beams behind this first focus. A HIFU device has been developed on this principle to treat liver metastases during an open procedure. Although these large lesions contribute to reduce treatment time, it is still needed to juxtapose 4 to 9 single HIFU lesions to treat liver metastasis (2 cm in diameter) with safety margins. In this work, a different toroidal geometry was used. With this transducer, the overlap area is located between the probe and the focal ring. The objective was to use this transducer with electronic focusing in order to create a spherical shape lesion with sufficient volume for the destruction of a metastasis of 2 cm in diameter without any mechanical displacement. The operating frequency of the toroidal transducer was 2.5 MHz. The radius of curvature was 70 mm with a diameter of 67 mm. The focal ring had a radius of 15 mm. The overlap zone extent between 35 to 55 mm from the emitting surface. An ultrasound-imaging probe (working at 7.5 MHz) was placed in a central circular opening of 26 mm in the HIFU transducer and was aligned with the focal plane. The transducer was divided into 32 rings of 78 mm2. Using a 32 channels amplifier with a phase resolution of 1.4 degrees, it was possible to change the diameter (0 to 15 mm) and depth (45 to 85 mm) of the focus circle to maximize dimensions of the lesion. Tests were conducted in vitro, in bovine liver samples. This toroidal geometry and the use of electronic beam steering allow the creation of roughly spherical lesions (diameter of 47 mm, depth of 35 mm). This treatment was obtained in 6 minutes and 10 seconds without any mechanical displacement of the transducer. The lesions obtained were homogeneous and no untreated area was observed. In conclusion, these results indicate that the treatment of a liver
On the use of a toroidal mirror to focus neutrons at the ILL neutron spin echo spectrometer IN15
Hayes, C.; Alefeld, B.; Copley, J.R.D.
1997-09-01
The IN15 neutron spin echo spectrometer at the Institut Laue-Langevin (Grenoble) has been designed to accomodate a toroidal focusing mirror. This mirror will be used to increase the intensity at the sample position for measurements at long neutron wavelengths and to perform measurements in the low q-range (10{sup -3} {angstrom}{sup -1}). This paper summarizes the results of ray-tracing simulations for the toroidal mirror system. These calculations were performed in order to assess the effects of the neutron wavelength, gravitational fall, wavelength resolution and spherical aberrations on the quality of the focused beam. The gain in flux that can be expected from the focusing geometry is estimated. The recent installation and characterisation of the mirror is also briefly described.
NASA Technical Reports Server (NTRS)
Mcdonough, T. R.
1974-01-01
The trapping of Titan's escaping atmosphere in the Saturnian system by a toroidal ring is discussed. The radius of the toroid is comparable to Titan's orbit, or about ten times larger than the visible rings. Theoretical atmospheric models are formulated that consider Saturn's gravitational attraction and magnetospheric properties in forming this toroid and in protecting toroid particles from direct ionization by solar wind particles.
Toroidal band limiter for a plasma containment device
Kelley, George G.
1978-01-01
This invention relates to a toroidal plasma confinement device having poloidal and toroidal magnetic fields for confining a toroidal plasma column with a plasma current induced therein along an endless, circular equilibrium axis in a torus vacuum cavity wherein the improvement comprises the use of a toroidal plasma band limiter mounted within the vacuum cavity in such a manner as to ensure that the plasma energy is distributed more uniformly over the limiter surface thereby avoiding intense local heating of the limiter while at the same time substantially preventing damage to the plasma containment wall of the cavity by the energetic particles diffusing out from the confined plasma. A plurality of poloidal plasma ring limiters are also utilized for containment wall protection during any disruptive instability that might occur during operation of the device.
System and method of operating toroidal magnetic confinement devices
Chance, M.S.; Jardin, S.C.; Stix, T.H.; Grimm, R.C.; Manickam, J.; Okabayashi, M.
1984-08-30
This invention pertains to methods and arrangements for attaining high beta values in plasma confinement devices. More specifically, this invention pertains to methods for accessing the second stability region of operation in toroidal magnetic confinement devices.
Equilibrium analysis of tokamak discharges with toroidal variation
Zwingmann, W.; Becoulet, M.; Moreau, Ph.; Nardon, E.
2006-11-30
Tokamaks provide a field structure that is almost axisymmetric around the torus axis. There are however always small toroidal variations due to the limited number of toroidal field coils, the magnetic field ripple. On the other hand, non-axisymmetric external fields are applied on purpose to ergodise the field structure close to the separatrix, to control the heat and particle transport across the plasma boundary. We present a perturbation method to calculate the magnetic field of tokamak discharges with with weak toroidal variation. The method is applied for the equilibrium reconstruction of Tore Supra discharges with toroidal ripple. The perturbation method does not rely on a flux surface representation and can therefore be applied to structures with magnetic islands. We obtain the plasma response to the field of ergodising external coils, as proposed for the ITER device.
High-frequency electric field measurement using a toroidal antenna
Lee, Ki Ha
2002-01-01
A simple and compact method and apparatus for detecting high frequency electric fields, particularly in the frequency range of 1 MHz to 100 MHz, uses a compact toroidal antenna. For typical geophysical applications the sensor will be used to detect electric fields for a wide range of spectrum starting from about 1 MHz, in particular in the frequency range between 1 to 100 MHz, to detect small objects in the upper few meters of the ground. Time-varying magnetic fields associated with time-varying electric fields induce an emf (voltage) in a toroidal coil. The electric field at the center of (and perpendicular to the plane of) the toroid is shown to be linearly related to this induced voltage. By measuring the voltage across a toroidal coil one can easily and accurately determine the electric field.
Melodelima, D.; N'Djin, W. A.; Parmentier, H.; Chapelon, J. Y.; Rivoire, M.
2009-04-14
A new geometry of HIFU transducer is described to enlarge the coagulated volume. The geometry of the transducer was not spherical. The surface of the transducer was built based on a toroid geometry. The transducer was generated by the revolution of a circle about an axis lying in its plane. Eight emitters operating at a frequency of 3 MHz were diced out of a single toroid piezocomposite element. Each of the eight emitters was divided into 32 transducers. The focal zone is conical and located at 70 mm from the transducer. A 7.5 MHz ultrasound imaging probe is placed in the centre of the device for guiding the treatment. Our long-term objective is to develop a device that can be used during surgery. In vivo trials have been performed on 13 pigs to demonstrate this new principle and to evaluate the vascular tolerance of the treatment. This new geometry combined with consecutive activation of the eight emitters around the toroid allows achieving a mean thermal ablation of 7.0{+-}2.5 cm3 in 40 seconds. All lesions were visible with high contrast on sonograms. The correlation between the size of lesions observed on sonograms and during gross examination was 92%. This allows the user to easily enlarge the coagulated volume by juxtaposing single lesions. The pigs tolerate the treatment well over the experimental period even when coagulation was produced through portal and/or hepatic veins.
Spatiotemporal toroidal waves from the transverse second-harmonic generation.
Saltiel, Solomon M; Neshev, Dragomir N; Fischer, Robert; Krolikowski, Wieslaw; Arie, Ady; Kivshar, Yuri S
2008-03-01
We study the second-harmonic generation via transversely matched interaction of two counterpropagating ultrashort pulses in chi(2) photonic structures. We show that the emitted second-harmonic wave attains the form of spatially expanding toroid with the initial thickness given by the cross correlation of the pulses. We demonstrate the formation of such toroidal waves in crystals with random ferroelectric domains as well as in annularly poled nonlinear photonic structures.
Compact toroid injection into C-2U
NASA Astrophysics Data System (ADS)
Roche, Thomas; Gota, H.; Garate, E.; Asai, T.; Matsumoto, T.; Sekiguchi, J.; Putvinski, S.; Allfrey, I.; Beall, M.; Cordero, M.; Granstedt, E.; Kinley, J.; Morehouse, M.; Sheftman, D.; Valentine, T.; Waggoner, W.; the TAE Team
2015-11-01
Sustainment of an advanced neutral beam-driven FRC for a period in excess of 5 ms is the primary goal of the C-2U machine at Tri Alpha Energy. In addition, a criteria for long-term global sustainment of any magnetically confined fusion reactor is particle refueling. To this end, a magnetized coaxial plasma-gun has been developed. Compact toroids (CT) are to be injected perpendicular to the axial magnetic field of C-2U. To simulate this environment, an experimental test-stand has been constructed. A transverse magnetic field of B ~ 1 kG is established (comparable to the C-2U axial field) and CTs are fired across it. As a minimal requirement, the CT must have energy density greater than that of the magnetic field it is to penetrate, i.e., 1/2 ρv2 >=B2 / 2μ0 . This criteria is easily met and indeed the CTs traverse the test-stand field. A preliminary experiment on C-2U shows the CT also capable of penetrating into FRC plasmas and refueling is observed resulting in a 20 - 30% increase in total particle number per single-pulsed CT injection. Results from test-stand and C-2U experiments will be presented.
Tearing Mode Stability of Evolving Toroidal Equilibria
NASA Astrophysics Data System (ADS)
Pletzer, A.; McCune, D.; Manickam, J.; Jardin, S. C.
2000-10-01
There are a number of toroidal equilibrium (such as JSOLVER, ESC, EFIT, and VMEC) and transport codes (such as TRANSP, BALDUR, and TSC) in our community that utilize differing equilibrium representations. There are also many heating and current drive (LSC and TORRAY), and stability (PEST1-3, GATO, NOVA, MARS, DCON, M3D) codes that require this equilibrium information. In an effort to provide seamless compatibility between the codes that produce and need these equilibria, we have developed two Fortran 90 modules, MEQ and XPLASMA, that serve as common interfaces between these two classes of codes. XPLASMA provides a common equilibrium representation for the heating and current drive applications while MEQ provides common equilibrium and associated metric information needed by MHD stability codes. We illustrate the utility of this approach by presenting results of PEST-3 tearing stability calculations of an NSTX discharge performed on profiles provided by the TRANSP code. Using the MEQ module, the TRANSP equilibrium data are stored in a Fortran 90 derived type and passed to PEST3 as a subroutine argument. All calculations are performed on the fly, as the profiles evolve.
Sawtooth Instability in the Compact Toroidal Hybrid
NASA Astrophysics Data System (ADS)
Herfindal, J. L.; Maurer, D. A.; Hartwell, G. J.; Ennis, D. A.; Knowlton, S. F.
2015-11-01
Sawtooth instabilities have been observed in the Compact Toroidal Hybrid (CTH), a current-carrying stellarator/tokamak hybrid device. The sawtooth instability is driven by ohmic heating of the core plasma until the safety factor drops below unity resulting in the growth of an m = 1 kink-tearing mode. Experiments varying the vacuum rotational transform from 0.02 to 0.13 are being conducted to study sawtooth property dependance on vacuum flux surface structure. The frequency of the sawtooth oscillations increase from 2 kHz to 2.8 kHz solely due the decrease in rise time of the oscillation, the crash time is unchanged. CTH has three two-color SXR cameras, a three-channel 1mm interferometer, and a new bolometer system capable of detecting the signatures of sawtooth instabilities. The new bolometer system consists of two cameras, each containing a pair of diode arrays viewing the plasma directly or through a beryllium filter. Electron temperature measurements are found with the two-color SXR cameras through a ratio of the SXR intensities. Impurity radiation can drastically affect the electron temperature measurement, therefore new filters consisting of aluminum and carbon were selected to avoid problematic line radiation while maximizing the signal for a 100 eV plasma. This work is supported by U.S. Department of Energy Grant No. DE-FG02-00ER54610.
Toroidal bubble entrapment under an impacting drop
NASA Astrophysics Data System (ADS)
Thoraval, Marie-Jean; Thoroddsen, Sigurdur T.; Takehara, Kohsei; Etoh, Takeharu Goji
2012-11-01
We use ultra-high-speed imaging and numerical simulations (GERRIS, http://gfs.sf.net) to observe and analyze the formation of up to 14 air tori when a water drop impacts on a thin liquid film of water or other miscible liquids. They form during the early contact between the drop and the pool by the vertical oscillations of the ejecta sheet. They then break in micro-bubble rings by the Rayleigh instability. Their formation is associated with the shedding of an axisymmetric vortex street into the liquid from the free surface. These vorticity structures and their dynamics are made apparent by the dynamics of the micro-bubbles, added seed particles and the difference of refractive index for different liquids in the drop and the pool. More robust entrapments are observed for a thin film of ethanol or methanol. We show that while the non-spherical drop shape is not responsible for the toroidal bubble entrapments, the number of rings is increasing for more oblate drops. Individual bubble entrapments are also observed from azimuthal destabilizations of the neck between the drop and the pool.
Toroidal nanotraps for cold polar molecules
Salhi, Marouane; Passian, Ali; Siopsis, George
2015-09-14
Electronic excitations in metallic nanoparticles in the optical regime that have been of great importance in surface-enhanced spectroscopy and emerging applications of molecular plasmonics, due to control and confinement of electromagnetic energy, may also be of potential to control the motion of nanoparticles and molecules. Here, we propose a concept for trapping polarizable particles and molecules using toroidal metallic nanoparticles. Specifically, gold nanorings are investigated for their scattering properties and field distribution to computationally show that the response of these optically resonant particles to incident photons permit the formation of a nanoscale trap when proper aspect ratio, photon wavelength, andmore » polarization are considered. However, interestingly the resonant plasmonic response of the nanoring is shown to be detrimental to the trap formation. The results are in good agreement with analytic calculations in the quasistatic limit within the first-order perturbation of the scalar electric potential. The possibility of extending the single nanoring trapping properties to two-dimensional arrays of nanorings is suggested by obtaining the field distribution of nanoring dimers and trimers.« less
Toroidal nanotraps for cold polar molecules
Salhi, Marouane; Passian, Ali; Siopsis, George
2015-09-14
Electronic excitations in metallic nanoparticles in the optical regime that have been of great importance in surface-enhanced spectroscopy and emerging applications of molecular plasmonics, due to control and confinement of electromagnetic energy, may also be of potential to control the motion of nanoparticles and molecules. Here, we propose a concept for trapping polarizable particles and molecules using toroidal metallic nanoparticles. Specifically, gold nanorings are investigated for their scattering properties and field distribution to computationally show that the response of these optically resonant particles to incident photons permit the formation of a nanoscale trap when proper aspect ratio, photon wavelength, and polarization are considered. However, interestingly the resonant plasmonic response of the nanoring is shown to be detrimental to the trap formation. The results are in good agreement with analytic calculations in the quasistatic limit within the first-order perturbation of the scalar electric potential. The possibility of extending the single nanoring trapping properties to two-dimensional arrays of nanorings is suggested by obtaining the field distribution of nanoring dimers and trimers.
Spontaneous toroidal flow generation due to negative effective momentum diffusivity
McMillan, Ben F.
2015-02-15
Spontaneous structure formation, and in particular, zonal flows, is observed in a broad range of natural and engineered systems, often arising dynamically as the saturated state of a linear instability. Flows in tokamaks are known to self-organise on small scales, but large scale toroidal flows also arise even when externally applied torques are zero. This has previously been interpreted as the result of small externally imposed breaking of a symmetry. However, we show that for large enough field line pitch, a robust spontaneous symmetry breaking occurs, leading to the generation of strong toroidal flow structures; parameters are typical of Spherical Tokamak discharges with reversed shear profiles. The short wavelength dynamics are qualitatively similar to the growth of poloidal flow structures, and toroidal flow gradients nonlinearly saturate at levels where the shearing rate is comparable to linear growth rate. On long wavelengths, we measure Prandtl numbers of around zero for these systems, in conjunction with the formation of structured toroidal flows, and we show that this is consistent with a model of momentum transport where fluxes act to reinforce small flow gradients: the effective momentum diffusivity is negative. Toroidal flow structures are largely unaffected by collisional damping, so this may allow toroidal bulk flows of order the ion thermal velocity to be maintained with zero momentum input. This phenomenon also provides a mechanism for the generation of localised meso-scale structures like transport barriers.
Spontaneous toroidal flow generation due to negative effective momentum diffusivity
NASA Astrophysics Data System (ADS)
McMillan, Ben F.
2015-02-01
Spontaneous structure formation, and in particular, zonal flows, is observed in a broad range of natural and engineered systems, often arising dynamically as the saturated state of a linear instability. Flows in tokamaks are known to self-organise on small scales, but large scale toroidal flows also arise even when externally applied torques are zero. This has previously been interpreted as the result of small externally imposed breaking of a symmetry. However, we show that for large enough field line pitch, a robust spontaneous symmetry breaking occurs, leading to the generation of strong toroidal flow structures; parameters are typical of Spherical Tokamak discharges with reversed shear profiles. The short wavelength dynamics are qualitatively similar to the growth of poloidal flow structures, and toroidal flow gradients nonlinearly saturate at levels where the shearing rate is comparable to linear growth rate. On long wavelengths, we measure Prandtl numbers of around zero for these systems, in conjunction with the formation of structured toroidal flows, and we show that this is consistent with a model of momentum transport where fluxes act to reinforce small flow gradients: the effective momentum diffusivity is negative. Toroidal flow structures are largely unaffected by collisional damping, so this may allow toroidal bulk flows of order the ion thermal velocity to be maintained with zero momentum input. This phenomenon also provides a mechanism for the generation of localised meso-scale structures like transport barriers.
Kimin Kim, et al
2013-04-23
Accurate calculation of perturbed distribution function δf and perturbed magnetic fi eld δB is essential to achieve prediction of non-ambipolar transport and neoclassical toroidal viscosity (NTV) in perturbed tokamaks. This paper reports a study of the NTV with a δf particle code (POCA) and improved understanding of magnetic braking in tokamak experiments. POCA calculates the NTV by computing f with guiding-center orbit motion and using B from the ideal perturbed equilibrium code (IPEC). POCA simulations are compared with experimental estimations for NTV, which are measured from angular momentum balance (DIII-D) and toroidal rotational damping rate (NSTX). The calculation shows good agreement in total NTV torque for the DIII-D discharge, where an analytic neoclassical theory also gives a consistent result thanks to relatively large aspect-ratio and slow toroidal rotations. In NSTX discharges, where the aspect-ratio is small and the rotation is fast, the theory only gives a qualitative guide for predicting NTV. However, the POCA simulation largely improves the quantitative NTV prediction for NSTX. It is discussed that a self- consistent calculation of δ B using general perturbed equilibria is eventually necessary since a non-ideal plasma response can change the perturbed eld and thereby the NTV torque.
New picture of the 1/1 internal kink and sawtooth in compressible toroidal plasmas
NASA Astrophysics Data System (ADS)
Sugiyama, Linda
2013-10-01
The m = 1 , n = 1 internal kink mode and the sawtooth crash have been analyzed extensively in magnetically confined toroidal plasmas. Nevertheless, many questions remain. A new analysis, with the aid of numerical simulation, shows that small parameter expansions such as large aspect ratio break down in general for the MHD compressible toroidal 1/1 instability with realistically small growth rates. The perpendicular momentum rate of change ρ ∂v⊥ / ∂ t must be very small compared to the individual terms in - ρ (v . ∇) v |⊥ + J × B |⊥ -∇⊥ p . The lowest order mode still has the standard 1/1 internal kink form, but the v⊥ magnitude and growth rate are determined by the higher order terms. Terms containing B~ϕ , nominally associated with the compressional Alfvén wave are important. One corollary is that reduced MHD (RMHD) fails completely and Sweet-Parker-type reconnection never develops. At a critical nonlinear amplitude, associated with the growth of the higher toroidal harmonics, a fast, explosive crash begins with rapidly accelerating velocity growth that matches observations. Other transverse MHD instabilities experience analogous effects. Work supported by the U.S. Department of Energy.
Peeters, A. G.; Angioni, C.; Strintzi, D.
2007-06-29
In this Letter, the influence of the ''Coriolis drift'' on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiment000.
Peeters, A G; Angioni, C; Strintzi, D
2007-06-29
In this Letter, the influence of the "Coriolis drift" on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.
Global theory to understand toroidal drift waves in steep gradient
NASA Astrophysics Data System (ADS)
Xie, Hua-sheng; Li, Bo
2016-08-01
Toroidal drift waves with unconventional mode structures and non-ground eigenstates, which differ from a typical ballooning structure mode, are found to be important recently by large scale global gyrokinetic simulations and especially become dominant at strong gradient edge plasmas [cf. H. S. Xie and Y. Xiao, Phys. Plasmas 22, 090703 (2015)]. The global stability and mode structures of drift wave in this steep edge density and temperature gradients are examined by both direct numerical solutions of a model two-dimensional eigen equation and analytical theory employing WKB-ballooning approach. Theory agrees with numerical solutions quite well. Our results indicate that (i) non-ground eigenstates and unconventional mode structures generally exist and can be roughly described by two parameters "quantum number" l and ballooning angle ϑk , (ii) local model can overestimate the growth rate largely, say, >50 % , and (iii) the narrow steep equilibrium profile leads to twisting (triangle-like) radial mode structures. With velocity space integral, semi-local theory predicts that the critical jump gradient of the most unstable ion temperature gradient mode from ground state l = 0 to non-ground state l = 1 is LT-1R ˜50 . These features can have important consequences to turbulent transport.
VISCOUS AND RESISTIVE EFFECTS ON THE MAGNETOROTATIONAL INSTABILITY WITH A NET TOROIDAL FIELD
Simon, Jacob B.; Hawley, John F.
2009-12-10
Resistivity and viscosity have a significant role in establishing the energy levels in turbulence driven by the magnetorotational instability (MRI) in local astrophysical disk models. This study uses the Athena code to characterize the effects of a constant shear viscosity nu and Ohmic resistivity eta in unstratified shearing box simulations with a net toroidal magnetic flux. A previous study of shearing boxes with zero net magnetic field performed with the ZEUS code found that turbulence dies out for values of the magnetic Prandtl number, P {sub m} = nu/eta, below P {sub m} approx 1; for P {sub m} approx> 1, time- and volume-averaged stress levels increase with P {sub m}. We repeat these experiments with Athena and obtain consistent results. Next, the influence of viscosity and resistivity on the toroidal field MRI is investigated both for linear growth and for fully developed turbulence. In the linear regime, a sufficiently large nu or eta can prevent MRI growth; P {sub m} itself has little direct influence on growth from linear perturbations. By applying a range of values for nu and eta to an initial state consisting of fully developed turbulence in the presence of a background toroidal field, we investigate their effects in the fully nonlinear system. Here, increased viscosity enhances the turbulence, and the turbulence decays only if the resistivity is above a critical value; turbulence can be sustained even when P {sub m} < 1, in contrast to the zero net field model. While we find preliminary evidence that the stress converges to a small range of values when nu and eta become small enough, the influence of dissipation terms on MRI-driven turbulence for relatively large eta and nu is significant, independent of field geometry.
NASA Astrophysics Data System (ADS)
Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan; Taylor, Washington
2015-11-01
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.
The geometry of sound rays in a wind
NASA Astrophysics Data System (ADS)
Gibbons, G. W.; Warnick, C. M.
2011-05-01
We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known as Finsler geometry is needed. We develop these geometries ab initio, with examples, and in particular show how sound rays in a stratified atmosphere with a wind can be mapped to a problem of circles and straight lines.
Theoretical modelling of the feedback stabilization of external MHD modes in toroidal geometry
NASA Astrophysics Data System (ADS)
Chance, M. S.; Chu, M. S.; Okabayashi, M.; Turnbull, A. D.
2002-03-01
A theoretical framework for understanding the feedback mechanism for stabilization of external MHD modes has been formulated. Efficient computational tools - the GATO stability code coupled with a substantially modified VACUUM code - have been developed to effectively design viable feedback systems against these modes. The analysis assumed a thin resistive shell and a feedback coil structure accurately modelled in θ and phi, albeit with only a single harmonic variation in phi. Time constants and induced currents in the enclosing resistive shell are calculated. An optimized configuration based on an idealized model has been computed for the DIII-D device. Up to 90% of the effectiveness of an ideal wall can be achieved.
Advances in the simulation of toroidal gyro Landau fluid model turbulence
Waltz, R.E.; Kerbel, G.D.; Milovich, J.; Hammett, G.W.
1994-12-01
The gyro-Landau fluid (GLF) model equations for toroidal geometry have been recently applied to the study ion temperature gradient (ITG) mode turbulence using the 3D nonlinear ballooning mode representation (BMR). The present paper extends this work by treating some unresolved issues conceming ITG turbulence with adiabatic electrons. Although eddies are highly elongated in the radial direction long time radial correlation lengths are short and comparable to poloidal lengths. Although transport at vanishing shear is not particularly large, transport at reverse global shear, is significantly less. Electrostatic transport at moderate shear is not much effected by inclusion of local shear and average favorable curvature. Transport is suppressed when critical E{times}B rotational shear is comparable to the maximum linear growth rate with only a weak dependence on magnetic shear. Self consistent turbulent transport of toroidal momentum can result in a transport bifurcation at suffciently large r/(Rq). However the main thrust of the new formulation in the paper deals with advances in the development of finite beta GLF models with trapped electron and BMR numerical methods for treating the fast parallel field motion of the untrapped electrons.
Asymmetric toroidal eddy currents (ATEC) to explain sideways forces at JET
NASA Astrophysics Data System (ADS)
Roccella, R.; Roccella, M.; Riccardo, V.; Chiocchio, S.; Contributors, JET
2016-10-01
During some JET vertical displacement events (VDEs) plasma current and position are found to be toroidally asymmetric. When asymmetries lock, the vessel has been observed to move horizontally, consequently strong horizontal forces are expected following plasma asymmetries, whether locked or rotating. The cause of horizontal forces is, as already identified in previous works, the asymmetric circulation of current in the structures. The physics mechanism responsible for these asymmetric currents is instead an open issue and it is the object of the present analysis. In particular it will be shown that the asymmetry is not due to a direct exchange of current between plasma and structure (as in the case of halo currents) but to asymmetric conductive paths which arise, in the structures, when the plasma column asymmetrically wets the wall. Simulations of this phenomenon using finite element (FE) models have been conducted to reproduce the JET observation during locked and rotating asymmetric VDEs. Estimated sideways force, asymmetry (I\\text{p}\\text{asym} ) and normalized asymmetry (A\\text{p}\\text{asym} ) of plasma current, vertical position at different toroidal locations during the disruption and halo current asymmetry have been compared with measurements done at JET during upward AVDEs. The substantial match between experiments and simulations confirms the soundness of the assumptions. Furthermore, the same physical model applied to downward VDEs shows that divertor support and coils, together with the geometry of the limiting surfaces, considerably lessen asymmetric loads as experienced at JET after installing those components.
Micro-focusing of attosecond pulses by grazing-incidence toroidal mirrors.
Poletto, L; Frassetto, F; Calegari, F; Anumula, S; Trabattoni, A; Nisoli, M
2013-06-01
The design of optical systems for micro-focusing of extreme-ultraviolet (XUV) attosecond pulses through grazing-incidence toroidal mirrors is presented. Aim of the proposed configuration is to provide a micro-focused image through a high demagnification of the XUV source with the following characteristics: i) almost negligible aberrations; ii) long exit arm to easily accommodate at the output the experimental setups required for the applications of the focused attosecond pulses; iii) possibility to have an intermediate region where the XUV beam is collimated, in order to insert a plane split-mirror for the generation of two XUV pulse replicas to be used in a XUV-pump/XUV-probe setup. We present the analytical and numerical study of two optical configurations characterized by two sections based on the use of toroidal mirrors. The first section provides a demagnified image of the source in an intermediate focus that is free from defocusing but has a large coma aberration. The second section consists of a relay mirror that is mounted in Z-shaped geometry with respect to the previous one, in order to give a stigmatic image with a coma that is opposite to that provided by the first section. An example is provided to demonstrate the capability to achieve spot sizes in the 5-15 μm range with a demagnification higher than 10 in a compact envelope.
ERIC Educational Resources Information Center
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
Current relaxation time scales in toroidal plasmas
Mikkelsen, D.R.
1987-02-01
An approximate normal mode analysis of plasma current diffusion in tokamaks is presented. The work is based on numerical solutions of the current diffusion equation in cylindrical geometry. Eigenvalues and eigenfunctions are shown for a broad range of plasma conductivity profile shapes. Three classes of solutions are considered which correspond to three types of tokamak operation. Convenient approximations to the three lowest eigenvalues in each class are presented and simple formulae for the current relaxation time scales are given.
Toroidal dust motion in magnetized plasmas
Reichstein, Torben; Pilch, Iris; Piel, Alexander
2010-09-15
In a magnetized anodic plasma, dust particles can be confined in a torus-shaped cloud with a distinct dust-free region (void) in its center. The formation of these clouds and their dynamical behavior are experimentally studied with a new observation geometry. The particles rotate about the major axis of the torus. A refined model for the description of the particle dynamics is presented that accounts for inertia and many-body effects.
Calculation of the vacuum Green's function valid for high toroidal mode number in tokamaks.
NASA Astrophysics Data System (ADS)
Chance, Morrell; Turnbull, Alan
2005-10-01
The present evaluation of the Green's function used for the magmetic scalar potential in vacuum calculations for axisymmetric geometry in the vacuum segments of gato, pest and other mhd stability codes has been found to be deficient for moderately high toroidal mode numbers. This was due to the loss of numerical precision arising from the upward recursion relation used for generating the functions to high mode numbers. The recursion is initiated from the complete elliptic integrals of the first and second kinds. To ameliorate this, a direct integration of the integral representation of the function was crafted to achieve the necessary high accuracy for moderately high mode numbers. At very high mode numbers the loss of numerical precision due to the oscillatory behavior of the integrand is further avoided by judiciously deforming the integration contour in the complex plane. Machine precision, roughly 14 -- 16 digits, accuracy can be achieved by using a combination of both these techniques.
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
NASA Astrophysics Data System (ADS)
Throumoulopoulos, George; Kuiroukidis, Apostolos; Tasso, Henri
2015-11-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis. This work has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018 under grant agreement No 633053.
Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure
Kuiroukidis, Ap; Throumoulopoulos, G. N.; Tasso, H.
2015-08-15
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Toroidal Superheavy Nuclei in Skyrme-Hartree-Fock Approach
Staszczak, A.; Wong, Cheuk-Yin
2009-01-01
Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of superheavy elements. For nuclei with a sufficient oblate deformation (Q_{20} < -200 b), it becomes energetically favorable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state energy is strongly dependent both on the atomic number Z and the mass number A. We discuss the region of Z and A where the toroidal SHF+BCS total energy begins to be a global minimum.
Bi-2223 HTS winding in toroidal configuration for SMES coil
NASA Astrophysics Data System (ADS)
Kondratowicz-Kucewicz, B.; Janowski, T.; Kozak, S.; Kozak, J.; Wojtasiewicz, G.; Majka, M.
2010-06-01
Energy can be stored in the magnetic field of a coil. Superconducting Magnetic Energy Storage (SMES) is very promising as a power storage system for load levelling or power stabilizer. However, the strong electromagnetic force caused by high magnetic field and large coil current is a problem in SMES systems. A toroidal configuration would have a much less extensive external magnetic field and electromagnetic forces in winding. The paper describes the design of HTS winding for SMES coil in modular toroid configuration consist of seven Bi-2223 double-pancakes as well as numerical analysis of SMES magnet model using FLUX 3D package. As the results of analysis the paper presents the optimal coil configuration and the parameters such as radius of toroidal magnet, energy stored in magnet and magnetic field distribution.
Profiling compact toroid plasma density on CTIX with laser deflection
NASA Astrophysics Data System (ADS)
Brockington, Samuel Joseph Erwin
A laser deflectometer measures line-integrated plasma density gradient using laser diodes and amplified point detectors. A laser passing through an optically thin plasma is refracted by an amount proportional to the line-integrated electron density gradient. I have designed, installed, and operated a deflection diagnostic for the Compact Toroid Injection Experiment (CTIX), a plasma rail gun which can create compact toroid (CT) plasmas of controllable density and velocity. The diagnostic design and motivation are discussed, as well as three experiments performed with deflectometry. Thus, my thesis consists of the design of the deflectometer diagnostic, a comparison of its accuracy to interferometer density measurements, and finally a survey of compact toroid density profiles in two dimensions conducted with an array of detectors.
High-Q toroidal cavities for high frequency klystrons.
NASA Technical Reports Server (NTRS)
Branch, G. M.
1972-01-01
A toroidal cavity developed for a 4-KW 12 GHz satellite-borne television transmitter klystron is described. The cavity has an internal Q 40% higher than that of a conventional cylindrical doubly reentrant cavity, thus yielding higher circuit efficiency and conserving energy which cannot be recovered in multistage depressed potential beam collectors. As a result of optimization studies with a digital computer program for obtaining cavity field distributions by a relaxation method and for computing the intrinsic cavity parameters, a particular cavity configuration with conical reentrant tunnel tips and toroidal walls is shown to provide good thermal characteristics and mechanical rigidity as well as low internal losses.
Field calculation of D0 toroids and comparison with measurement
Yamada, R.; Ostiguy, F.; Brzezniak, J.
1992-06-01
The magnetic structure of the D0 detector is described in an earlier report. The two-dimensional code POISSON was used for the initial design of the magnetic structures and the magnetic properties of the D0 toroids. During the construction, the two-dimensional code ANSYS was used to perform more detailed calculations. Full three-dimensional analysis was also performed using the code TOSCA. These new results are reported here and compared with measurements. In this study the magnetic flux in all toroids, CF, EF, and SAMUS is set in the same direction.
Initial-temperature profiles on the PDX inner toroidal limiter
Ulrickson, M.; Kugel, H.W.
1983-09-01
The temperature profiles resulting from plasma operation on the PDX vertical, large area, inner toroidal limiter have been measured during both ohmic and neutral-beam-heated discharges using a scanning infrared camera. An asymmetric double-peaked temperature profile is seen after neutral-beam-heated discharges. Disruptions in ohmically heated discharges are found to be preceded by a single-peaked deposition and succeeded by an initially symmetric double-peaked deposition. The results were compared with the Schmidt model for scrape-off at a toroidal limiter and it was found that the measured double-peaked temperature profiles yielded scrape-off lengths consistent with previous measurements.
Initial temperature profiles of the PDX inner toroidal limiter
Ulrickson, M.; Kugel, H.W.
1983-09-01
The temperature profiles resulting from plasma operation on the PDX vertical, large area, inner toroidal limiter have been measured during both ohmic and neutral beam heated discharges using a scanning infrared camera. An asymmetric double peaked temperature profile is seen after neutral beam heated discharges. Disruptions in ohmically heated discharges are found to be preceded by a single peaked deposition and succeeded by a initially symmetric double peaked deposition. The results were compared with the Schmidt model for scrapeoff at a toroidal limiter and it was found that the measured double peaked temperature profiles yielded scrape-off lengths consistent with previous measurements.
Grazing incidence toroidal mirror pairs in imaging and spectroscopic applications.
Malvezzi, A M; Tondello, G
1983-08-15
The optical performance of pairs of toroidal mirrors in grazing incidence has been studied analytically and numerically. Two types of toroidal surface are possible: football and bicycle tire. In grazing incidence and for configurations that compensate up to second-order aberrations, there are significant differences in performance between the two types. For football-type tori the best configuration appears to be Z-shaped with tangential and sagittal foci at the middle point between the mirrors. For bicycle tire-type tori the best configuration is U-shaped with the tangential focus at the middle point and the sagittal at infinity.
Comparison of Microinstability Properties for Stellarator Magnetic Geometries
G. Rewoldt; L.-P. Ku; W.M. Tang
2005-06-16
The microinstability properties of seven distinct magnetic geometries corresponding to different operating and planned stellarators with differing symmetry properties are compared. Specifically, the kinetic stability properties (linear growth rates and real frequencies) of toroidal microinstabilities (driven by ion temperature gradients and trapped-electron dynamics) are compared, as parameters are varied. The familiar ballooning representation is used to enable efficient treatment of the spatial variations along the equilibrium magnetic field lines. These studies provide useful insights for understanding the differences in the relative strengths of the instabilities caused by the differing localizations of good and bad magnetic curvature and of the presence of trapped particles. The associated differences in growth rates due to magnetic geometry are large for small values of the temperature gradient parameter n identical to d ln T/d ln n, whereas for large values of n, the mode is strongly unstable for all of the different magnetic geometries.
Combinatorial Geometry Printer Plotting.
1987-01-05
Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.
The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
NASA Astrophysics Data System (ADS)
Glasser, A. H.
2016-07-01
A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for fixed-boundary modes in a cylindrical plasma. For toroidal mode number n ≠ 0 , the stability problem is reduced to the numerical integration of a high-order complex system of ordinary differential equations, the Euler-Lagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straight-fieldline flux coordinate system. Unlike the cylindrical case, different poloidal harmonics couple to each other, which introduces coupling between adjacent singular intervals. A boundary condition is used at each singular surface, where m = nq and q ( ψ ) is the safety factor, to cross the singular surface and continue the solutions beyond it. Fixed-boundary instability is indicated by the vanishing of a real determinant of a Hermitian complex matrix constructed from the fundamental matrix of solutions, the generalization of Newcomb's crossing criterion. In the absence of fixed-boundary instabilities, an M × M plasma response matrix W P , with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum boundary. This is added to a vacuum response matrix W V to form a total response matrix W T . The existence of negative eigenvalues of W T indicates the presence of free-boundary instabilities. The method is implemented in the fast and accurate DCON code.
Podesta, M.; Bell, R. E.; Fredrickson, E. D.; Gorelenkov, N. N.; LeBlanc, B. P.; Heidbrink, W. W.; Crocker, N. A.; Kubota, S.; Yuh, H.
2010-12-15
The effects of a sheared toroidal rotation on the dynamics of bursting toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)]. The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of decorrelation of the modes by the sheared rotation is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes on NSTX.
Podesta, M; Fredrickson, E D; Gorelenkov, N N; LeBlanc, B P; Heidbrink, W W; Crocker, N A; Kubota, S
2010-08-19
The effects of a sheared toroidal rotation on the dynamics of bursting Toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40 557 (2000)]. The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of increased damping is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes.
ERIC Educational Resources Information Center
McDonald, Nathaniel J.
2001-01-01
Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…
Geometry of area without length
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming; Inami, Takeo
2016-01-01
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.
Geometry and Education in the Internet Age.
ERIC Educational Resources Information Center
Kortenkamp, Ulrich H.; Richter-Gebert, Jurgen
This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…
Hud, Nicholas V.; Downing, Kenneth H.
2001-01-01
DNA toroids produced by the condensation of λ phage DNA with hexammine cobalt (III) have been investigated by cryoelectron microscopy. Image resolution obtained by this technique has allowed unprecedented views of DNA packing within toroidal condensates. Toroids oriented coplanar with the microscope image plane exhibit circular fringes with a repeat spacing of 2.4 nm. For some toroids these fringes are observed around almost the entire circumference of the toroid. However, for most toroids well-defined fringes are limited to less than one-third of the total toroid circumference. Some toroids oriented perpendicular to the image plane reveal DNA polymers organized in a hexagonal close-packed lattice; however, for other toroids alternative packing arrangements are observed. To aid interpretation of electron micrographs, three-dimensional model toroids were generated with perfect hexagonal DNA packing throughout, as well as more physically realistic models that contain crossover points between DNA loops. Simulated transmission electron microscopy images of these model toroids in different orientations faithfully reproduce most features observed in cryoelectron micrographs of actual toroids. PMID:11734630
Collisional damping of the geodesic acoustic mode with toroidal rotation. I. Viscous damping
NASA Astrophysics Data System (ADS)
Gong, Xueyu; Xie, Baoyi; Guo, Wenfeng; Chen, You; Yu, Jiangmei; Yu, Jun
2016-03-01
With the dispersion relation derived for the geodesic acoustic mode in toroidally rotating tokamak plasmas using the fluid model, the effect of the toroidal rotation on the collisional viscous damping of the geodesic acoustic mode is investigated. It is found that the collisional viscous damping of the geodesic acoustic mode has weak increase with respect to the toroidal Mach number.
Development of a high capacity toroidal Ni/Cd cell
NASA Technical Reports Server (NTRS)
Holleck, G. L.; Foos, J. S.; Avery, J. W.; Feiman, V.
1981-01-01
A nickel cadmium battery design which can offer better thermal management, higher energy density and much lower cost than the state-of-the-art is emphasized. A toroidal Ni/Cd cell concept is described. It was critically reviewed and used to develop two cell designs for practical implementation. One is a double swaged and the other a swaged welded configuration.
Computational Knowledge for Toroidal Confinement Physics: Part I
Chang, C. S.
2009-02-19
Basic high level computational knowledge for studying the toroidal confinement physics is discussed. Topics include the primacy hierarchy of simulation quantities in statistical plasma physics, importance of the nonlinear-multiscale self-organization phenomena in a computational study, different types of codes for different applications, and different types of computer architectures for different types of codes.
Flat-band assembly for toroidal transformer cores
NASA Technical Reports Server (NTRS)
Mclyman, W. T.
1973-01-01
Toroidal transformer cores are often banded together by means of strap. Spot welds secure strap. Proper tension is obtained by use of special fixture in conjunction with winding of wire which is placed temporarily on core; winding is excited by dc current to hold core halves together magnetically during alignment.
NASA Astrophysics Data System (ADS)
Lee, S. Y.; Kwak, S. Y.; Seo, J. H.; Lee, S. Y.; Park, S. H.; Kim, W. S.; Lee, J. K.; Bae, J. H.; Kim, S. H.; Sim, K. D.; Seong, K. C.; Jung, H. K.; Choi, K.; Hahn, S.
2009-10-01
Superconducting magnetic energy storage (SMES) is one of the promising power system applications of superconducting technology and has been actively researched and developed worldwide. Generally, there are three types of SMES-solenoid, multiple solenoid, and toroid. Among these types, toroid type seems to require more wires than solenoid type and multiple solenoid type at the same operating current. However toroid type reduces normal field in the wire and stray field dramatically because magnetic field is confined inside the coil. So, the total length of wire in the toroid type can be reduced in comparison with that in the solenoid type by increasing operating current. In this paper, a 2.5 MJ class SMES with HTS magnets of single solenoid, multiple solenoid and modular toroid type were optimized using a recently developed multi-modal optimization technique named multi-grouped particle swarm optimization (MGPSO). The objective of the optimization was to minimize the total length of HTS superconductor wires satisfying some equality and inequality constraints. The stored energy and constraints were calculated using 3D magnetic field analysis techniques and an automatic tetrahedral mesh generator. Optimized results were verified by 3D finite element method (FEM).
Entropy production and Onsager symmetry in neoclassical transport processes of toroidal plasmas
Sugama, H.; Horton, W.
1996-01-01
Entropy production and Onsager symmetry in neoclassical transport processes of magnetically confined plasmas are studied in detail for general toroidal systems, including nonaxisymmetric configurations. It is found that the flux surface average of the entropy production defined from the linearized collision operator and the gyroangle-averaged distribution function coincides with the sum of the inner products of the thermodynamic forces and the conjugate fluxes consisting of the Pfirsch-Schlueter, banana-plateau, nonaxisymmetric parts of the neoclassical radial fluxes and the parallel current. It is proved from the self-adjointness of the linearized collision operator that the Onsager symmetry is robustly valid for the neoclassical transport equations in the cases of general toroidal plasmas consisting of electrons and multi-species ions with arbitrary collision frequencies. It is shown that the Onsager symmetry holds whether or not the ambipolarity condition is used to reduce the number of the conjugate pairs of the transport fluxes and the thermodynamic forces. The full transport coefficients for the banana-plateau and nonaxisymmetric parts are separately derived, and their symmetry properties are investigated. The nonaxisymmetric transport equations are obtained for arbitrary collision frequencies in the Pfirsch{endash}Schlueter and plateau regimes, and it is directly confirmed that the total banana-plateau and nonaxisymmetric transport equations satisfy the Onsager symmetry. {copyright} {ital 1996 American Institute of Physics.}
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Transport-driven toroidal rotation in the tokamak edge
NASA Astrophysics Data System (ADS)
Stoltzfus-Dueck, T.
2011-10-01
The edge of H-mode tokamak plasmas without external momentum input almost always rotates toroidally in the co-current direction, which has prompted a theoretical search for non-diffusive momentum transport mechanisms. In contrast to these efforts, the present work treats a model drift-kinetic ion equation for the pedestal and SOL containing only parallel free streaming, magnetic drifts, and spatially inhomogeneous but purely diffusive transport. The solution demonstrates that passing-ion orbits and spatially inhomogeneous diffusion interact to cause a variation of the orbit-averaged diffusivities that depends on the sign of v∥, typically resulting in preferential transport of counter-current ions. If the plasma at the boundary with the core is allowed to rotate toroidally to annihilate toroidal momentum transport, the resulting pedestal-top rotation reaches experimentally relevant values and exhibits several features in qualitative agreement with experiment. It is almost always in the co-current direction, with a rate that is proportional to Ti|ped-top /BpolLTe for small qρi /LTe , thus inversely proportional to Ip in accord with Rice scaling. It is independent of the toroidal velocity and its radial gradient, representing a residual stress. The Ti|ped-top /BpolLTe scaling implies co-current spin-up at the transition to H-mode, as Ti increases and the gradient of Te steepens. Untested predictions of the model include a sensitivity of the rotation to the major-radial position of the X-point, with a more inboard X-point leading to stronger co-current rotation. Beyond intrinsic rotation predictions, comparison of heat and momentum transport reveals that neutral beam injection must be significantly unbalanced in the counter-current direction to cause zero toroidal rotation at the pedestal top. Work supported by a research fellowship from the Alexander von Humboldt Foundation.
Radescu, E E; Vaman, G
2002-04-01
An exact calculation of the radiation intensity, angular momentum loss, and the recoil force for the most general type of source, characterized by electric, magnetic, and toroid multipole moments and radii of any multipolarity and an arbitrary time dependence, is presented. The results are expressed in terms of time derivatives of the multipole moments and mean radii of the corresponding distributions. Although quite cumbersome, the formulas found by us represent exact results in the correct multipole analysis of configurations of charges and currents that contain toroidal sources. So the longstanding problem in classical electrodynamics of relating the radiation properties of a system to quantities completely describing its internal electromagnetic structure is thereby exactly solved. By particularizations to the first multipole contributions, corrections to the familiar formulas from books are found, mostly on account of the toroid moments and their interference with the usual electric and magnetic ones.
Surface grid generation for complex three-dimensional geometries
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung
1988-01-01
An outline is presented for the creation of surface grids from primitive geometry data such as obtained from CAD/CAM systems. The general procedure is applicable to any geometry including full aircraft with wing, nacelle, and empennage. When developed in an interactive graphics environment, a code base on this procedure is expected to substantially improve the turn around time for generating surface grids on complex geometries. Results are shown for a general hypersonic airplane geometry.
Surface grid generation for complex three-dimensional geometries
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung
1988-01-01
An outline is presented for the creation of surface grids from primitive geometry data such as obtained from CAD/CAM systems. The general procedure is applicable to any geometry including full aircraft with wing, nacelle, and empennage. When developed in an interactive graphics environment, a code based on this procedure is expected to substantially improve the turn around time for generating surface grids on complex geometries. Results are shown for a general hypersonic airplane geometry.
Magnetic field compression of an accelerated compact toroid in a conical drift section
NASA Astrophysics Data System (ADS)
Horton, R. D.; Hwang, D. Q.; Evans, R. W.; Liu, F.; Klauser, R.; Umont, Glenn
2008-11-01
There are numerous applications for spheromak-like compact toroids (SCTs)with high plasma density and internal magnetic field. Previous experiments have demonstrated density and field compression of SCTs using coaxial conical electrodes [1,2]. For some applications, however, use of a central electrode may not be practical, and compression must be performed by tapering the outer electrode alone. A tapered conical electrode has been added to the CTIX device to measure magnetic field compression in this geometry. The absence of a center electrode allows magnetic field to be measured via magnetic probes at an adjustable range of axial positions, or by conventional recessed probes on the outer electrode at fixed positions. The field data serves as a benchmark for a smoothed-particle hydrodynamics (SPH) code currently under development. Results will be used to optimize compression cone geometry for the best conversion of SCT kinetic energy into thermal and magnetic energy. [1] J. H. Hammer, et al., PRL 61, 2843 (1988) [2] A.W. Molvik et al., PRL 66, 165 (1991)
Pahari, Sambaran; Lachhvani, Lavkesh; Bajpai, Manu; Rathod, Karan; Yeole, Yogesh; Chattopadhyay, P K
2015-08-01
A suitable charge-collector has been designed and developed to estimate charge-content of electron plasmas in a Small Aspect Ratio Toroidal Experiment in a C-shaped trap (SMARTEX-C). The electrons are periodically injected and held in the trap with the aid of electrostatic end-fields and a toroidal magnetic field. After a preset "hold" time, the trapped charges are dumped onto a grounded collector (by gating it). As the charges flow along the magnetic field lines onto the collector, the integrated current gives the charge-content of the plasma at the instant of dump. In designing such a charge collector, several challenges peculiar to the geometry of the trap and the nature of the plasma had to be addressed. Instantaneous charge measurements synchronised with the E × B drift of the plasma, along with fast transit times of electrons to the collector (few 100 ns or less) (due to the low aspect ratio of the trap) essentially require fast gating of the collector. The resulting large capacitive transients alongside low charge content (few nC) of such plasmas further lead to increasing demands on response and sensitivity of the collector. Complete cancellation of such transients is shown to be possible, in principle, by including the return path in our measurement circuit but the "non-neutrality" of the plasma acts as a further impediment. Ultimately, appropriate shielding and measurement circuits allow us to (re)distribute the capacitance and delineate the paths of these currents, leading to effective cancellation of transients and marked improvement in sensitivity. Improved charge-collector has thus been used to successfully estimate the time evolution of total charge of the confined electron plasma in SMARTEX-C.
Pahari, Sambaran; Lachhvani, Lavkesh Bajpai, Manu; Rathod, Karan; Yeole, Yogesh; Chattopadhyay, P. K.
2015-08-15
A suitable charge-collector has been designed and developed to estimate charge-content of electron plasmas in a Small Aspect Ratio Toroidal Experiment in a C-shaped trap (SMARTEX-C). The electrons are periodically injected and held in the trap with the aid of electrostatic end-fields and a toroidal magnetic field. After a preset “hold” time, the trapped charges are dumped onto a grounded collector (by gating it). As the charges flow along the magnetic field lines onto the collector, the integrated current gives the charge-content of the plasma at the instant of dump. In designing such a charge collector, several challenges peculiar to the geometry of the trap and the nature of the plasma had to be addressed. Instantaneous charge measurements synchronised with the E × B drift of the plasma, along with fast transit times of electrons to the collector (few 100 ns or less) (due to the low aspect ratio of the trap) essentially require fast gating of the collector. The resulting large capacitive transients alongside low charge content (few nC) of such plasmas further lead to increasing demands on response and sensitivity of the collector. Complete cancellation of such transients is shown to be possible, in principle, by including the return path in our measurement circuit but the “non-neutrality” of the plasma acts as a further impediment. Ultimately, appropriate shielding and measurement circuits allow us to (re)distribute the capacitance and delineate the paths of these currents, leading to effective cancellation of transients and marked improvement in sensitivity. Improved charge-collector has thus been used to successfully estimate the time evolution of total charge of the confined electron plasma in SMARTEX-C.
Summary of US-Japan Exchange 2004 New Directions and Physics for Compact Toroids
Intrator, T; Nagata, M; Hoffman, A; Guo, H; Steinhauer, L; Ryutov, D; Miller, R; Okada, S
2005-08-15
relaxation. A variety of key themes surrounding the physics of CT's were found to recur during this conference. These included questions and answers touching upon magnetic flux build up in CT's, generalized relaxation processes that extend beyond the Taylor picture, the importance of plasma flows, toroidal magnetic fields in FRC's, and CT power plant considerations. This document briefly outlines the tenor of these discussions.
SV40 late protein VP4 forms toroidal pores to disrupt membranes for viral release.
Raghava, Smita; Giorda, Kristina M; Romano, Fabian B; Heuck, Alejandro P; Hebert, Daniel N
2013-06-01
Nonenveloped viruses are generally released from the cell by the timely lysis of host cell membranes. SV40 has been used as a model virus for the study of the lytic nonenveloped virus life cycle. The expression of SV40 VP4 at later times during infection is concomitant with cell lysis. To investigate the role of VP4 in viral release and its mechanism of action, VP4 was expressed and purified from bacteria as a fusion protein for use in membrane disruption assays. Purified VP4 perforated membranes as demonstrated by the release of fluorescent markers encapsulated within large unilamellar vesicles or liposomes. Dynamic light scattering results revealed that VP4 treatment did not cause membrane lysis or change the size of the liposomes. Liposomes encapsulated with 4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-3-indacene-labeled streptavidin were used to show that VP4 formed stable pores in membranes. These VP4 pores had an inner diameter of 1-5 nm. Asymmetrical liposomes containing pyrene-labeled lipids in the outer monolayer were employed to monitor transbilayer lipid diffusion. Consistent with VP4 forming toroidal pore structures in membranes, VP4 induced transbilayer lipid diffusion or lipid flip-flop. Altogether, these studies support a central role for VP4 acting as a viroporin in the disruption of cellular membranes to trigger SV40 viral release by forming toroidal pores that unite the outer and inner leaflets of membrane bilayers. PMID:23651212
Toroidal Alfvén Eigenmodes in TFTR Deuterium-Tritium Plasmas
G.Y. Fu; H. Berk; R. Nazikian; S.H. Batha; Z. Chang; et al
1998-01-01
Purely alpha-particle-driven Toroidal Alfvén Eigenmodes (TAEs) with toroidal mode numbers n=1-6 have been observed in Deuterium-Tritium (D-T) plasmas on the Tokamak Fusion Test Reactor [D.J. Grove and D.M. Meade, Nucl. Fusion 25, 1167 (1985)]. The appearance of mode activity following termination of neutral beam injection in plasmas with q(0)>1 is generally consistent with theoretical predictions of TAE stability [G.Y. Fu et al., Phys. Plasmas 3, 4036 (1996]. Internal reflectometer measurements of TAE activity is compared with theoretical calculations of the radial mode structure. Core localization of the modes to the region of reduced central magnetic shear is confirmed, however the mode structure can deviate significantly from theoretical estimates. The peak measured TAE amplitude of delta n/n~10(superscript -4) at r/a~0.3-0.4 corresponds to delta B/B~10-5, while dB/B~10(superscript -8) is measured at the plasma edge. Enhanced alpha particle loss associated with TAE activity has not been observed.
Modeling non-saturated ferrite-based devices: Application to twin toroid ferrite phase shifters
NASA Astrophysics Data System (ADS)
Le Gouellec, A.; Vérissimo, G.; Laur, V.; Queffelec, P.; Albert, I.; Girard, T.
2016-08-01
This article describes a new set of tools developed to improve the conception and modeling of non-saturated ferrite-based devices such as twin toroid phase shifters. These new simulation tools benefit from a generalized permeability tensor model able to describe the permeability tensor of a ferrite sample whatever its magnetization state. This model is coupled to a homemade 3D multi-scale magnetostatic analysis program, which describes the evolution of the magnetization through the definition of a hysteresis loop in every mesh cell. These computed spectra are then integrated into 3D electromagnetic simulation software that retains the spatial variations of the ferrite properties by using freshly developed macro programming functions. This new approach allows the designers to accurately model complex ferrite devices such as twin toroid phase shifters. In particular, we demonstrated a good agreement between simulated and measured phase shifts as a function of applied current values with a predicted maximum phase shift of 0.96 times the measured value.
Exceptional geometry and Borcherds superalgebras
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2015-11-01
We study generalized diffeomorphisms in exceptional geometry with U-duality group E n( n) from an algebraic point of view. By extending the Lie algebra {e}_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to {e}_{n+1} , the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n ≤ 7. The closure of the transformations then follows from the Jacobi identity and the grading of {e}_{n+1} with respect to {e}_n.
ERIC Educational Resources Information Center
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
Euclidean Geometry via Programming.
ERIC Educational Resources Information Center
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code
NASA Astrophysics Data System (ADS)
Jiang, Peng; Lin, Zhihong; Ihor, Holod; Xiao, Chijie
2016-02-01
The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code (GTC). The ion and electron density profiles become partially flattened inside the islands. The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side, which do not move along the perturbed magnetic field lines. When the fraction of trapped particles decreases, the density profile at the low field becomes more flattened. supported by National Special Research Program of China for ITER (Nos. 2013GB111000 and 2014GB107004), China Scholarship Council (No. 2011601098), U.S. DOE Grants DE-SC0010416 and DE-FG02-07ER54916
An Ultraviolet Survey of the Compact Toroid Injection Experiment
NASA Astrophysics Data System (ADS)
Merritt, Elizabeth; Howard, Stephen; Horton, Robert; Hwang, David Q.; Evans, Russell; Brockington, Samuel; Beiersdorfer, Peter
2006-10-01
Light is emitted during the formation and acceleration of a compact toroid (CT) plasma in the Compact Toroid Injection Experiment (CTIX). A low-resolution (35nm) survey in the 150 to 500 nm range of the ultraviolet spectrum of this light will be taken using a 1-meter Acton spectrometer using a 300 line/mm grating, on loan from the Electron-Beam Ion-Trap group at LLNL, with a 16-channel linear photodiode array. This survey will allow bright regions of the emitted spectrum to be identified for various diagnostic purposes. At moderate spectrometer resolution, line intensities may be used to infer plasma impurity content, while line ratios may be used to infer plasma temperatures. At high resolution, axial plasma velocity can be determined using Doppler shifts, while plasma temperature can be determined using Doppler broadening. Higher resolution experiments will be completed if time allows or continued by a future student.
Neoclassical electron and ion transport in toroidally rotating plasmas
Sugama, H.; Horton, W.
1997-06-01
Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch{endash}Schl{umlt u}ter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the radial thermodynamic forces conjugate to the inward fluxes, respectively. {copyright} {ital 1997 American Institute of Physics.}
Stabilization of ballooning modes with sheared toroidal rotation
Miller, R.L.; Waelbroeck, F.W.; Lao, L.L.; Taylor, T.S.
1994-11-01
A new code demonstrates the stabilization of MHD ballooning modes by sheared toroidal rotation. A shifted-circle model is used to elucidate the physics and numerically reconstructed equilibria are used to analyze DIII-D discharges. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (d{Omega}/dq where {Omega} is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and, in the shifted circle model, direct stable access to the second stability regime occurs when this frequency is a fraction of the Alfven frequency {omega}{sub A} = V{sub A}/qR. Shear stabilization is also demonstrated for an equilibrium reconstruction of a DIII-D VH-mode.
Reevaluation of the Braginskii viscous force for toroidal plasma
NASA Astrophysics Data System (ADS)
Johnson, Robert W.
2011-12-01
The model by Braginskii [1] (Braginskii, S. I. 1965 Transport processes in plasma. In: Review of Plasma Physics, Vol. 1 (ed. M.A. Leontovich). New York, NY: Consultants Bureau, pp. 205-311) for the viscous stress tensor is used to determine the shear and gyroviscous forces acting within a toroidally confined plasma. Comparison is made to a previous evaluation, which contains an inconsistent treatment of the radial derivative and neglects the effect of the pitch angle. Parallel viscosity contributes a radial shear viscous force, which may develop for sufficient vertical asymmetry to the ion velocity profile. An evaluation is performed of this radial viscous force for a tokamak near equilibrium, which indicates qualitative agreement between theory and measurement for impure plasma discharges with strong toroidal flow.
Unstable resonator misalignment in ring and linear toroidal resonators.
Schnurr, A D
1983-01-15
Optical axis motion in a ring resonator is investigated as a function of resonator mirror misalignment by constructing an equivalent paraxial model and applying the ray matrix formalism. Analytical expressions are derived for the optical axis motion. The paraxial model of the ring is shown to imply a linear resonator as a specific case, and the ring resonator expressions collapse to the familiar Krupke-Sooy results for that case. Using this method, new misalignment expressions are determined for more complex linear resonators. Uncorrectable misalignment conditions caused by toroidal mirror parameter errors are studied analytically and with a geometric optics code, and resulting phase front errors are given for a special case. These results are also examined as a basis for toroidal mirror quality specifications. PMID:18195782
Nuclear magnetic resonance tomography with a toroid cavity detector
Woelk, K.; Rathke, J.W.; Klingler, R.J.
1995-02-01
A new type of nuclear magnetic resonance (NMR) tomography has been developed at Argonne National Laboratory. The method uses the strong radio frequency field gradient within a cylindrical toroid cavity to provide high-resolution NMR spectral information while simultaneously resolving distances on the micron scale. The toroid cavity imaging technique differs from conventional magnetic resonance imaging (MRI) in that NMR structural information is not lost during signal processing. The new technique could find a wide range of applications in the characterization of surface layers and in the production of advanced materials. Potential areas of application include in situ monitoring of growth sites during ceramic formation processes, analysis of the oxygen annealing step for wires coated with high-temperature superconducting films, and investigation of the reaction chemistry as a function of distance within the diffusion layer for electrochemical processes.
Experimental studies of compact toroids. Progress report, 1990--1991
Not Available
1991-12-01
The Berkeley Compact Toroid Experiment (BCTX) device is a plasma device with a Marshall-gun generated, low aspect ratio toroidal plasma. The device is capable of producing spheromak-type discharges and may, with some modification, produce low-aspect ratio tokamak configurations. A unique aspect of this experimenal devie is its large lower hybrid (LH) heating system, which consists of two 450MHz klystron tubes generating 20 megawatts each into a brambilla-type launching structure. Successful operation with one klystron at virtually full power (18 MW) has been accomplished with 110 {mu}s pulse length. A second klystron is currently installed in its socket and magnet but has not been added to the RF drive system. This report describes current activities and accomplishments and describes the anticipated results of next year`s activity.
Toroidal qubits: naturally-decoupled quiet artificial atoms
Zagoskin, Alexandre M.; Chipouline, Arkadi; Il’ichev, Evgeni; Johansson, J. Robert; Nori, Franco
2015-01-01
The requirements of quantum computations impose high demands on the level of qubit protection from perturbations; in particular, from those produced by the environment. Here we propose a superconducting flux qubit design that is naturally protected from ambient noise. This decoupling is due to the qubit interacting with the electromagnetic field only through its toroidal moment, which provides an unusual qubit-field interaction, which is suppressed at low frequencies. PMID:26607667
Operating tokamaks with steady-state toroidal current
Fisch, N.J.
1981-04-01
Continuous operation of a tokamak requires, among other things, a means of continuously providing the toroidal current. Various methods have been proposed to provide this current including methods which utilize radio-frequency waves in any of several frequency regimes. Here we elaborate on the prospects of incorporating these current-drive techniques in tokamak reactors, concentrating on the theoretical minimization of the power requirements.
Toroidal constant-tension superconducting magnetic energy storage units
Herring, J. Stephen
1992-01-01
A superconducting magnetic energy storage unit is provided in which the magnet is wound in a toroidal fashion such that the magnetic field produced is contained only within the bore of the magnet, and thus producing a very low external field. The superconducting magnet includes a coolant channel disposed through the wire. The bore of the magnet comprises a storage volume in which cryogenic coolant is stored, and this volume supplies the coolant to be delivered to the coolant channel in the magnet.
Miniature anastigmatic spectrometer design with a concave toroidal mirror.
Dong, Jianing; Chen, He; Zhang, Yinchao; Chen, Siying; Guo, Pan
2016-03-01
An advanced optical design for a low-cost and astigmatism-corrected spectrometer with a high resolution is presented. The theory and method of astigmatism correction are determined with the use of a concave toroidal mirror. The performances of a modified spectrometer and a traditional spectrometer are compared, and the analysis is verified. Experimentally, the limiting resolution of our spectrometer is 0.1 nm full width at half-maximum, as measured for 579.1 nm.
Evolution of the alpha particle driven toroidicity induced Alfven mode
Wu, Y.; White, R.B.; Cheng, C.Z.
1994-04-01
The interaction of alpha particles with a toroidicity induced Alfven eigenmode is investigated self-consistently by using a kinetic dispersion relation. All important poloidal harmonics and their radial mode profiles are included. A Hamiltonian guiding center code is used to simulate the alpha particle motion. The simulations include particle orbit width, nonlinear particle dynamics and the effects of the modes on the particles. Modification of the particle distribution leading to mode saturation is observed. There is no significant alpha particle loss.
Planetary Image Geometry Library
NASA Technical Reports Server (NTRS)
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks
NASA Astrophysics Data System (ADS)
Lazzaro, E.
2016-05-01
In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co- I p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.
Expansions of non-symmetric toroidal magnetohydrodynamic equilibria
NASA Astrophysics Data System (ADS)
Weitzner, Harold
2016-06-01
Expansions of non-symmetric toroidal ideal magnetohydrodynamic equilibria with nested flux surfaces are carried out for two cases. The first expansion is in a topological torus in three dimensions, in which physical quantities are periodic of period 2 π in y and z. Data is given on the flux surface x = 0. Despite the possibility of magnetic resonances the power series expansion can be carried to all orders in a parameter which measures the flux between x = 0 and the surface in question. Resonances are resolved by appropriate addition resonant fields, as by Weitzner, [Phys. Plasmas 21, 022515 (2014)]. The second expansion is about a circular magnetic axis in a true torus. It is also assumed that the cross section of a flux surface at constant toroidal angle is approximately circular. The expansion is in an analogous flux coordinate, and despite potential resonance singularities, may be carried to all orders. Non-analytic behavior occurs near the magnetic axis. Physical quantities have a finite number of derivatives there. The results, even though no convergence proofs are given, support the possibility of smooth, well-behaved non-symmetric toroidal equilibria.
3D toroidal physics: Testing the boundaries of symmetry breaking
Spong, Donald A.
2015-05-15
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.
3D toroidal physics: Testing the boundaries of symmetry breakinga)
NASA Astrophysics Data System (ADS)
Spong, Donald A.
2015-05-01
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.
Nanospheres, nanotubes, toroids, and gels with controlled macroscopic chirality.
Arias, Sandra; Freire, Félix; Quiñoá, Emilio; Riguera, Ricardo
2014-12-01
The interaction of a highly dynamic poly(aryl acetylene) (poly-1) with Li(+), Na(+), and Ag(+) leads to macroscopically chiral supramolecular nanospheres, nanotubes, toroids, and gels. With Ag(+), nanospheres with M helicity and tunable sizes are generated, which complement those obtained from the same polymer with divalent cations. With Li(+) or Na(+), poly-1 yields chiral nanotubes, gels, or toroids with encapsulating properties and M helicity. Right-handed supramolecular structures can be obtained by using the enantiomeric polymer. The interaction of poly-1 with Na(+) produces nanostructures whose helicity is highly dependent on the solvation state of the cation. Therefore, structures with either of the two helicities can be prepared from the same polymer by manipulation of the cosolvent. Such chiral nanotubes, toroids, and gels have previously not been obtained from helical polymer-metal complexes. Chiral nanospheres made of poly(aryl acetylene) that were previously assembled with metal(II) species can now be obtained with metal(I) species. PMID:25209219
Radial Localization of Toroidal Alfven Eigenmode in Tokamak Plasmas
NASA Astrophysics Data System (ADS)
Wang, Zhixuan; Lin, Zhihong; Heidbrink, William; Tobias, Benjamin; van Zeeland, Michael
2013-10-01
Toroidal Alfven eigenmode (TAE) with radially extended structures can be driven unstable by pressure gradients of energetic particles (EP). These unstable Alfveneigenmodes (AE) have been routinely observed in fusion experiments to induce a large EP transport, whichcould degrade overall plasma confinement and damagefusion devices.In the well-accepted paradigm, the growth rate of the AEs can be calculated from a perturbative EP contribution to a fixedmode structure and real frequency given by magnetohydrodynamic (MHD) properties of thermal plasmas. However, linear and nonlinear kinetic effects of both EP and thermal plasmasare important and should be treated on the same footing. The gyrokinetic simulation has thus emerged as anecessary and powerful tool for studying the linear andnonlinear dynamics of AEs. In the current work, the gyrokinetic toroidal code(GTC) linear simulation of the tokamakexperiment finds a radial localization of the TAE dueto the non-perturbative EP contribution. The EP-drivenTAE has a radial mode width much smaller than thatpredicted by the MHD theory. The TAE radial positionpeaks at and moves with the location of the strongest EPpressure gradients. Experimental data confirms that the eigenfunction drifts quicklyoutward radially. The non-perturbativeEP contribution also breaks the radial symmetry of the mode structure and induces a TAE frequency dependence on the toroidal mode number, in excellent agreement with the experimental measurements.
Connection formula for banana-drift neoclassical toroidal viscosity
NASA Astrophysics Data System (ADS)
Cole, A. J.; Hegna, C. C.; Callen, J. D.
2010-11-01
Non-resonant magnetic perturbations can affect plasma rotation in toroidally confined plasmas through their modification to |B|. Variations along a field line induce nonambipolar radial transport and produce a global neoclassical toroidal viscous force [NTV]. In this work, a previously calculated WKB-type solution smoothly connecting the low-collisionality ``1/ν'' and ``ν-√ν'' regimes is extended to include the superbanana plateau [sbp] regime [1]. The sbp effect occurs for particles whose toroidal ExB precessional drift vanishes. In this case, the relevant drift kinetic equation exhibits a ``turning point'' and the WKB method fails. We employ the connection formula method of Langer [2] which continuously varies between the previous WKB result and the superbanana regime without difficultly at the turning point. The resultant smoothed NTV is presented in terms of flows along flux surfaces. [4pt] [1] K. C. Shaing, S. A. Sabbagh, and M. S. Chu, PPCF 51, 035009 (2009), and refs. cited therein. [0pt] [2] R. E. Langer, Phys. Rev. 51, 669 (1937).
Impact of plasma poloidal rotation on resistive wall mode instability in toroidally rotating plasmas
Aiba, N.; Shiraishi, J.; Tokuda, S.
2011-02-15
Stability of resistive wall mode (RWM) is investigated in a cylindrical plasma and an axisymmetric toroidal plasma by taking into account not only toroidal rotation but also poloidal rotation. Since the Doppler shifted frequency is responsible for the RWM stability, the modification of this Doppler shifted frequency by poloidal rotation affects the rotation effect on RWM. When a poloidal rotation frequency is not so large, the effect of poloidal rotation on the RWM stability can be approximately treated with the modified toroidal rotation frequency. In a toroidal plasma, this modified frequency is determined by subtracting a toroidal component of the rotation parallel to the magnetic field from the toroidal rotation frequency. The poloidal rotation that counteracts the effect of the Doppler shift strongly reduces the stabilizing effect of toroidal rotation, but by changing the rotational direction, the poloidal rotation enhances this stabilizing effect. This trend is confirmed in not only a cylindrical plasma but also a toroidal plasma. This result indicates that poloidal rotation produces the dependence of the critical toroidal rotation frequency for stabilizing RWM on the rotational direction of toroidal rotation in the same magnetic configuration.
NASA Astrophysics Data System (ADS)
Aetukuri, Nagaphani B.; McCloskey, Bryan D.; García, Jeannette M.; Krupp, Leslie E.; Viswanathan, Venkatasubramanian; Luntz, Alan C.
2015-01-01
Given their high theoretical specific energy, lithium-oxygen batteries have received enormous attention as possible alternatives to current state-of-the-art rechargeable Li-ion batteries. However, the maximum discharge capacity in non-aqueous lithium-oxygen batteries is limited to a small fraction of its theoretical value due to the build-up of insulating lithium peroxide (Li2O2), the battery’s primary discharge product. The discharge capacity can be increased if Li2O2 forms as large toroidal particles rather than as a thin conformal layer. Here, we show that trace amounts of electrolyte additives, such as H2O, enhance the formation of Li2O2 toroids and result in significant improvements in capacity. Our experimental observations and a growth model show that the solvating properties of the additives prompt a solution-based mechanism that is responsible for the growth of Li2O2 toroids. We present a general formalism describing an additive’s tendency to trigger the solution process, providing a rational design route for electrolytes that afford larger lithium-oxygen battery capacities.
Geometry-induced modification of fluctuation spectrum in quasi-two-dimensional condensates
NASA Astrophysics Data System (ADS)
Roy, Arko; Angom, D.
2016-08-01
We report the structural transformation of the low-lying spectral modes, especially the Kohn mode, from radial to circular topology as harmonic confining potential is modified to a toroidal one, and this corresponds to a transition from simply to multiply connected geometry. For this we employ the Hartree–Fock–Bogoliubov theory to examine the evolution of low energy quasiparticles. We, then, use the Hartree–Fock–Bogoliubov theory with the Popov approximation to demonstrate the two striking features of quantum and thermal fluctuations. At T = 0, the non-condensate density due to interaction induced quantum fluctuations increases with the transformation from pancake to toroidal geometry. The other feature is, there is a marked change in the density profile of the non-condensate density at finite temperatures with the modification of trapping potential. In particular, the condensate and non-condensate density distributions have overlapping maxima in the toroidal condensate, which is in stark contrast to the case of pancake geometry. The genesis of this difference lies in the nature of the thermal fluctuations.
Computed tomography of Spheromak-like compact toroid injection
NASA Astrophysics Data System (ADS)
Terry, Stephen Donald
1999-12-01
The construction and installation of a tomographic imaging system on the Compact Toroid Injection Experiment is described. This system is used to examine the physical processes which are in effect during the penetration of a vacuum magnetic field by a Spheromak-like Compact Toroid (SCT). Compact toroid fueling is an alternative fueling concept to pellet injection. It has the potential to provide central fueling at high repetition rates while minimizing injector size. Several physics issues need to be settled to demonstrate the practicality of this fueling system for fusion power reactors. One of these issues is the interaction between the SCT and the tokamak magnetic field. Several processes which can occur during this interaction are presented. They include compression and heating. Some possible mechanisms for these processes are hypothesized. The Compact Toroid Injection Experiment (CTIX) at the Davis Diverted Tokamak (DDT) is an experiment to study the physics of SCT fueling. The diagnostics available on the machine are described. The theories of SCT formation and accelleration are presented and the operation of the injector is described. A tomographic imaging system has been built and installed in the drift tube section of the injector. This system measures the total radiated power from the SCT. The data is then used to construct a two dimensional plasma emissivity profile. This is done with a software routine based on the Second Order Regularization method. The performance of this algorithm is compared to other reconstruction algorithms and the calibration of the system is described. The results of several measurements of SCT parameters are described. Radial compression of the SCT in the tokamak magnetic field is indicated by the absence of magnetic probe signal for high toroidal field strengths. Heating of the electrons is shown by obtaining the electron energy distribution function. An enhancement of SCT radiation in the tokamak magnetic field has been
Density Limits in Toroidal Magnetic Confinement Experiments
NASA Astrophysics Data System (ADS)
Greenwald, Martin
2001-10-01
The density limit represents one of the fundamental operating boundaries for magnetic confinement devices - one with practical importance to the goal of fusion power. With fusion reactivity maximized at a plasma temperature on the order of 10 keV and a reaction rate scaling as n^2, an optimum density can be calculated which is not guaranteed to be achievable in any given device. Unlike operational limits for plasma current or pressure, the density limit cannot be explained by magneto-hydrodynamics alone. There is general agreement that the proximate cause for the disruptive limit in the tokamak is cooling of the plasma edge and subsequent current profile shrinkage. The edge cooling may be dominated by atomic physics processes or as suggested in recent experiments, by anomalous transport. A similar picture is emerging for the reversed field pinch (RFP), while the limit in stellarators is apparently due to loss of thermal equilibrium from radiation. Empirical scaling laws in which the maximum plasma density is proportional to the average current density have been fairly successful in predicting the limit for subsequent experiments. Surprisingly, the density limits found in tokamaks and RFPs are virtually identical. Currentless stellarators reach similar density limits, though the expression needs to be recast in terms of the rotational transform. While scaling laws have done a reasonable job in describing data from many recent experiments, they can only give hints at the underlying physics. Understanding the mechanism for the density limit is crucial for extrapolating machine performance into untested regimes and so far, a completely satisfactory theory has not emerged. It seems likely that robust, reliable predictions will only come from the development of a first-principles theory backed up by detailed experimental observations. The extensive work already accomplished and reviewed here should provide a solid basis for such development.
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Toroidal cell and battery. [storage battery for high amp-hour load applications
NASA Technical Reports Server (NTRS)
Nagle, W. J. (Inventor)
1981-01-01
A toroidal storage battery designed to handle relatively high amp-hour loads is described. The cell includes a wound core disposed within a pair of toroidal channel shaped electrodes spaced apart by nylon insulator. The shape of the case electrodes of this toroidal cell allows a first planar doughnut shaped surface and the inner cylindrical case wall to be used as a first electrode and a second planar doughnut shaped surface and the outer cylindrical case wall to be used as a second electrode. Connectors may be used to stack two or more toroidal cells together by connecting substantially the entire surface area of the first electrode of a first cell to substantially the entire surface area of the second electrode of a second cell. The central cavity of each toroidal cell may be used as a conduit for pumping a fluid through the toroidal cell to thereby cool the cell.
Electrical and mechanical design report of the muon toroids for the beamline to the muon laboratory
Visser, A.; Western, J.; Skraboly, A.
1987-03-01
This report describes two large steel toroids used to remove beam halo for experiment 665. One toroid is 88 inch diameter and 30 feet long. The other is 120 inch diameter and 20 feet long. Both have a 7 inch diameter center hole for passage of the beam and the excitation windings. The assembled hybrid coil has water-cooled conductors in the center hole and cables on the outside. This permits the use of one piece steel plates through which the center core is inserted after assembly of the toroid steel. These toroids have advantages over conventional toroids in many aspects. The main ones being its reduced power consumption, simplicity of machining and assembly, and lower coil costs. Estimates of the induction and a simple method to buck the remnant magnetic field are included. The bucking method does not completely degauss all the toroid steel.
2005-01-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less
Formation and dynamics of a toroidal bubble during laser propelling a cavity object in water.
Chen, Jun; Zhang, Hong-Chao; Shen, Zhong-Hua; Lu, Jian; Ni, Xiao-Wu
2013-10-01
We captured stable self-oscillations of a toroidal bubble moving away from a laser propelled cavity object in water using a high-speed imaging system. The entire laser propelling process generates a hemispherical bubble, two toroidal bubbles, and a microbubble cluster. The hemispherical bubble is formed by laser breakdown in water. The toroidal bubbles are formed by the variation of the pressure field as a result of the propagation, reflection, and convergence of the laser plasma shockwave in the cavity.
Dynamic spin-flip shot noise of mesoscopic transport through a toroidal carbon nanotube
NASA Astrophysics Data System (ADS)
Zhao, H. K.; Zhang, J.; Wang, J.
2015-01-01
The shot noise in a toroidal carbon nanotube (TCN) interferometer under the perturbation of a rotating magnetic field (RMF) has been investigated. A general shot noise formula has been derived by calculating the current correlation. It was found that photon absorption and emission induce novel features of dynamic shot noise. The oscillatory behavior of shot noise and Fano factor vary with the Aharonov-Bohm (AB) magnetic flux, and they are sensitively dependent on the Zeeman energy, frequency of RMF, and source-drain bias. By adjusting the Zeeman energy, the AB oscillation structures of shot noise and Fano factor show valley-to-peak transformation. The shot noise increases nonlinearly with increasing the Zeeman energy and photon energy. The enhancement and asymmetry of shot noise can be attributed to the spin-flip effect.
Wall thickness effect on the resistive wall mode stability in toroidal plasmas
Zheng, L.-J.; Kotschenreuther, M.T.
2005-07-15
The effect of finite wall thickness on the stability of n=1 resistive wall modes in toroidal plasmas is investigated. A fusion reactor-relevant configuration is examined. The investigation employs a novel ideal-magnetohydrodynamics adaptive shooting code for axisymmetric plasmas, extended to take into account the wall thickness. Although finite wall thickness generally reduces the growth rate of the resistive wall modes, no contribution to stabilization is found to be made by the portion of the wall that is located beyond the critical position for perfectly conducting wall stabilization. Thus, when the inner side of the wall lies near the critical wall position, the scaling of the growth rate versus wall thickness in the realistic thick-wall calculation is significantly different from that of the usual thin-wall theory. The thin-wall estimate is relevant only when the wall is brought very close to the plasma and is not too thick.
Asymptotics of Height Change on Toroidal Temperleyan Dimer Models
NASA Astrophysics Data System (ADS)
Dubédat, Julien; Gheissari, Reza
2015-04-01
The dimer model is an exactly solvable model of planar statistical mechanics. In its critical phase, various aspects of its scaling limit are known to be described by the Gaussian free field. For periodic graphs, criticality is an algebraic condition on the spectral curve of the model, determined by the edge weights (Kenyon et al. in Ann Math (2) 163(3):1019-1056, 2006); isoradial graphs provide another class of critical dimer models, in which the edge weights are determined by the local geometry. In the present article, we consider another class of graphs: general Temperleyan graphs, i.e. graphs arising in the (generalized) Temperley bijection between spanning trees and dimer models. Building in particular on Forman's formula and representations of Laplacian determinants in terms of Poisson operators, and under a minimal assumption—viz. that the underlying random walk converges to Brownian motion—we show that the natural topological observable on macroscopic tori converges in law to its universal limit, i.e. the law of the periods of the dimer height function converges to that of the periods of a compactified free field.
Self-Assembly and Tissue Fusion of Toroid-Shaped Minimal Building Units
Livoti, Christine M.
2010-01-01
A significant challenge of tissue engineering is to build tissues whose size is not limited by diffusion. We are investigating the use of scaffold-free lumen containing toroid-shaped microtissues as minimal building units. Monodispersed H35 cells, a rat hepatocyte cell line, were seeded onto micromolded agarose, forming self-assembled multicellular toroids within 48 h. Toroid and lumen diameter were easily controlled by micromold design, and toroid thickness was controlled by seeding density. When harvested, toroids were stable, but underwent predictable changes over time with their lumens narrowing. When brought into contact, these building units fused in the x–y plane, forming a double-lumen structure, as well as the z plane, forming a tubular structure, which completed within 72 h. Large, multi-luminal structures were assembled by multidimensional fusion of many toroids. Toroid settling was not entirely random, with most toroids lying flat with their lumens oriented along the z axis. The rapid production of toroid building units of controlled dimension and lumen size that undergo predictable changes and that can be fused to form larger structures is a step closer to tissue engineering large porous three-dimensional tissues with high cell density. PMID:20109063
NASA Astrophysics Data System (ADS)
Balbaky, Abed; Sokolov, Vladimir; Sen, Amiya K.
2015-05-01
Electron temperature gradient (ETG) modes are suspected sources of anomalous electron thermal transport in magnetically confined plasmas as in tokamaks. Prior work in the Columbia Linear Machine (CLM) has been able to produce and identify slab ETG modes in a slab geometry [Wei et al., Phys. Plasmas 17, 042108 (2010)]. Now by modifying CLM to introduce curvature to the confining axial magnetic field, we have excited mixed slab-toroidal modes. Linear theory predicts a transition between slab and toroidal ETG modes when /k ∥ R c k y ρ ˜ 1 [J. Kim and W. Horton, Phys. Fluids B 3, 1167 (1991)]. We observe changes in the mode amplitude for levels of curvature Rc - 1 ≪ /k ∥ , s l a b k ⊥ ρ , which may be explained by reductions in k ∥ in the transition from slab to mixed slab-toroidal modes, as also predicted by theory. We present mode amplitude scaling as a function of magnetic field curvature. Over the range of curvature available in CLM experimentally we find a modest increase in saturated ETG potential fluctuations (˜1.5×), and a substantial increase in the power density of individual mode peaks (˜4-5×).
(Injection of compact toroids for tokamak fueling and current drive)
Hwang, D.Q.; Rogers, J.H.; Thomas, J.C.; Evans, R.; Foley, R.; Hillyer, T.
1991-01-01
The experimental goals for the 1990--1991 period were the operation of the Davis Diverted Tokamak(DDT), the beat wave experiment, and the construction of the compact toroid injection experiment(CTIX). The experiment results from these areas are summarized in the posters given in the APS meeting past November. Here we shall describe the technical progress of the development of the diagnostic system for beat wave experiment, and CT injection especially in relation to the up coming injection experiments into DDT tokamak. The tokamak operation of DDT over the past year has been focused in two parameter ranges. The long pulse discharges (over 100 msec), and the low q short pulse discharges (about 10 msec). We found that the long pulse discharges required a position feedback more sophisticated than the simple passive program that we have. We are in the process of assembling this system. We also found an interesting low q(a) operating regime. Here an equilibrium can be established for a toroidal field between .5 and 1 kG. The typical plasma current is > 5kA. The density of the plasma is between 10{sup 12} and 10{sup 13} cm{sup {minus}3}. The plasma condition in these discharge are sufficiently mild that diagnostic probes can be used to measure various plasma fluctuations. We believe that this will be the regime best suited to study the interaction between the tokamak plasma and the compact toroid. A sophisticated probe system of both electrostatic and electromagnetic types similar to those used in the beat wave experiment has been designed for the up coming experiments.
Alpha particle destabilization of the toroidicity-induced Alfven eigenmodes
Cheng, C.Z.
1990-10-01
The high frequency, low mode number toroidicity-induced Alfven eigenmodes (TAE) are shown to be driven unstable by the circulating and/or trapped {alpha}-particles through the wave-particle resonances. Satisfying the resonance condition requires that the {alpha}-particle birth speed v{sub {alpha}} {ge} v{sub A}/2{vert bar}m-nq{vert bar}, where v{sub A} is the Alfven speed, m is the poloidal model number, and n is the toroidal mode number. To destabilize the TAE modes, the inverse Landau damping associated with the {alpha}-particle pressure gradient free energy must overcome the velocity space Landau damping due to both the {alpha}-particles and the core electrons and ions. The growth rate was studied analytically with a perturbative formula derived from the quadratic dispersion relation, and numerically with the aid of the NOVA-K code. Stability criteria in terms of the {alpha}-particle beta {beta}{sub {alpha}}, {alpha}-particle pressure gradient parameter ({omega}{sub {asterisk}}/{omega}{sub A}) ({omega}{sub {asterisk}} is the {alpha}-particle diamagnetic drift frequency), and (v{sub {alpha}}/v{sub A}) parameters will be presented for TFTR, CIT, and ITER tokamaks. The volume averaged {alpha}-particle beta threshold for TAE instability also depends sensitively on the core electron and ion temperature. Typically the volume averaged {alpha}-particle beta threshold is in the order of 10{sup {minus}4}. Typical growth rates of the n=1 TAE mode can be in the order of 10{sup {minus}2}{omega}{sub A}, where {omega}{sub A}=v{sub A}/qR. Other types of global Alfven waves are stable in D-T tokamaks due to toroidal coupling effects.
Observation of Central Toroidal Rotation Induced by ICRF on EAST
NASA Astrophysics Data System (ADS)
Pan, Xiayun; Wang, Fudi; Zhang, Xinjun; Lyu, Bo; Chen, Jun; Li, Yingying; Fu, Jia; Shi, Yuejiang; Yu, Yi; Ye, Minyou; Wan, Baonian
2016-02-01
Core plasma rotation of both L-mode and H-mode discharges with ion cyclotron range of frequency (ICRF) minority heating (MH) scheme was measured with a tangential X-ray imaging crystal spectrometer on EAST (Experimental Advanced Superconducting Tokamak). Co-current central impurity toroidal rotation change was observed in ICRF-heated L- and H-mode plasmas. Rotation increment as high as 30 km/s was generated at ∼1.7 MW ICRF power. Scaling results showed similar trend as the Rice scaling but with significant scattering, especially in L-mode plasmas. We varied the plasma current, toroidal field and magnetic configuration individually to study their effect on L-mode plasma rotation, while keeping the other major plasma parameters and heating unchanged during the scanning. It was found that larger plasma current could induce plasma rotation more efficiently. A scan of the toroidal magnetic field indicated that the largest rotation was obtained for on-axis ICRF heating. A comparison between lower-single-null (LSN) and double-null (DN) configurations showed that LSN discharges rendered a larger rotation change for the same power input and plasma parameters. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB112004 and 2015GB103002), National Natural Science Foundation of China (Nos. 11175208, 11305212, 11375235, 11405212 and 11261140328), the Innovative Program of Development Foundation of Hefei Center for Physical Science and Technology (2014FXCX003) and Brain Korea 21 Program for Leading Universities & Students (BK21 PLUS)
Toroidal-Core Microinductors Biased by Permanent Magnets
NASA Technical Reports Server (NTRS)
Lieneweg, Udo; Blaes, Brent
2003-01-01
The designs of microscopic toroidal-core inductors in integrated circuits of DC-to-DC voltage converters would be modified, according to a proposal, by filling the gaps in the cores with permanent magnets that would apply bias fluxes (see figure). The magnitudes and polarities of the bias fluxes would be tailored to counteract the DC fluxes generated by the DC components of the currents in the inductor windings, such that it would be possible to either reduce the sizes of the cores or increase the AC components of the currents in the cores without incurring adverse effects. Reducing the sizes of the cores could save significant amounts of space on integrated circuits because relative to other integrated-circuit components, microinductors occupy large areas - of the order of a square millimeter each. An important consideration in the design of such an inductor is preventing magnetic saturation of the core at current levels up to the maximum anticipated operating current. The requirement to prevent saturation, as well as other requirements and constraints upon the design of the core are expressed by several equations based on the traditional magnetic-circuit approximation. The equations involve the core and gap dimensions and the magnetic-property parameters of the core and magnet materials. The equations show that, other things remaining equal, as the maximum current is increased, one must increase the size of the core to prevent the flux density from rising to the saturation level. By using a permanent bias flux to oppose the flux generated by the DC component of the current, one would reduce the net DC component of flux in the core, making it possible to reduce the core size needed to prevent the total flux density (sum of DC and AC components) from rising to the saturation level. Alternatively, one could take advantage of the reduction of the net DC component of flux by increasing the allowable AC component of flux and the corresponding AC component of current
White, T.L.; Bigelow, T.S.; Kimrey, H.D. Jr.
1987-01-01
The Advanced Toroidal Facility (ATF) is a moderate aspect ratio torsatron that will utilize 53.2 GHz 200 kW Electron Cyclotron Heating (ECH) to produce nearly current-free target plasmas suitable for subsequent heating by strong neutral beam injection. The initial configuration of the ECH system from the gyrotron to ATF consists of an optical arc detector, three bellows, a waveguide mode analyzer, two TiO/sub 2/ mode absorbers, two 90/sup 0/ miter bends, two waveguide pumpouts, an insulating break, a gate valve, and miscellaneous straight waveguide sections feeding a launcher radiating in the TE/sub 02/ mode. Later, a focusing Vlasov launcher will be added to beam the ECH power to the saddle point in ATF magnetic geometry for optimum power deposition. The ECH system has several unique features; namely, the entire ECH system is evacuated, the ECH system is broadband, forward power is monitored by a newly developed waveguide mode analyzer, phase correcting miter bends will be employed, and the ECH system will be capable of operating short pulse to cw. Initial high-power tests show that the overall system efficiency is 87%. The waveguide mode analyzer shows that the gyrotron mode output consists of 13% TE/sub 01/, 82.6% TE/sub 02/, 2.5% TE/sub 03/, and 1.9% TE/sub 04/. 4 refs.
Design and implementation of a Thomson scattering diagnostic for the Compact Toroidal Hybrid
NASA Astrophysics Data System (ADS)
Traverso, P. J.; Maurer, D. A.; Hartwell, G. J.; Knowlton, S. F.; Archmiller, M. C.; Goforth, M. M.
2013-10-01
The Compact Toroidal Hybrid (CTH) experiment is investigating the avoidance of disruptions in ohmically driven torsaton plasmas as the ratio of vacuum transform to the total transform is changed. To better characterize these plasmas under this wide range of magnetic configurations, a new Thomson scattering diagnostic is being implemented to measure electron temperature and density profiles. These important internal profile measurements will be incorporated into the V3FIT code to enable better 3D equilibrium reconstruction. The Thomson scattering system uses a frequency doubled Continuum PL DLS 2 J Nd:YaG laser. The incident beam is passed vertically through an entrance Brewster window and a baffle system to minimize stray laser light. The beam exits through another Brewster window to an external beam dump. Polarization optics are planned to maximize the scattered light directed to the collection system for the specific scattering geometry of CTH. This work is supported by the USDoE under grant DE-FG02-00ER54610.
Fredrickson, E. D.; Bell, R. E.; Darrow, D. S.; Gorelenkov, N. N.; Kramer, G. J.; Medley, S. S.; White, R. B.; Crocker, N. A.; Kubota, S.; Levinton, F. M.; Yuh, H.; Liu, D.; Podesta, M.; Tritz, K.
2009-12-15
Experiments on the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] found strong bursts of toroidal Alfven eigenmode (TAE) activity correlated with abrupt drops in the neutron rate. A fairly complete data set offers the opportunity to benchmark the NOVA[C. Z. Cheng, Phys. Rep. 211, 1 (1992)] and ORBIT[R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)] codes in the low aspect ratio tokamak (ST) geometry. The internal structure of TAE was modeled with NOVA and good agreement is found with measurements made with an array of five fixed-frequency reflectometers. The fast-ion transport resulting from these bursts of multiple TAE was then modeled with the ORBIT code. The simulations are reasonably consistent with the observed drop in neutron rate, however, further refinements in both the simulation of the TAE structure and in the modeling of the fast-ion transport are needed. Benchmarking stability codes against present experiments is an important step in developing the predictive capability needed to plan future experiments.
NASA Astrophysics Data System (ADS)
Zhang, Xu-Dong; Fan, Bao-Chun; Gui, Ming-Yue; Pan, Zhen-Hua; Dong, Gang
2012-02-01
Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonationshock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interesting properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.
First Results from a Coherence Imaging Diagnostic for the Compact Toroidal Hybrid
NASA Astrophysics Data System (ADS)
Ennis, D. A.; Hartwell, G. J.; Johnson, C. A.; Maurer, D. A.; Allen, S. L.
2015-11-01
An optical coherence imaging diagnostic is being commissioned for time-resolved measurements (~ 10 ms) of ion emissivity, velocity, and temperature in the Compact Toroidal Hybrid (CTH) experiment. The Coherence Imaging (CI) technique measures the spectral coherence of an emission line with an imaging interferometer of fixed delay. CI has a number of advantages when compared to dispersive Doppler spectroscopy, including higher throughput and the capability to provide 2D spectral images, making it advantageous for investigating the non-axisymmetric geometry of CTH plasmas. A spectral survey of the visible and ultraviolet emission for a range of CTH discharges has identified helium and carbon impurity lines that will be utilized for CI measurements in CTH. First CI measurements of He II (468.6 nm) emission from CTH plasmas will be presented along with interferograms from a calibration light source and details of the instrument design. Results from this diagnostic will aid in characterizing the equilibrium ion parameters in both the edge and core of CTH plasmas for planned island divertor and MHD mode-locking experiments. Work supported by USDoE grant DE-FG02-00ER54610.
Resistive demountable toroidal-field coils for tokamak reactors
Jassby, D.L.; Jacobsen, R.A.; Kalnavarns, J.; Masson, L.S.; Sekot, J.P.
1981-07-01
Readily demountable TF (toroidal-field) coils allow complete access to the internal components of a tokamak reactor for maintenance of replacement. The requirement of readily demountable joints dictates the use of water-cooled resistive coils, which have a host of decisive advantages over superconducting coils. Previous papers have shown that resistive TF coils for tokamak reactors can operate in the steady state with acceptable power dissipation (typically, 175 to 300 MW). This paper summarizes results of parametric studies of size optimization of rectangular TF coils and of a finite-element stress analysis, and examines several candidate methods of implementing demountable joints for rectangular coils constructed of plate segments.
Hydraulic jumps in inhomogeneous strongly coupled toroidal dust flows
NASA Astrophysics Data System (ADS)
Piel, Alexander; Wilms, Jochen
2016-07-01
The inhomogeneous flow of strongly coupled dust particles in a toroidal particle trap with harmonic radial confinement is analyzed in the incompressible fluid limit. It is shown that the flow can spontaneously generate shock-like events, which are similar to the hydraulic jump in open channel flows. A definition of the Froude number for this model is given and the critical speed is recovered as the group velocity of surface waves. This hydraulic model is compared with molecular-dynamics simulations, which show that a sudden bifurcation of the flow lines and a localized temperature peak appear just at the point where the critical condition for the hydraulic jump is located.
An experimental study of natural convection in a toroidal loop
Stern, C.H. ); Greif, R.; Humphrey, J.A.C. )
1988-11-01
Velocity and temperature profiles were measured at the entrance and exit to the heating section of a toroidal thermosyphon loop operating under steady flow conditions for a range of heat inputs. Velocity measurements were made with a laser-Doppler velocimeter and temperature measurements with a small thermocouple probe. Detailed results are presented for the longitudinal and circumferential components of the velocity for four heat inputs. The data for cross-stream secondary flows and streamwise flow reversals emphasize the importance of including three-dimensional effects in analyses of these systems.
Variable control of neutron albedo in toroidal fusion devices
Jassby, Daniel L.; Micklich, Bradley J.
1986-01-01
An arrangement is provided for controlling neutron albedo in toroidal fusion devices having inboard and outboard vacuum vessel walls for containment of the neutrons of a fusion plasma. Neutron albedo material is disposed immediately adjacent the inboard wall, and is movable, preferably in vertical directions, so as to be brought into and out of neutron modifying communication with the fusion neutrons. Neutron albedo material preferably comprises a liquid form, but may also take pebble, stringer and curtain-like forms. A neutron flux valve, rotatable about a vertical axis is also disclosed.
Excitation of the steady toroidal magnetic field in solar interior
NASA Astrophysics Data System (ADS)
Krivodubskij, Valery
This investigation deals with the problem of the asymmetry of sunspot activity maximums in neighbouring solar cycles. The Gnevyshev-Ohl rule (Gnevyshev and Ohl 1948, Astron. Zhurn. 25, 18) is a likely evidence for the radiative interior pervaded by a strong steady magnetic field. Therefore, some effects are required to ensure existence this deep-laid field for long-duration times. The way for search of excitation mechanism of strong magnetic field give us the helioseismological experiments. We take the physical parameters of the interiors from standard solar model by Allen (1973, Astrophysical Quantities, London) for calculations. It was found that main limiting factor on the magnetic field value is the magnetic flux loss due to buoyancy in the radiative (non-turbulent) zone (RZ) which overcomes the rate of the field decay caused by ohmic dissipation. The helioseismology inversions indicate that the radial, but not latitudinal, shear in the internal rotation of the Sun penetrates rather deep, almost to the solar core (Duval et al.1984, Nature 310, 22; Brown 1985, Nature 317, 591; Libbrecht 1986, Nature 319, 753). This radial differential rotation, acting on a weak relict poloidal magnetic field, about 1 G, in the stable RZ, can excite the rather strong steady toroidal fields (10 KG -10 MG). Obtained estimations agree with the helioseismically determined magnetic intensities in the solar interiors (Dziembowski and Goode 1989, ApJ 347, 540; Antia, Chitre and Thompson 2003, AA 399, 329). We assume that due to magnetic buoyancy and meridional circulation at the upper boundary of the RZ the power toroidal field may penetrate, partly, into the convective zone (CZ). Here stationary steady directed field will be add to oscillating toroidal field excited by alpha-Omega dynamo. Since the oscillating dynamo-field changes their own direction with 11-years cycle-period, then the amplitude of total, oscillating plus steady, toroidal field in the CZ has to be a few differing in
Theory and application of maximum magnetic energy in toroidal plasmas
Chu, T.K.
1992-02-01
The magnetic energy in an inductively driven steady-state toroidal plasma is a maximum for a given rate of dissipation of energy (Poynting flux). A purely resistive steady state of the piecewise force-free configuration, however, cannot exist, as the periodic removal of the excess poloidal flux and pressure, due to heating, ruptures the static equilibrium of the partitioning rational surfaces intermittently. The rupture necessitates a plasma with a negative q{prime}/q (as in reverse field pinches and spheromaks) to have the same {alpha} in all its force-free regions and with a positive q{prime}/q (as in tokamaks) to have centrally peaked {alpha}`s.
Theory and application of maximum magnetic energy in toroidal plasmas
Chu, T.K.
1992-02-01
The magnetic energy in an inductively driven steady-state toroidal plasma is a maximum for a given rate of dissipation of energy (Poynting flux). A purely resistive steady state of the piecewise force-free configuration, however, cannot exist, as the periodic removal of the excess poloidal flux and pressure, due to heating, ruptures the static equilibrium of the partitioning rational surfaces intermittently. The rupture necessitates a plasma with a negative q{prime}/q (as in reverse field pinches and spheromaks) to have the same {alpha} in all its force-free regions and with a positive q{prime}/q (as in tokamaks) to have centrally peaked {alpha}'s.
Experimental observation of crystalline particle flows in toroidal dust clouds
Wilms, Jochen Piel, Alexander; Reichstein, Torben
2015-06-15
The dust flow in a toroidal dust trap is studied experimentally. The flow is driven by the Hall component of the ion drag force in a magnetized plasma. Dust density waves are found in a torus with a large minor radius a, which allows for several wavelength, 2a>5λ, in the (mostly) radial direction of the ion flow. Beyond an intermediate state with radial sloshing oscillations, a crystalline dust flow with suppressed wave activity could be realized for 2a<2λ. The particles arrange themselves in distinct layers with hexagonal-like local order. Smooth transitions between states with different numbers of layers are found in the inhomogeneous flow.
Toroidal constant-tension superconducting magnetic energy storage units
Herring, J.S.
1992-11-03
A superconducting magnetic energy storage unit is provided in which the magnet is wound in a toroidal fashion such that the magnetic field produced is contained only within the bore of the magnet, and thus producing a very low external field. The superconducting magnet includes a coolant channel disposed through the wire. The bore of the magnet comprises a storage volume in which cryogenic coolant is stored, and this volume supplies the coolant to be delivered to the coolant channel in the magnet. 6 figs.
System and method of operating toroidal magnetic confinement devices
Chance, Morrell S.; Jardin, Stephen C.; Stix, Thomas H.; Grimm, deceased, Ray C.; Manickam, Janardhan; Okabayashi, Michio
1987-01-01
For toroidal magnetic confinement devices the second region of stability against ballooning modes can be accessed with controlled operation. Under certain modes of operation, the first and second stability regions may be joined together. Accessing the second region of stability is accomplished by forming a bean-shaped plasma and increasing the indentation until a critical value of indentation is reached. A pusher coil, located at the inner-major-radius side of the device, is engaged to form a bean-shaped poloidal cross-section in the plasma.
Simulation of dust streaming in toroidal traps: Stationary flows
Reichstein, Torben; Piel, Alexander
2011-08-15
Molecular-dynamic simulations were performed to study dust motion in a toroidal trap under the influence of the ion drag force driven by a Hall motion of the ions in E x B direction, gravity, inter-particle forces, and friction with the neutral gas. This article is focused on the inhomogeneous stationary streaming motion. Depending on the strength of friction, the spontaneous formation of a stationary shock or a spatial bifurcation into a fast flow and a slow vortex flow is observed. In the quiescent streaming region, the particle flow features a shell structure which undergoes a structural phase transition along the flow direction.
Simulated and experimental compression of a compact toroid
Johnson, J N; Hwang, D Q; Horton, R D; Evans, R W; Owen, J M
2009-05-06
We present simulation results and experimental data for the compression of a compact toroid by a conducting nozzle without a center electrode. In both simulation and experiment, the flow of the plasma is greatly obstructed by even modest magnetic fields. A simple mechanism for this obstruction is suggested by our simulations. In particular, the configuration of the plasmoid's magnetic field plays a significant role in the success of the experiment. We analyze two types of plasma configurations under compression and demonstrate that the results from the simulations matches those from the experiments, and that the mechanism predicts the different behaviors observed in the two cases.
Linear tearing mode stability equations for a low collisionality toroidal plasma
NASA Astrophysics Data System (ADS)
Connor, J. W.; Hastie, R. J.; Helander, P.
2009-01-01
et al (1983 Phys. Fluids 26 2509) to toroidal geometry.
NASA Astrophysics Data System (ADS)
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2011-01-01
Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions. PMID:21880160
Students Discovering Spherical Geometry Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Computational synthetic geometry
Sturmfels, B. )
1988-01-01
This book deals with methods for realizing abstract geometric objects in concrete vector spaces. It considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It appears that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems, a variety of symbolic algorithms are discussed, and the methods are applied to obtain mathematical results on convex polytopes, projective configurations and the combinatories of Grassmann varieties.
NASA Astrophysics Data System (ADS)
Liu, Yueqiang; Ryan, D.; Kirk, A.; Li, Li; Suttrop, W.; Dunne, M.; Fischer, R.; Fuchs, J. C.; Kurzan, B.; Piovesan, P.; Willensdorfer, M.; the ASDEX Upgrade Team; the EUROfusion MST1 Team
2016-05-01
The plasma response to the vacuum resonant magnetic perturbation (RMP) fields, produced by the ELM control coils in ASDEX Upgrade experiments, is computationally modelled using the MARS-F/K codes (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). A systematic investigation is carried out, considering various plasma and coil configurations as in the ELM control experiments. The low q plasmas, with {{q}95}˜ 3.8 (q 95 is the safety factor q value at 95% of the equilibrium poloidal flux), responding to low n (n is the toroidal mode number) field perturbations from each single row of the ELM coils, generates a core kink amplification effect. Combining two rows, with different toroidal phasing, thus leads to either cancellation or reinforcement of the core kink response, which in turn determines the poloidal location of the peak plasma surface displacement. The core kink response is typically weak for the n = 4 coil configuration at low q, and for the n = 2 configuration but only at high q ({{q}95}˜ 5.5 ). A phase shift of around 60 degrees for low q plasmas, and around 90 degrees for high q plasmas, is found in the coil phasing, between the plasma response field and the vacuum RMP field, that maximizes the edge resonant field component. This leads to an optimal coil phasing of about 100 (-100) degrees for low (high) q plasmas, that maximizes both the edge resonant field component and the plasma surface displacement near the X-point of the separatrix. This optimal phasing closely corresponds to the best ELM mitigation observed in experiments. A strong parallel sound wave damping moderately reduces the core kink response but has minor effect on the edge peeling response. For low q plasmas, modelling shows that both the resonant electromagnetic torque and the neoclassical toroidal viscous (NTV) torque (due to the presence of 3D magnetic field perturbations) contribute to the toroidal flow damping, in particular near the
NASA Astrophysics Data System (ADS)
Liu, Yueqiang; Ryan, D.; Kirk, A.; Li, Li; Suttrop, W.; Dunne, M.; Fischer, R.; Fuchs, J. C.; Kurzan, B.; Piovesan, P.; Willensdorfer, M.; the ASDEX Upgrade Team; the EUROfusion MST1 Team
2016-05-01
The plasma response to the vacuum resonant magnetic perturbation (RMP) fields, produced by the ELM control coils in ASDEX Upgrade experiments, is computationally modelled using the MARS-F/K codes (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). A systematic investigation is carried out, considering various plasma and coil configurations as in the ELM control experiments. The low q plasmas, with {{q}95}∼ 3.8 (q 95 is the safety factor q value at 95% of the equilibrium poloidal flux), responding to low n (n is the toroidal mode number) field perturbations from each single row of the ELM coils, generates a core kink amplification effect. Combining two rows, with different toroidal phasing, thus leads to either cancellation or reinforcement of the core kink response, which in turn determines the poloidal location of the peak plasma surface displacement. The core kink response is typically weak for the n = 4 coil configuration at low q, and for the n = 2 configuration but only at high q ({{q}95}∼ 5.5 ). A phase shift of around 60 degrees for low q plasmas, and around 90 degrees for high q plasmas, is found in the coil phasing, between the plasma response field and the vacuum RMP field, that maximizes the edge resonant field component. This leads to an optimal coil phasing of about 100 (‑100) degrees for low (high) q plasmas, that maximizes both the edge resonant field component and the plasma surface displacement near the X-point of the separatrix. This optimal phasing closely corresponds to the best ELM mitigation observed in experiments. A strong parallel sound wave damping moderately reduces the core kink response but has minor effect on the edge peeling response. For low q plasmas, modelling shows that both the resonant electromagnetic torque and the neoclassical toroidal viscous (NTV) torque (due to the presence of 3D magnetic field perturbations) contribute to the toroidal flow damping, in particular near the
Pole-phase modulated toroidal winding for an induction machine
Miller, John Michael; Ostovic, Vlado
1999-11-02
A stator (10) for an induction machine for a vehicle has a cylindrical core (12) with inner and outer slots (26, 28) extending longitudinally along the inner and outer peripheries between the end faces (22, 24). Each outer slot is associated with several adjacent inner slots. A plurality of toroidal coils (14) are wound about the core and laid in the inner and outer slots. Each coil occupies a single inner slot and is laid in the associated outer slot thereby minimizing the distance the coil extends from the end faces and minimizing the length of the induction machine. The toroidal coils are configured for an arbitrary pole phase modulation wherein the coils are configured with variable numbers of phases and poles for providing maximum torque for cranking and switchable to a another phase and pole configuration for alternator operation. An adaptor ring (36) circumferentially positioned about the stator improves mechanical strength, and provides a coolant channel manifold (34) for removing heat produced in stator windings during operation.
Kinetic and electromagnetic transport processes in toroidal devices
Moses, R.W.; Schoenberg, K.F.
1990-01-01
A brief review of transport processes in toroidal devices is presented. Particular attention is given to radial transport of power by the Poynting's vector and kinetic electron flow. This work is primarily focused on the Reversed Field Pinch (RFP) which holds the added complexity of a dynamo process that sustains poloidal current in the edge region, where the toroidal field is reversed. The experimental observation of superthermal unidirectional electrons in the plasma edge of ZT-40M and HBTX1C is noted, and the rapid, nonclassical ion heating in RFPs is taken account of. Radial transport parallel to fluctuating magnetic field lines is deemed a likely candidate for both electromagnetic and kinetic energy transport. Two models are discussed and compared. It is concluded that electromagnetic transport using a local Ohm's law best describes nonclassical ion heating, and the transport of kinetic energy by long mean free path electrons best represents the half-Maxwellian of electrons observed in the edge of several RFPs. A nonlocal Ohm's law is essential for the kinetic electron model. 18 refs.
Toroidal midplane neutral beam armor and plasma limiter
Kugel, Henry W.; Hand Jr, Samuel W.; Ksayian, Haig
1986-02-04
For use in a tokamak fusion reactor having a midplane magnetic coil on the inner wall of an evacuated toriodal chamber within which a neutral beam heated, fusing plasma is magnetically confined, a neutral beam armor shield and plasma limiter is provided on the inner wall of the toroidal chamber to shield the midplane coil from neutral beam shine-thru and plasma deposition. The armor shield/plasma limiter forms a semicircular enclosure around the midplane coil with the outer surface of the armor shield/plasma limiter shaped to match, as closely as practical, the inner limiting magnetic flux surface of the toroidally confined, indented, bean-shaped plasma. The armor shield/plasma limiter includes a plurality of semicircular graphite plates each having a pair of coupled upper and lower sections with each plate positioned in intimate contact with an adjacent plate on each side thereof so as to form a closed, planar structure around the entire outer periphery of the circular midplane coil. The upper and lower plate sections are adapted for coupling to heat sensing thermocouples and to a circulating water conduit system for cooling the armor shield/plasma limiter.The inner center portion of each graphite plate is adapted to receive and enclose a section of a circular diagnostic magnetic flux loop so as to minimize the power from the plasma confinement chamber incident upon the flux loop.
Toroidal midplane neutral beam armor and plasma limiter
Kugel, Henry W.; Hand, Jr, Samuel W.; Ksayian, Haig
1986-01-01
For use in a tokamak fusion reactor having a midplane magnetic coil on the inner wall of an evacuated toriodal chamber within which a neutral beam heated, fusing plasma is magnetically confined, a neutral beam armor shield and plasma limiter is provided on the inner wall of the toroidal chamber to shield the midplane coil from neutral beam shine-thru and plasma deposition. The armor shield/plasma limiter forms a semicircular enclosure around the midplane coil with the outer surface of the armor shield/plasma limiter shaped to match, as closely as practical, the inner limiting magnetic flux surface of the toroidally confined, indented, bean-shaped plasma. The armor shield/plasma limiter includes a plurality of semicircular graphite plates each having a pair of coupled upper and lower sections with each plate positioned in intimate contact with an adjacent plate on each side thereof so as to form a closed, planar structure around the entire outer periphery of the circular midplane coil. The upper and lower plate sections are adapted for coupling to heat sensing thermocouples and to a circulating water conduit system for cooling the armor shield/plasma limiter.The inner center portion of each graphite plate is adapted to receive and enclose a section of a circular diagnostic magnetic flux loop so as to minimize the power from the plasma confinement chamber incident upon the flux loop.
Interplay between toroidal rotation and flow shear in turbulence stabilisation
NASA Astrophysics Data System (ADS)
Camenen, Y.; Casson, F. J.; Manas, P.; Peeters, A. G.
2016-02-01
The interplay between toroidal rotation u, parallel flow shear u', and perpendicular flow shear γE in the stabilisation of tokamak turbulence is investigated in non-linear flux-tube gyrokinetic simulations. The simulations are performed for a reference L-mode DIII-D plasma (the so-called shortfall case) at r /a =0.8 , varying the flow parameters around their nominal values. Depending on the respective signs of u, u', and γE, turbulence is found to be enhanced, reduced, or unchanged. When the coupling is favorable, the overall effect on the non-linear heat fluxes can be very large, even at moderate flow values. The ion heat flux is, for instance, decreased by a factor of 3 when the direction of the parallel flow shear is reversed with respect to its nominal value. Even more surprising, keeping u' and γE at their nominal values, the ion heat flux decreases by more than 50% when the toroidal flow is reversed. The relevance of this mechanism in the experiments which depends on the ability to decouple u, u', and γE is discussed. The interplay between u and u' observed in the non-linear simulations qualitatively follows the linear stability results and is interpreted in the frame of a simple fluid model.
Theoretical Analysis of the Electron Spiral Toroid Concept
NASA Technical Reports Server (NTRS)
Cambier, Jean-Luc; Micheletti, David A.; Bushnell, Dennis M. (Technical Monitor)
2000-01-01
This report describes the analysis of the Electron Spiral Toroid (EST) concept being promoted by Electron Power Systems Inc. (EPS). The EST is described as a toroidal plasma structure composed Of ion and electron shells. It is claimed that the EST requires little or no external confinement, despite the extraordinarily large energy densities resulting from the self-generating magnetic fields. The present analysis is based upon documentation made available by EPS, a previous description of the model by the Massachusetts Institute of Technology (MIT), and direct discussions with EPS and MIT. It is found that claims of absolute stability and large energy storage capacities of the EST concept have not been substantiated. Notably, it can be demonstrated that the ion fluid is fundamentally unstable. Although various scenarios for ion confinement were subsequently suggested by EPS and MIT, none were found to be plausible. Although the experimental data does not prove the existence of EST configurations, there is undeniable experimental evidence that some type of plasma structures whose characteristics remain to be determined are observed. However, more realistic theoretical models must first be developed to explain their existence and properties before applications of interest to NASA can he assessed and developed.
Design study of toroidal traction CVT for electric vehicles
NASA Technical Reports Server (NTRS)
Raynard, A. E.; Kraus, J.; Bell, D. D.
1980-01-01
The development, evaluation, and optimization of a preliminary design concept for a continuously variable transmission (CVT) to couple the high-speed output shaft of an energy storage flywheel to the drive train of an electric vehicle is discussed. An existing computer simulation program was modified and used to compare the performance of five CVT design configurations. Based on this analysis, a dual-cavity full-toroidal drive with regenerative gearing is selected for the CVT design configuration. Three areas are identified that will require some technological development: the ratio control system, the traction fluid properities, and evaluation of the traction contact performance. Finally, the suitability of the selected CVT design concept for alternate electric and hybrid vehicle applications and alternate vehicle sizes and maximum output torques is determined. In all cases the toroidal traction drive design concept is applicable to the vehicle system. The regenerative gearing could be eliminated in the electric powered vehicle because of the reduced ratio range requirements. In other cases the CVT with regenerative gearing would meet the design requirements after appropriate adjustments in size and reduction gearing ratio.
Compact Toroidal Hybrid Research Program: Recent Progress and Future Plans
NASA Astrophysics Data System (ADS)
Maurer, D. A.; Cianciosa, M.; Hanson, J. D.; Hartwell, G. J.; Hebert, J. D.; Herfindal, J. L.; Knowlton, S. F.; Archmiller, M. C.; Traverso, P.; Pandya, M.; Ma, X.
2012-10-01
Understanding the control and avoidance of major disruptions in current carrying toroidal plasmas is important in mitigating the effects of rapid loss of confinement in future devices. The Compact Toroidal Hybrid (CTH) experiment is investigating the passive avoidance of disruptions with the addition of a small amount of vacuum transform provided by external coils. In ohmically-driven stellarator plasmas no disruptions of any kind are observed if the vacuum transform exceeds ˜ 0.11. Recent progress on the suppression of low-qa (high a), density limit, and vertically unstable plasma disruptions is overviewed. Interpretation of these results makes use of 3D equilibrium reconstructions using the V3FIT code [1]. Several new diagnostic tools have recently been developed and implemented on CTH. These new research tools include multi-chord interferometry, bolometry, Hα emission detection, a two-color soft x-ray camera, and upgraded magnetic sensor arrays. In addition to these diagnostic improvements, a new 200 kW gyrotron system will provide additional heating power for stellarator target plasmas. Future research directions and plans will also be discussed. [4pt] [1] J. D. Hanson, S. P. Hirshman, S. F. Knowlton, L. L. Lao, E. A. Lazarus, J. M. Shields, Nucl. Fusion, 49 (2009) 075031
On the toroidal plasma rotations induced by lower hybrid waves
NASA Astrophysics Data System (ADS)
Guan, Xiaoyin; Qin, Hong; Liu, Jian; Fisch, Nathaniel J.
2013-02-01
A theoretical model is developed to explain the plasma rotations induced by lower hybrid waves in Alcator C-Mod. In this model, torodial rotations are driven by the Lorentz force on the bulk-electron flow across flux surfaces, which is a response of the plasma to the resonant-electron flow across flux surfaces induced by the lower hybrid waves. The flow across flux surfaces of the resonant electrons and the bulk electrons are coupled through the radial electric field initiated by the resonant electrons, and the friction between ions and electrons transfers the toroidal momentum to ions from electrons. An improved quasilinear theory with gyrophase dependent distribution function is developed to calculate the perpendicular resonant-electron flow. Toroidal rotations are determined using a set of fluid equations for bulk electrons and ions, which are solved numerically by a finite-difference method. Numerical results agree well with the experimental observations in terms of flow profile and amplitude. The model explains the strong correlation between torodial flow and internal inductance observed experimentally, and predicts both counter-current and co-current flows, depending on the perpendicular wave vectors of the lower hybrid waves.
Dynamic processes in field-reversed-configuration compact toroids
NASA Astrophysics Data System (ADS)
Rej, D. J.
The dynamic processes involved in field-reversed configuration (FRC) formation, translation, and compression are reviewed. Though the FRC is related to the field-reversed mirror concept, the formation method used in most experiments is a variant of the field-reversed THETA-pinch. Formation of the FRC eqilibrium occurs rapidly, usually in less than 20 microsec. The formation sequence consists of several coupled processes: preionization; radial implosion and compression; magnetic field line closure; axial contraction; equilibrium formation. Recent experiments and theory have led to a significantly improved understanding of these processes; however, the experimental method still relies on a somewhat empirical approach which involves the optimization of initial preionization plasma parameters and symmetry. New improvements in FRC formation methods include the use of lower voltages which extrapolate better to larger devices. The axial translation of compact toroid plasmas offers an attractive engineering convenience in a fusion reactor. FRC translation has been demonstrated in experiments worldwide, and these plasmas are found to be robust, moving at speeds up to the Alfven velocity over distances of up to 16 m, with no degradation in the confinement. Compact toroids are ideal for magnetic compression. Translated FRCs have been compressed and heated by imploding liners. Upcoming experiments will rely on external flux compression to heat a translater FRC at 1-GW power levels.
Major disruption characteristics with a toroidal limiter in PDX
NASA Astrophysics Data System (ADS)
McGuire, K.; Buchenauer, D.; Couture, P.; Izzo, R.; Kawahata, K.; Monticello, D.; Okano, K.; Sauthoff, N.
1984-05-01
The PDX tokamak provides an experimental facility for the comparison of a variety of limiter configurations. A large data base of disruption characteristics has been obtained during operation with (a) an inner wall toroidal limiter with its limiting surface at 85 cm, giving a = 40 cm for R = 125 cm, (b) top and bottom carbon rail limiter giving R = 143 cm, a = 40 cm, and (c) an outboard scoop limiter giving R = 153 cm, a = 40 cm. The results show that the average current decay rate {ΔI}/{ΔT} (kA/ms) for disruptions on the inner wall limiter is about four times faster than for those on the rail or scoop limiters. In addition, the achievement of discharges with qψ less than 3 ( qψ is the equilibrium safety factor calculated by a MHD code) with the inner wall toroidal limiter is extremely difficult, due to the rapid growth of an m = 3, n = 1 mode as q approaches three. However, the disruption is often triggered by the growth of an m = 2, n = 1 mode after the m = 3, n = 1 mode has saturated in amplitude. The transport phase of the disruption phenomena has the same time scale regardless of limiter configuration. Numerical calculations of resistive MHD stability have been used to explain some of these disruption characteristics.
On the Toroidal Plasma Rotations Induced by Lower Hybrid Waves
Guan, Xiaoyin; Qin, Hong; Liu, Jian; Fisch, Nathaniel J.
2012-11-14
A theoretical model is developed to explain the plasma rotations induced by lower hybrid waves in Alcator C-Mod. In this model, torodial rotations are driven by the Lorentz force on the bulk electron flow across flux surfaces, which is a response of the plasma to the resonant-electron flow across flux surfaces induced by the lower hybrid waves. The flow across flux surfaces of the resonant electrons and the bulk electrons are coupled through the radial electric fi eld initiated by the resonant electrons, and the friction between ions and electrons transfers the toroidal momentum to ions from electrons. An improved quasilinear theory with gyrophase dependent distribution function is developed to calculate the perpendicular resonant-electron flow. Toroidal rotations are determined using a set of fluid equations for bulk electrons and ions, which are solved numerically by a fi nite- difference method. Numerical results agree well with the experimental observations in terms of flow pro file and amplitude. The model explains the strong correlation between torodial flow and internal inductance observed experimentally, and predicts both counter-current and co-current flows, depending on the perpendicular wave vectors of the lower hybrid waves. __________________________________________________
Island Divertor Plate Modeling for the Compact Toroidal Hybrid Experiment
NASA Astrophysics Data System (ADS)
Hartwell, G. J.; Massidda, S. D.; Ennis, D. A.; Knowlton, S. F.; Maurer, D. A.; Bader, A.
2015-11-01
Edge magnetic island divertors can be used as a method of plasma particle and heat exhaust in long pulse stellarator experiments. Detailed power loading on these structures and its relationship to the long connection length scrape off layer physics is a new Compact Toroidal Hybrid (CTH) research thrust. CTH is a five field period, l = 2 torsatron with R0 = 0 . 75 m, ap ~ 0 . 2 m, and | B | <= 0 . 7 T. For these studies CTH is configured as a pure stellarator using a 28 GHz, 200 kW gyrotron operating at 2nd harmonic for ECRH. We report the results of EMC3-EIRENE modeling of divertor plates near magnetic island structures. The edge rotational transform is varied by adjusting the ratio of currents in the helical and toroidal field coils. A poloidal field coil adjusts the shear of the rotational transform profile, and width of the magnetic island, while the phase of the island is rotated with a set of five error coils producing an n = 1 perturbation. For the studies conducted, a magnetic configuration with a large n = 1 , m = 3 magnetic island at the edge is generated. Results from multiple potential divertor plate locations will be presented and discussed. This work is supported by U.S. Department of Energy Grant No. DE-FG02-00ER54610.
Network geometry with flavor: From complexity to quantum geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Geometry of modified Newtonian dynamics
NASA Astrophysics Data System (ADS)
Skordis, Constantinos; Zlosnik, Tom
2012-02-01
Modified Newtonian dynamics is an empirical modification to Poisson’s equation which has had success in accounting for the “gravitational field” Φ in a variety of astrophysical systems. The field Φ may be interpreted in terms of the weak-field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the aquadratic Lagrangian (AQUAL) theory, tensor-vector-scalar (TeVeS) theory and generalized Einstein-aether theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit TeVeS solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of generalized Einstein-aether, a disformal symmetry of the action emerges in the limit of ∇→Φ→0. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
NASA Astrophysics Data System (ADS)
Chen, Yang
2000-10-01
The physics of kinetic electrons and electromagnetic fluctuations are key challenges in microturbulence simulation research. Recently, we have made progress in this area by developing a drift-kinetic electron model using both the ``split-weight scheme"(I. Manuilskiy and W. W. Lee, Phys. Plasmas 7 1381 (2000)) and the canonical parallel momemtum formulation of gyrokinetics(T. S. Hahm, W. W. Lee and A. Brizard, Phys. Fluids 31(1988) 1940) in a fully nonlinear three-dimensional toroidal field-line-following simulation. This model includes magnetic field perturbations perpendicular to the equilibrium magnetic field. Numerical issues arising from the resolution of the magnetic skin depth(J. Cummings, Ph.D. Thesis, Princeton Univ. (1994)) currently limit these simulations to small <≈ β, β m_i/me <≈ O(1) and progress in this area will be reported. A complementary hybrid simulation with fully gyrokinetic ions and a zero-inertia electron fluid has been developed as well. The electron fluid equations are derived from moments of the drift kinetic equation and a predictor-corrector scheme for the fluid-hybrid model has been implemented in three-dimensional toroidal field-line-following geometry. This is a much simpler electron model and works well at high β. We are currently using both models to study the effects of electron dynamics on turbulence, including particle transport (which is zero in simulations using adiabatic response), kinetic Alfvén modes and modification to zonal flows due to kinetic electrons and the generation of zonal fields through including A_allel(A. Das and P. H. Diamond, "Kinetic theory of the zonal flow instability in electromagnetic drift-wave turbulence", to appear in Phys. Plasmas). Both hybrid and the fully kinetic simulations have been carefully benchmarked with linear theory in the slab limit. Simulation results for turbulence with both trapped-electron drive and ion-temperature-gradient drive will be presented. We will report results
Convection in three dimensions with surface plates - Generation of toroidal flow
NASA Technical Reports Server (NTRS)
Gable, Carl W.; O'Connell, Richard J.; Travis, Bryan J.
1991-01-01
This work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics. The model is three-dimensional and includes surface plates; it allows plate velocity to change dynamically according to the forces which result from convection. It is shown that plates are an effective means of introducing a toroidal component into the flow field. After initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimize the toroidal flow field. The toroidal field decays with depth from its value at the surface; the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries. Layered viscosity increasing with depth causes the toroidal field to decay more rapidly, effectively confining it to the upper, low-viscosity layer. The effect of viscosity layering on the poloidal field is relatively small, which is attributed to its generation by temperature variations distributed throughout the system. The generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the earth. A low-viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle. The resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles.
Toroidal Flow Generation by the ICRF Minority Heating and RF Wave Field Profile Dependence
NASA Astrophysics Data System (ADS)
Murakami, S.; Itoh, K.; Zheng, L. J.; Van Dam, J. W.; Fukuyama, A.
2011-12-01
The toroidal flow generation by the ICRF minority heating is investigated in the Alcator C-Mod like tokamak plasma applying GNET code, in which the drift kinetic equation is solved in 5D phase-space. An asymmetry of velocity distribution function in the parallel direction is found and two kinds of toroidal flows are observed. One is the sheared flow near the RF power absorption region depending on the sign of k∥ and the other is the toroidal flow, which is larger than the previous one, independent of the sign of k∥. It is found that the k∥ sign dependent flow would be related to the mechanism proposed by Ohkawa et al. [Phys. Plasmas 12 (2005) 094506.] and that the k∥ sign independent toroidal flow is generated by the net toroidal motion of energetic tail ions. We also investigate the effect of RF wave field profile on the toroidal flow generation comparing the local and broad heating cases. A broader toroidal flow is obtained and about 5 times of ICRF heating power is necessary for generating the similar amplitude of toroidal flow in the broad heating case.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Spacetime and Euclidean geometry
NASA Astrophysics Data System (ADS)
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
Teaching Geometry with Tangrams.
ERIC Educational Resources Information Center
Russell, Dorothy S.; Bologna, Elaine M.
1982-01-01
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
ERIC Educational Resources Information Center
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
ERIC Educational Resources Information Center
KLIER, KATHERINE M.
PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…
Observation of the self-generated toroidal magnetic field in rotamak
Petrov, Yuri; Zhong Fangchuan; Huang Tiansen
2005-08-15
An experimental study of the self-generated toroidal magnetic field in rotamak field-reversed configuration plasmas is performed in the case of high input power (200 kW), long-duration (40 ms) discharges. In one round of experiments, the polarity of the toroidal field in the poloidal cross section is different not only from one hemisphere to another but also in radial direction. In another round of experiments, the toroidal field is seen to reverse its sign in the course of a shot. The data for the field are fitted with the vector spherical harmonic functions. The poloidally swirling currents associated with the self-generated toroidal field are shown to contribute to the formation of the two-peak structure of the toroidal plasma current.
An introduction to Minkowski geometries
NASA Astrophysics Data System (ADS)
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
Toroidal and poloidal momentum transport studies in tokamaks
NASA Astrophysics Data System (ADS)
Tala, T.; Crombé, K.; de Vries, P. C.; Ferreira, J.; Mantica, P.; Peeters, A. G.; Andrew, Y.; Budny, R.; Corrigan, G.; Eriksson, A.; Garbet, X.; Giroud, C.; Hua, M.-D.; Nordman, H.; Naulin, V.; Nave, M. F. F.; Parail, V.; Rantamäki, K.; Scott, B. D.; Strand, P.; Tardini, G.; Thyagaraja, A.; Weiland, J.; Zastrow, K.-D.; Contributors, JET-EFDA
2007-12-01
The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. τE/τphi ≈ 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χphieff/χi,eff among different tokamaks can be found. For example, the value of effective Prandtl number is typically around χphieff/χi,eff ≈ 0.2 on JET while still τE/τphi ≈ 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number χphi/χi of around 1 is valid if there is an additional, significant inward momentum pinch which is required to explain the amplitude and phase behaviour of the momentum perturbation. The experimental results, i.e. the high Prandtl number and pinch, are in good qualitative and to some extent also in quantitative agreement with linear gyro-kinetic simulations. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E × B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly
3D toroidal physics: testing the boundaries of symmetry breaking
NASA Astrophysics Data System (ADS)
Spong, Don
2014-10-01
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to lead to a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D ELM-suppression fields to stellarators with more dominant 3D field structures. There is considerable interest in the development of unified physics models for the full range of 3D effects. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. Fortunately, significant progress is underway in theory, computation and plasma diagnostics on many issues such as magnetic surface quality, plasma screening vs. amplification of 3D perturbations, 3D transport, influence on edge pedestal structures, MHD stability effects, modification of fast ion-driven instabilities, prediction of energetic particle heat loads on plasma-facing materials, effects of 3D fields on turbulence, and magnetic coil design. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with future fusion reactors. The development of models to address 3D physics and progress in these areas will be described. This work is supported both by the US Department of Energy under Contract DE
Siemon, R.E.
1981-03-01
This document contains papers contributed by the participants of the Third Symposium on Physics and Technology of Compact Toroids in the Magnetic Fusion Energy Program. Subjects include reactor aspects of compact toroids, energetic particle rings, spheromak configurations (a mixture of toroidal and poloidal fields), and field-reversed configurations (FRC's that contain purely poloidal field).
Nebeck, H.E.
1986-08-01
The MAZE mesh generator represents an arbitrary two dimensional region of space as an ordered collection of quadrilateral elements. Each element is defined by its four corner points (nodes) and an integer material number. Models are created by subdividing the region(s) of interest into one or more PARTS and specifying the element distribution in each part. Then, parts can be merged together to form the meshed representation of the entire region. Applying boundary conditions and describing material properties completes the model construction process. This activity takes place in three distinct phases: phase I-define geometry, subdivide regions into elements; phase II-refine geometry, establish interface and boundary conditions; phase III-describe material properties. This work presents explanations and examples of the phase I commands, along with an overview of the MAZE mesh generation process.
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Mathematics: Algebra and Geometry. GED Scoreboost.
ERIC Educational Resources Information Center
Hoyt, Cathy
GED "Scoreboost" materials target exactly the skills one needs to pass the General Educational Development (GED) tests. This book focuses on the GED Mathematics test. To prepare for the test, the test taker needs to learn skills in number and operation sense, data and statistics, geometry and measurement, and algebra. To pass the test, the test…
The Geometry of the Universe: Part 1
ERIC Educational Resources Information Center
Francis, Stephanie
2009-01-01
This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…
Geodesic acoustic mode in toroidally rotating anisotropic tokamaks
Ren, Haijun
2015-07-15
Effects of anisotropy on the geodesic acoustic mode (GAM) are analyzed by using gyro-kinetic equations applicable to low-frequency microinstabilities in a toroidally rotating tokamak plasma. Dispersion relation in the presence of arbitrary Mach number M, anisotropy strength σ, and the temperature ration τ is analytically derived. It is shown that when σ is less than 3 + 2τ, the increased electron temperature with fixed ion parallel temperature increases the normalized GAM frequency. When σ is larger than 3 + 2τ, the increasing of electron temperature decreases the GAM frequency. The anisotropy σ always tends to enlarge the GAM frequency. The Landau damping rate is dramatically decreased by the increasing τ or σ.
Ultimate Diagnostics for the Measurement of Turbulence in Toroidal Devices
NASA Astrophysics Data System (ADS)
Park, H.; Mazzucato, E.; Hahm, T. S.; Lee, W. W.; Rewoldt, G.; Synakowski, E.; Domier, C. W.; Luhmann, N. C., Jr.
1998-11-01
Relentless efforts in plasma diagnostics concepts (E. Mazzucato, Rev. Sci. Instrum. 69, 1691 (1998), H. Hase, H. Hartfuss,12th HTPD conference, F-16, June 1998.) and technology (R.P. Hsia et al., Rev. Sci. Instrum. 68, 488 (1997).) R&D enable us to design a system capable of simultaneous 3-D imaging of the temperature and density turbulence spectrum in toroidal devices such as tokamak and stellarator. Measurement of multi-dimensional correlation between Te and ne turbulence is extremely important in understanding the current transport model. In this paper, the details of the concept design such as accessibility, machine parameters, detection system and relevant frequencies will be discussed for a various devices. Special attention will be given to obtain ω and k spectra with sufficient spatial resolution so that the results can be readily compared with remarkable visual results produced by gyro-kinetic (GK) and/or gyro-fluid (GF) simulations.
Ion temperature and toroidal rotation in JET's low torque plasmas
NASA Astrophysics Data System (ADS)
Bernardo, J.; Nave, M. F. F.; Giroud, C.; Reyes Cortes, S.; Bizarro, João P. S.
2016-11-01
This paper reports on the procedure developed as the best method to provide an accurate and reliable estimation of the ion temperature Ti and the toroidal velocity vϕ from Charge-eXchange Recombination Spectroscopy (CXRS) data from intrinsic rotation experiments at the Joint European Torus with the carbon wall. The low impurity content observed in such plasmas, resulting in low active CXRS signal, alongside low Doppler shifts makes the determination of Ti and vϕ particularly difficult. The beam modulation method will be discussed along with the measures taken to increase photon statistics and minimise errors from the absolute calibration and magneto-hydro-dynamics effects that may impact the CXRS passive emission.
Dynamic deformation of strongly nonlinear toroidal rubber elements
NASA Astrophysics Data System (ADS)
Lee, Chien-Wei; Nesterenko, Vitali F.
2013-08-01
Dynamic deformation of rubber toroidal elements (o-rings) was investigated under dynamic loading conditions at strain rates 102 s-1. The forces acting on o-rings were simultaneously monitored using an accelerometer and strain gauges, while global engineering strains were independently determined by a synchronized high speed camera. Dynamic non-linear stress-strain relation was compared with empirical relation obtained from static loading of o-rings. The paper presents first experimental results and analysis of dissipative properties of o-rings during dynamic compression and unloading. The strongly nonlinear force-strain and strain-rate dependent behavior was described using nonlinear viscoelastic relation with only one adjustable parameter.
High beta plasma operation in a toroidal plasma producing device
Clarke, John F.
1978-01-01
A high beta plasma is produced in a plasma producing device of toroidal configuration by ohmic heating and auxiliary heating. The plasma pressure is continuously monitored and used in a control system to program the current in the poloidal field windings. Throughout the heating process, magnetic flux is conserved inside the plasma and the distortion of the flux surfaces drives a current in the plasma. As a consequence, the total current increases and the poloidal field windings are driven with an equal and opposing increasing current. The spatial distribution of the current in the poloidal field windings is determined by the plasma pressure. Plasma equilibrium is maintained thereby, and high temperature, high beta operation results.
The Virtual-casing Principle For 3D Toroidal Systems
Lazerson, Samuel A.
2014-02-24
The capability to calculate the magnetic field due to the plasma currents in a toroidally confined magnetic fusion equilibrium is of manifest relevance to equilibrium reconstruction and stellarator divertor design. Two methodologies arise for calculating such quantities. The first being a volume integral over the plasma current density for a given equilibrium. Such an integral is computationally expensive. The second is a surface integral over a surface current on the equilibrium boundary. This method is computationally desirable as the calculation does not grow as the radial resolution of the volume integral. This surface integral method has come to be known as the "virtual-casing principle". In this paper, a full derivation of this method is presented along with a discussion regarding its optimal application.
Analysis of Recurrent Patterns in Toroidal Magnetic Fields
Tricoche, Xavier; Kruger, Scott E; Breslau, Joshua
2010-01-01
In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the field's topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincare map of the sampled fieldlines in a Poincare section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactive parallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.
Process analyses of ITER Toroidal Field Structure cooling scheme
NASA Astrophysics Data System (ADS)
Maekawa, R.; Takami, S.; Iwamoto, A.; Chang, H. S.; Forgeas, A.; Chalifour, M.; Serio, L.
2014-09-01
Process studies for Toroidal Field Structure (TF ST) system with a dedicated Auxiliary Cold Box (ACB-ST) have been conducted under 15 MA baseline, including plasma disruptions. ACB-ST consists of two heat exchangers immersed in the Liquid Helium (LHe) subcooler, which are placed at the inlet/outlet of a Supercritical Helium (SHe) cold circulator (centrifugal pump). Robustness of ACB-ST is a key to achieve the stability of TF coil operation since it provides the thermal barrier at the interface of the TF Winding Pack (WP) with ST. The paper discusses the control logic for the nominal plasma operating scenario and for Mitigation to regulate the dynamic heat loads on ST. In addition, the operation field of a cold circulator is described in the case of plasma disruptions. The required performance of heat exchangers in the ACB-ST is assessed based on the expected operating conditions.
Analysis of recurrent patterns in toroidal magnetic fields.
Sanderson, Allen R; Chen, Guoning; Tricoche, Xavier; Pugmire, David; Kruger, Scott; Breslau, Joshua
2010-01-01
In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the field's topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactive parallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.
Equilibrium and Stability of Partial Toroidal Plasma Discharges
Oz, E.; Myers, C. E.; Yamada, M.; Ji, H.; Kulsrud, R.; Xie, J.
2011-01-04
The equilibrium and stability of partial toroidal flux ropes are studied in detail in the laboratory, motivated by ubiquitous loop structures on the solar surface. The flux ropes studied here are magnetized arc discharges formed in the Magnetic Reconnection Experiment (MRX). It is found that these loops robustly maintain their equilibrium on time scales much longer than the Alfven time over a wide range of plasma current, guide eld strength, and angle between electrodes, even in the absence of a strapping fi eld. Additionally, the external kink stability of these flux ropes is found to be governed by the Kruskal-Shafranov limit for a flux rope with line-tied boundary conditions at both ends (q > 1).
Modeling the rapid de-swelling of toroidal hydrogels
NASA Astrophysics Data System (ADS)
Nikolov, Svetoslav; Chang, Ya-Wen; Alexeev, Alexander; Fernandez de Las Nieves, Alberto
2015-03-01
The utilization of synthetic hydrogel networks as 3-D cell culture platforms has allowed researchers to more effectively study how epigenetic factors affect cell growth and physiology. As a whole, this has emphasized the biomechanical role of scaffold structures and led to a number of advances in tissue engineering. Our current research focuses on modeling temperature activated shape transformations of toroidal poly(N-isopropylacrylamide) pNIPAM gels. We use dissipative particle dynamics (DPD) to simulate the steady (slow heating rates) and unsteady (fast heating rates) de-swelling behavior of these thermo-sensitive gels. Our simulations show that for slow heating rates the aspect ratio of the tori remains constant during de-swelling. For rapid heating rates we observe buckling instabilities. Our simulations agree with the experimental observations. Financial support by NSF CAREER Award DMR-1255288 is gratefully acknowledged.
Toroid Joining Gun. [thermoplastic welding system using induction heating
NASA Technical Reports Server (NTRS)
Buckley, J. D.; Fox, R. L.; Swaim, R J.
1985-01-01
The Toroid Joining Gun is a low cost, self-contained, portable low powered (100-400 watts) thermoplastic welding system developed at Langley Research Center for joining plastic and composite parts using an induction heating technique. The device developed for use in the fabrication of large space sructures (LSST Program) can be used in any atmosphere or in a vacuum. Components can be joined in situ, whether on earth or on a space platform. The expanded application of this welding gun is in the joining of thermoplastic composites, thermosetting composites, metals, and combinations of these materials. Its low-power requirements, light weight, rapid response, low cost, portability, and effective joining make it a candidate for solving many varied and unique bonding tasks.
Transport scaling in interchange-driven toroidal plasmas
Ricci, Paolo; Rogers, B. N.
2009-06-15
Two-dimensional fluid simulations of a simple magnetized torus are presented, in which the vertical and toroidal components of the magnetic field create helicoidal field lines that terminate on the upper and lower walls of the plasma chamber. The simulations self-consistently evolve the full radial profiles of the electric potential, density, and electron temperature in the presence of three competing effects: the cross-field turbulent transport driven by the interchange instability, parallel losses to the upper and lower walls, and the input of particles and heat by external plasma sources. Considering parameter regimes in which equilibrium ExB shear flow effects are weak, we study the dependence of the plasma profiles--in particular the pressure profile scale length--on the parameters of the system. Analytical scalings are obtained that show remarkable agreement with the simulations.
EMPACT: Electrons Muons Partons with Air Core Toroids
Marx, M.D. )
1990-05-25
The EMPACT experiment utilizes a broad approach to maximize its discovery potential for new phenomena accessible at the SSC. The high resolution detector has a balances emphasis on, and large acceptance for, electrons, muons, jets, and noninteracting particles, and is capable of utilizing the ultimate luminosity of the SSC. The detector emphasizes excellent calorimetry augmented by TRD tracking, and employs an innovative system of superconducting air core toroids for muon measurements. Significant engineering effort has established the feasibility of a baseline detector concept and has addressed the related issues of support facilities, assembly, and detector integration. The design has been tested against the challenges of predicted phenomena, with the expectation that this will optimize the capacity for observing the unexpected. EMPACT's international collaboration has unprecedented support from major aerospace industries who are providing tools and expertise for project design and integration, which will assure that a detector optimized for performance and cost will be available for the first collisions at the new laboratory.
Vortex excitation in a stirred toroidal Bose-Einstein condensate
NASA Astrophysics Data System (ADS)
Yakimenko, A. I.; Isaieva, K. O.; Vilchinskii, S. I.; Ostrovskaya, E. A.
2015-02-01
Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. A 88, 063633 (2013), 10.1103/PhysRevA.88.063633], we investigate the microscopic mechanism for excitation of vortices and formation of a persistent current in an annular BEC stirred by a narrow blue-detuned optical beam. In the framework of a two-dimensional mean-field model, we study the dissipative dynamics of the condensate with parameters that reflect realistic experimental conditions. Vortex-antivortex pairs appear near the center of the stirrer in the bulk of the condensate for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, an outer edge surface mode develops and breaks into the vortices entering the condensate annulus. We determine the conditions for creation of vortex excitations in the stirred toroidal condensate and compare our results with experimental observations.
Evolution of toroidal Alfven eigenmode instability in TFTR
Wong, K.L.; Majeski, R.; Petrov, M.
1996-07-01
The nonlinear behavior of the Toroidal Alfven Eigenmode (TAE) driven unstable by energetic ions in TFTR is studied. The evolution of instabilities can take on several scenarios: a single mode or several modes can be driven unstable at the same time, the spectrum can be steady or pulsating and there can be negligible or anomalous loss associated with the instability. This paper presents a comparison between experimental results and recently developed nonlinear theory. The authors find many features observed in experiment are compatible with the consequences of the nonlinear theory. Examples include the structure of the saturated pulse that emerges from the onset of instability of a single mode and the decrease but persistence of TAE signals when the applied rf power is reduced or shut off.
Fluid simulations of toroidal ion temperature gradient turbulence
Sandberg, I.; Isliker, H.; Pavlenko, V.P.; Hizanidis, K.; Vlahos, L.
2006-02-15
The evolution of the toroidal ion temperature gradient mode instability is numerically studied by using the equations based on the standard reactive fluid model. The long-term dynamics of the instability are investigated using random-phase, small-amplitude fluctuations for initial conditions. The main events during the evolution of the instability that lead to the formation of large-scale coherent structures are described and the role of the dominant nonlinearities is clarified. The polarization drift nonlinearity leads to the inverse energy cascade while the convective ion heat nonlinearity is responsible for the saturation of the instability. Finally, the sensitivity of the saturated state to the initial plasma conditions is examined.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Freezing in confined geometries
NASA Technical Reports Server (NTRS)
Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.
1992-01-01
Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS_{3}/CFT_{2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS_{3} whose kinematic space is two-dimensional de Sitter space.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less
Emergent Complex Network Geometry
NASA Astrophysics Data System (ADS)
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-05-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
Quasars: a supermassive rotating toroidal black hole interpretation
NASA Astrophysics Data System (ADS)
Spivey, R. J.
2000-08-01
A supermassive rotating toroidal black hole (TBH) is proposed as the fundamental structure of quasars and other jet-producing active galactic nuclei. Rotating protogalaxies gather matter from the central gaseous region leading to the birth of massive toroidal stars, the internal nuclear reactions of which proceed very rapidly. Once the nuclear fuel is spent, gravitational collapse produces a slender ring-shaped TBH remnant. Transitory electron and neutron degeneracy stabilized collapse phases, although possible, are unlikely owing to the large masses involved thus these events are typically the first supernovae of the host galaxies. Given time, the TBH mass increases through continued accretion by several orders of magnitude, the event horizon swells whilst the central aperture shrinks. The difference in angular velocities between the accreting matter and the TBH induces a magnetic field that is strongest in the region of the central aperture and innermost ergoregion. Owing to the presence of negative energy states when such a gravitational vortex is immersed in an electromagnetic field, circumstances are near ideal for energy extraction via non-thermal radiation including the Penrose process and superradiant scattering. This establishes a self-sustaining mechanism whereby the transport of angular momentum away from the quasar by relativistic bi-directional jets reinforces both the modulating magnetic field and the TBH/accretion disc angular velocity differential. Continued mass-capture by the TBH results in contraction of the central aperture until the TBH topology transitions to being spheroidal, extinguishing quasar behaviour. Similar mechanisms may be operating in microquasars, supernovae and sources of repeating gamma-ray bursts when neutron density or black hole tori arise. Long-term TBH stability seems to require either a negative cosmological constant, a non-stationary space-time resulting from the presence of accreting matter or the intervention of quantum
Transport, Equilibrium, and Stability of a Toroidal Edge Plasma
NASA Astrophysics Data System (ADS)
McCarthy, Daniel Raymund
The stability and transport of the drift resistive ballooning mode (DRBM) and its impact on the dynamics of a toroidal edge plasma is studied. The linear stability of the DRBM is calculated analytically and numerically, and is found to be unstable over a broad range of mode numbers. The nonlinear dynamics of the mode were studied using a fully nonlinear, three dimensional finite difference code. It was found that the saturated turbulent transport was anomalously large and exhibited a large ballooning -like poloidal asymmetry. The growth and saturation of this mode occurred on the time scale t_ {B} = (c_{s}/sqrt{RL _{n}})^{-1}.. Nonlinear two dimensional axisymmetric toroidal simulations of a tokamak edge and scrape off layer were performed to study the effect of this transport on the edge dynamics. Large parallel flows of order the local sound speed c_{s} were generated on the longer time scale t_{s } = (c_{s}/qR)^ {-1}. The stability of this 'equilibrium' depends upon the parameter alpha equiv rho_{s}qR/aL_{r}. For alpha << 1, the edge was unstable to the Stringer spin up instability. For weak magnetic pumping (H-mode), a poloidal rotation of order the poloidal sound speed ac_{s }/qR was generated in the electron diamagnetic drift direction. For strong pumping (L-mode), the rotation opposed the ion diamagnetic drift. The impact of particle sources at various poloidal locations was also studied. For alpha > 1 the edge was unstable to the parallel velocity shear instability. The turbulence gave order unity fluctuation levels and was localized inside the last closed flux surface and on the inner side of the torus.
Design and installation of a ferromagnetic wall in tokamak geometry.
Hughes, P E; Levesque, J P; Rivera, N; Mauel, M E; Navratil, G A
2015-10-01
Low-activation ferritic steels are leading material candidates for use in next-generation fusion development experiments such as a prospective component test facility and DEMO power reactor. Understanding the interaction of plasmas with a ferromagnetic wall will provide crucial physics for these facilities. In order to study ferromagnetic effects in toroidal geometry, a ferritic wall upgrade was designed and installed in the High Beta Tokamak-Extended Pulse (HBT-EP). Several material options were investigated based on conductivity, magnetic permeability, vacuum compatibility, and other criteria, and the material of choice (high-cobalt steel) is characterized. Installation was accomplished quickly, with minimal impact on existing diagnostics and overall machine performance, and initial results demonstrate the effects of the ferritic wall on plasma stability.
Design and installation of a ferromagnetic wall in tokamak geometry
Hughes, P. E. Levesque, J. P.; Rivera, N.; Mauel, M. E.; Navratil, G. A.
2015-10-15
Low-activation ferritic steels are leading material candidates for use in next-generation fusion development experiments such as a prospective component test facility and DEMO power reactor. Understanding the interaction of plasmas with a ferromagnetic wall will provide crucial physics for these facilities. In order to study ferromagnetic effects in toroidal geometry, a ferritic wall upgrade was designed and installed in the High Beta Tokamak–Extended Pulse (HBT-EP). Several material options were investigated based on conductivity, magnetic permeability, vacuum compatibility, and other criteria, and the material of choice (high-cobalt steel) is characterized. Installation was accomplished quickly, with minimal impact on existing diagnostics and overall machine performance, and initial results demonstrate the effects of the ferritic wall on plasma stability.
Alternative cosmology from cusp geometries
NASA Astrophysics Data System (ADS)
Rosa, Reinaldo; Herbin Stalder Díaz, Diego
We study an alternative geometrical approach on the problem of classical cosmological singularity. It is based on a generalized function f(x,y)=x(2+y^2=(1-z)z^n) which consists of a cusped projected coupled isosurface. Such a projected geometry is computed and analized into the context of Friedmann singularity-free cosmology where a pre-big bang scenario is considered. Assuming that the mechanism of cusp formation is described by non-linear oscillations of a pre- big bang extended very high energy density field (>3x10^{94} kg/m^3$), we show that the action under the gravitational field follows a tautochrone of revolution, understood here as the primary projected geometry that alternatively replaces the Friedmann singularity in the standard big bang theory. As shown here this new approach allows us to interpret the nature of both matter and dark energy from first geometric principles [1]. [1] Rosa et al. DOI: 10.1063/1.4756991
Weyl gravity and Cartan geometry
NASA Astrophysics Data System (ADS)
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Tobias, B.; Chen, M.; Classen, I. G. J.; Domier, C. W.; Fitzpatrick, R.; Grierson, B. A.; Luhmann, N. C.; Muscatello, C. M.; Okabayashi, M.; Olofsson, K. E. J.; et al
2016-04-15
The electromagnetic coupling of helical modes, including those having different toroidal mode numbers, modifies the distribution of toroidal angular momentum in tokamak discharges. This can have deleterious effects on other transport channels as well as on magnetohydrodynamic (MHD) stability and disruptivity. At low levels of externally injected momentum, the coupling of core-localized modes initiates a chain of events, whereby flattening of the core rotation profile inside successive rational surfaces leads to the onset of a large m/n = 2/1 tearing mode and locked-mode disruption. Furthermore, with increased torque from neutral beam injection, neoclassical tearing modes in the core may phase-lockmore » to each other without locking to external fields or structures that are stationary in the laboratory frame. The dynamic processes observed in these cases are in general agreement with theory, and detailed diagnosis allows for momentum transport analysis to be performed, revealing a significant torque density that peaks near the 2/1 rational surface. However, as the coupled rational surfaces are brought closer together by reducing q95, additional momentum transport in excess of that required to attain a phase-locked state is sometimes observed. Rather than maintaining zero differential rotation (as is predicted to be dynamically stable by single-fluid, resistive MHD theory), these discharges develop hollow toroidal plasma fluid rotation profiles with reversed plasma flow shear in the region between the m/n = 3/2 and 2/1 islands. Additional forces expressed in this state are not readily accounted for, and therefore, analysis of these data highlights the impact of mode coupling on torque balance and the challenges associated with predicting the rotation dynamics of a fusion reactor-a key issue for ITER. Published by AIP Publishing.« less
NASA Astrophysics Data System (ADS)
Tobias, B.; Chen, M.; Classen, I. G. J.; Domier, C. W.; Fitzpatrick, R.; Grierson, B. A.; Luhmann, N. C.; Muscatello, C. M.; Okabayashi, M.; Olofsson, K. E. J.; Paz-Soldan, C.
2016-05-01
The electromagnetic coupling of helical modes, even those having different toroidal mode numbers, modifies the distribution of toroidal angular momentum in tokamak discharges. This can have deleterious effects on other transport channels as well as on magnetohydrodynamic (MHD) stability and disruptivity. At low levels of externally injected momentum, the coupling of core-localized modes initiates a chain of events, whereby flattening of the core rotation profile inside successive rational surfaces leads to the onset of a large m/n = 2/1 tearing mode and locked-mode disruption. With increased torque from neutral beam injection, neoclassical tearing modes in the core may phase-lock to each other without locking to external fields or structures that are stationary in the laboratory frame. The dynamic processes observed in these cases are in general agreement with theory, and detailed diagnosis allows for momentum transport analysis to be performed, revealing a significant torque density that peaks near the 2/1 rational surface. However, as the coupled rational surfaces are brought closer together by reducing q95, additional momentum transport in excess of that required to attain a phase-locked state is sometimes observed. Rather than maintaining zero differential rotation (as is predicted to be dynamically stable by single-fluid, resistive MHD theory), these discharges develop hollow toroidal plasma fluid rotation profiles with reversed plasma flow shear in the region between the m/n = 3/2 and 2/1 islands. The additional forces expressed in this state are not readily accounted for, and therefore, analysis of these data highlights the impact of mode coupling on torque balance and the challenges associated with predicting the rotation dynamics of a fusion reactor—a key issue for ITER.