Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Nonlinear gyrokinetic equations for tokamak microturbulence
Hahm, T.S.
1988-05-01
A nonlinear electrostatic gyrokinetic Vlasov equation, as well as Poisson equation, has been derived in a form suitable for particle simulation studies of tokamak microturbulence and associated anomalous transport. This work differs from the existing nonlinear gyrokinetic theories in toroidal geometry, since the present equations conserve energy while retaining the crucial linear and nonlinear polarization physics. In the derivation, the action-variational Lie perturbation method is utilized in order to preserve the Hamiltonian structure of the original Vlasov-Poisson system. Emphasis is placed on the dominant physics of the collective fluctuations in toroidal geometry, rather than on details of particle orbits. 13 refs.
NASA Astrophysics Data System (ADS)
Zarzoso, D.; Migliano, P.; Grandgirard, V.; Latu, G.; Passeron, C.
2017-07-01
The modification of radial structure, frequency and intensity of turbulent transport in the presence of energetic-particle-driven geodesic acoustic modes (EGAMs) is analysed by means of full-f global gyro-kinetic simulations using Gysela code. It is observed that turbulence leads to a smoother evolution of the distribution function, less pronounced flattening of the distribution function in velocity space during the nonlinear saturation of EGAMs and reduced saturation level of electrostatic potential with respect to the case where turbulence is artificially suppressed. It is shown that EGAMs are excited and impact turbulent transport in the region where the EP is localised, fading away the staircase structure observed in the absence of energetic particles. For the first time, evidences of a three-wave coupling between turbulent modes and EGAMs in gyro-kinetic simulations are provided by means of bispectral analysis using wavelet transform in time. The coupling evolves from the standard self-regulation of turbulence by the zero-frequency zonal component to a steady-state regime where turbulence dynamics is dominated by the zonal component oscillating at the EGAM frequency.
Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.
2009-07-15
In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino et al., Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino et al., Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker et al., Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Koenies et al., Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino et al., Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.
NASA Astrophysics Data System (ADS)
Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.
2009-07-01
In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino et al., Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino et al., Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker et al., Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Könies et al., Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino et al., Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.
NASA Astrophysics Data System (ADS)
Ernst, Darin
2008-11-01
#1#23pt1.5pt 1.5pt#1###2˜ > > Trapped electron mode (TEM) turbulence exhibits rich zonal flow dynamics, which depends strongly on plasma parameters. The role zonal flows in TEM turbulence is explored through a series of linear and nonlinear gyrokinetic simulations using both PIC (the GEM code) and continuum (the GS2 code) methods. A new nonlinear upshift [1,2] in the TEM critical density gradient (associated with zonal flow dominated states near threshold) increases strongly with collisionality, for density gradient driven cases. In contrast, zonal flows have little effect on TEM turbulence with strong electron temperature gradients and Te= 3Ti [3]. This apparent contradiction has been resolved in parameteric studies showing that zonal flows are weaker as the electron temperature gradient and Te/Ti increase [4]. The parametric variation of zonal flows is consistent with linear stability properties and nonlinear instability theory. A new stability diagram based on 2,000 GS2 simulations clarifies the roles of resonant and non-resonant TEM, ``ubiquitous,'' and electron temperature gradient (ETG) driven modes. Larger electron temperature gradients couple TEM and ETG modes, resulting in short wavelengths kαρs>1. Accordingly, a sudden onset of nonlinear fine scale structure is seen for ηe≡dTe/dne> 1. For short wavelengths, the ions are more adiabatic, the zonal flow potential <φ>˜
Electromagnetic nonlinear gyrokinetics with polarization drift
NASA Astrophysics Data System (ADS)
Duthoit, F.-X.; Hahm, T. S.; Wang, Lu
2014-08-01
A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.
Electromagnetic nonlinear gyrokinetics with polarization drift
Duthoit, F.-X.; Hahm, T. S.; Wang, Lu
2014-08-15
A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.
NASA Astrophysics Data System (ADS)
Kleiber, R.; Hatzky, R.; Könies, A.; Mishchenko, A.; Sonnendrücker, E.
2016-03-01
A new algorithm for electromagnetic gyrokinetic simulations, the so called "pullback transformation scheme" proposed by Mishchenko et al. [Phys. Plasmas 21, 092110 (2014)] is motivated as an explicit time integrator reset after each full timestep and investigated in detail. Using a numerical dispersion relation valid in slab geometry, it is shown that the linear properties of the scheme are comparable to those of an implicit v∥ -scheme. A nonlinear extension of the mixed variable formulation, derived consistently from a field Lagrangian, is proposed. The scheme shows excellent numerical properties with a low statistical noise level and a large time step especially for MHD modes. The example of a nonlinear slab tearing mode simulation is used to illustrate the properties of different formulations of the physical model equations.
A fully nonlinear characteristic method for gyrokinetic simulation
Parker, S.E.; Lee, W.W.
1992-07-01
We present a new scheme which evolves the perturbed part of the distribution function along a set of characteristics that solves the fully nonlinear gyrokinetic equations. This nonlinear characteristic method for particle simulation is an extension of the partially linear weighting scheme, and may be considered an improvement of existing {delta} f methods. Some of the features of this new method are: the ability to keep all of the nonlinearities, particularly those associated with parallel acceleration; the loading of the physical equilibrium distribution function f{sub o} (e.g., a Maxwellian), with or without the multiple spatial scale approximation; the use of a single of trajectories for the particles; and also, the retention of the conservation properties of the original gyrokinetic system in the numerically converged limit. Therefore, one can take advantage of the low noise property of the weighting scheme together with the quiet start techniques to simulate weak instabilities, with a substantially reduced number of particles than required for a conventional simulation. The new method is used to study a one dimensional drift wave model which isolates the parallel velocity nonlinearity. A mode coupling calculation of the saturation mechanism is given, which is in good agreement with the simulation results and predicts a considerably lower saturation level then the estimate of Sagdeev and Galeev. Finally, we extend the nonlinear characteristic method to the electromagnetic gyrokinetic equations in general geometry.
Nonlinear gyrokinetic theory for finite-BETA plasmas
Hahm, T.S.; Lee, W.W.; Brizard, A.
1988-02-01
A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.
Nonlinear canonical gyrokinetic Vlasov equation and computation of the gyrocenter motion in tokamaks
Xu Yingfeng; Wang Shaojie
2013-01-15
The nonlinear canonical gyrokinetic Vlasov equation is obtained from the nonlinear noncanonical gyrokinetic theory using the property of the coordinate transform. In the linear approximation, it exactly recovers the previous linear canonical gyrokinetic equations derived by the Lie-transform perturbation method. The computation of the test particle gyrocenter motion in tokamaks with a large magnetic perturbation is presented and discussed. The numerical results indicate that the second-order gyrocenter Hamiltonian is important for the gyrocenter motion of the trapped electron in tokamaks with a large magnetic perturbation.
Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas
NASA Astrophysics Data System (ADS)
Jenko, F.; Dorland, W.
2001-12-01
One of the central physics issues currently targeted by nonlinear gyrokinetic simulations is the role of finite-β effects. The latter change the MHD equilibrium, introduce new dynamical space and time scales, alter and enlarge the zoo of electrostatic microinstabilities and saturation mechanisms, and lead to turbulent transport along fluctuating magnetic field lines. It is shown that the electromagnetic effects on primarily electrostatic microinstabilities are generally weakly or moderately stabilizing. However, the saturation of these modes and hence the determination of the transport level in the quasi-stationary turbulent state can be dominated by nonlinear electromagnetic effects and yield surprising results. Despite this, the induced transport is generally electrostatic in nature well below the ideal ballooning limit.
Gyro-water-bag approach in nonlinear gyrokinetic turbulence
Besse, Nicolas Bertrand, Pierre
2009-06-20
Turbulent transport is a key issue for controlled thermonuclear fusion based on magnetic confinement. The thermal confinement of a magnetized fusion plasma is essentially determined by the turbulent heat conduction across the equilibrium magnetic field. It has long been acknowledged, that the prediction of turbulent transport requires to solve Vlasov-type gyrokinetic equations. Although the kinetic description is more accurate than fluid models (MHD, gyro-fluid), because among other things it takes into account nonlinear resonant wave-particle interaction, kinetic modeling has the drawback of a huge computer resource request. An unifying approach consists in considering water-bag-like weak solutions of kinetic collisionless equations, which allow to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations, while keeping its kinetic behaviour. As a result this exact reduction induces a multi-fluid numerical resolution cost. Therefore finding water-bag-like weak solutions of the gyrokinetic equations leads to the birth of the gyro-water-bag model. This model is suitable for studying linear and nonlinear low-frequency micro-instabilities and the associated anomalous transport in magnetically-confined plasmas. The present paper addresses the derivation of the nonlinear gyro-water-bag model, its quasilinear approximation and their numerical approximations by Runge-Kutta semi-Lagrangian methods and Runge-Kutta discontinuous Galerkin schemes respectively.
Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence
Hahm, T. S.; Wang, Lu; Madsen, J.
2008-08-01
An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E Χ B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Our generalized ordering takes ρ_{i}<< ρ_{θ¡} ~ L_{E} ~ L_{p} << R (here ρ_{i} is the thermal ion Larmor radius and ρ_{θ¡} = B/B_{θ}] ρ_{i}), as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. We take κ perpendicular to ρ_{i} ~ 1 for generality, and keep the relative fluctuation amplitudes eδφ /Τ_{i} ~ δΒ / Β up to the second order. Extending the electrostatic theory in the presence of high E Χ B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation.
Gyrokinetic simulations of particle transport in pellet fuelled JET discharges
NASA Astrophysics Data System (ADS)
Tegnered, D.; Oberparleiter, M.; Nordman, H.; Strand, P.; Garzotti, L.; Lupelli, I.; Roach, C. M.; Romanelli, M.; Valovič, M.; Contributors, JET
2017-10-01
Pellet injection is a likely fuelling method of reactor grade plasmas. When the pellet ablates, it will transiently perturb the density and temperature profiles of the plasma. This will in turn change dimensionless parameters such as a/{L}n,a/{L}T and plasma β. The microstability properties of the plasma then changes which influences the transport of heat and particles. In this paper, gyrokinetic simulations of a JET L-mode pellet fuelled discharge are performed. The ion temperature gradient/trapped electron mode turbulence is compared at the time point when the effect from the pellet is the most pronounced with a hollow density profile and when the profiles have relaxed again. Linear and nonlinear simulations are performed using the gyrokinetic code GENE including electromagnetic effects and collisions in a realistic geometry in local mode. Furthermore, global nonlinear simulations are performed in order to assess any nonlocal effects. It is found that the positive density gradient has a stabilizing effect that is partly counteracted by the increased temperature gradient in the this region. The effective diffusion coefficients are reduced in the positive density region region compared to the intra pellet time point. No major effect on the turbulent transport due to nonlocal effects are observed.
Gyrokinetic particle simulation of neoclassical transport
Lin, Z.; Tang, W.M.; Lee, W.W.
1995-08-01
A time varying weighting ({delta}{ital f} ) scheme for gyrokinetic particle simulation is applied to a steady-state, multispecies simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated that like-particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion--electron plasma. An important physics feature of the present scheme is the introduction of toroidal flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient-driven electron particle flux and the bootstrap current while reducing temperature gradient-driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examined by taking into account finite banana width effects. In general, in the present work a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes is demonstrated. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Second order gyrokinetic theory for particle-in-cell codes
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-15
The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell–Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell–Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell–Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.
Second order gyrokinetic theory for particle-in-cell codes
NASA Astrophysics Data System (ADS)
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-01
The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell-Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell-Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.
Gyrokinetic particle simulation of beta-induced Alfven eigenmode
Zhang, H. S.; Lin, Z.; Holod, I.; Xiao, Y.; Wang, X.; Zhang, W. L.
2010-11-15
The beta-induced Alfven eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.
Toroidal Alfvén eigenmodes with nonlinear gyrokinetic and fluid hybrid models
NASA Astrophysics Data System (ADS)
Cole, M. D. J.; Biancalani, A.; Bottino, A.; Kleiber, R.; Könies, A.; Mishchenko, A.
2017-02-01
Alfvén eigenmodes may be important in driving fast particle transport in magnetic confinement fusion devices, with potentially deleterious results. To explain and predict this behaviour, numerical simulations are necessary. In order to predict transport, modes must be simulated through to their nonlinear saturated state. In this work, the first simulations of non-linear wave-particle interaction between an energetic particle population and a Toroidal Alfvén Eigenmode are performed in which fluctuations responding self-consistently to modification of the fast particle profile are calculated with gyrokinetic treatment of all plasma species. Results from two such gyrokinetic codes are compared with new results from non-perturbative and perturbative fluid-gyrokinetic hybrid codes. There is a power-law relationship between the saturated magnetic perturbation amplitude, δB/B0, and the linear mode growth rate, γL. All models show a transition from a higher to a lower exponent regime with increasing γL. Measured values of the higher exponent from different codes fall in a range between 1.45 and 1.79, while the lower exponent falls in a range between 0.47 and 0.79. There is a consistent difference of 1.0 between the higher and lower exponents independent of the model. The absolute level of saturated δB/B0 is determined by the damping rate. In the fluid-gyrokinetic hybrid codes, an ad-hoc damping is applied, while in the gyrokinetic case the measured damping is consistent with the estimated rate of physical electron Landau damping.
Full f gyrokinetic method for particle simulation of tokamak transport
Heikkinen, J.A. Janhunen, S.J.; Kiviniemi, T.P.; Ogando, F.
2008-05-10
A gyrokinetic particle-in-cell approach with direct implicit construction of the coefficient matrix of the Poisson equation from ion polarization and electron parallel nonlinearity is described and applied in global electrostatic toroidal plasma transport simulations. The method is applicable for calculation of the evolution of particle distribution function f including as special cases strong plasma pressure profile evolution by transport and formation of neoclassical flows. This is made feasible by full f formulation and by recording the charge density changes due to the ion polarization drift and electron acceleration along the local magnetic field while particles are advanced. The code has been validated against the linear predictions of the unstable ion temperature gradient mode growth rates and frequencies. Convergence and saturation in both turbulent and neoclassical limit of the ion heat conductivity is obtained with numerical noise well suppressed by a sufficiently large number of simulation particles. A first global full f validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. At high Mach number (M{sub p}{approx}1) of the poloidal flow, the radial electric field is significantly enhanced over the standard neoclassical prediction. The neoclassical radial electric field together with the related GAM oscillations is found to regulate the turbulent heat and particle diffusion levels particularly strongly in a large aspect ratio tokamak at low plasma current.
Gyrokinetic particle simulation of a field reversed configuration
Fulton, D. P. Lau, C. K.; Holod, I.; Lin, Z.; Dettrick, S.
2016-01-15
Gyrokinetic particle simulation of the field-reversed configuration (FRC) has been developed using the gyrokinetic toroidal code (GTC). The magnetohydrodynamic equilibrium is mapped from cylindrical coordinates to Boozer coordinates for the FRC core and scrape-off layer (SOL), respectively. A field-aligned mesh is constructed for solving self-consistent electric fields using a semi-spectral solver in a partial torus FRC geometry. This new simulation capability has been successfully verified and driftwave instability in the FRC has been studied using the gyrokinetic simulation for the first time. Initial GTC simulations find that in the FRC core, the ion-scale driftwave is stabilized by the large ion gyroradius. In the SOL, the driftwave is unstable on both ion and electron scales.
Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra
NASA Astrophysics Data System (ADS)
Hatch, D. R.; Jenko, F.; Bañón Navarro, A.; Bratanov, V.; Terry, P. W.; Pueschel, M. J.
2016-07-01
A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.
Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra
Hatch, D. R.; Jenko, F.; Navarro, A. Banon; ...
2016-07-26
A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest inmore » the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.« less
Gyrokinetic δ particle simulation of trapped electron mode driven turbulence
NASA Astrophysics Data System (ADS)
Lang, Jianying
2007-11-01
Turbulent transport driven by collisionless trapped electron modes (CTEM) is systematically studied using gyrokinetic delta-f particle-in-cell simulation. Scaling with local plasma parameters, including density gradient, electron temperature gradient, magnetic shear, temperature ratio and aspect ratio, is investigated. Simulation results are compared with previous simulations and theoretical predictions. Nonlinearly the transport level increases with increasing magnetic shear. We explain the nonlinear magnetic shear scaling by differences in the radial correlation lengths caused by toroidal coupling. The turbulence is more radially elongated at higher magnetic shear compared with low magnetic shear. We show that the suppression effect of zonal flow on CTEM transport depends on both the electron temperature gradient and the electron to ion temperature ratio. This helps explain the previous contradictory conclusions on the importance of zonal flows in different parameter regimes.ootnotetextT. Dannert, F. Jenko, Phys. Plasmas 12, 072309 (2005); D. Ernst, et al., Phys. Plasmas 11, 2637 (2004). Zonal flow suppression is consistent with the rate of EXB shearing from the ambient turbulence as well as the radial broadening of the spectra. Strong geodesic acoustic modes (GAMs) are generated along with zonal flows and the frequency of the GAMs agrees well with kinetic theory.ootnotetextT. Watari, et al., Phys. Plasmas 13, 062504 (2006). We further explore the nonlinear saturation mechanism when the zonal flows are not important. We find that when only a single toroidal mode (and its conjugate) is kept, reasonable nonlinear saturation is obtained. Investigating a range of n, modes with larger mode number n saturate at a higher level relative to lower n modes, indicating a turbulent inverse cascade process.
NASA Astrophysics Data System (ADS)
White, A. E.; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G.; Mikkelsen, D. R.; Edlund, E. M.; Kung, C.; Holland, C.; Candy, J.; Petty, C. C.; Reinke, M. L.; Theiler, C.
2015-05-01
For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.
White, A. E. Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G.; Mikkelsen, D. R.; Edlund, E. M.; Kung, C.; Holland, C.; Candy, J.; Petty, C. C.; Reinke, M. L.; and others
2015-05-15
For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.
Advanced methods in global gyrokinetic full f particle simulation of tokamak transport
Ogando, F.; Heikkinen, J. A.; Henriksson, S.; Janhunen, S. J.; Kiviniemi, T. P.; Leerink, S.
2006-11-30
A new full f nonlinear gyrokinetic simulation code, named ELMFIRE, has been developed for simulating transport phenomena in tokamak plasmas. The code is based on a gyrokinetic particle-in-cell algorithm, which can consider electrons and ions jointly or separately, as well as arbitrary impurities. The implicit treatment of the ion polarization drift and the use of full f methods allow for simulations of strongly perturbed plasmas including wide orbit effects, steep gradients and rapid dynamic changes. This article presents in more detail the algorithms incorporated into ELMFIRE, as well as benchmarking comparisons to both neoclassical theory and other codes.Code ELMFIRE calculates plasma dynamics by following the evolution of a number of sample particles. Because of using an stochastic algorithm its results are influenced by statistical noise. The effect of noise on relevant magnitudes is analyzed.Turbulence spectra of FT-2 plasma has been calculated with ELMFIRE, obtaining results consistent with experimental data.
John A. Krommes
2007-10-09
The present state of the theory of fluctuations in gyrokinetic GK plasmas and especially its application to sampling noise in GK particle-in-cell PIC simulations is reviewed. Topics addressed include the Δf method, the fluctuation-dissipation theorem for both classical and GK many-body plasmas, the Klimontovich formalism, sampling noise in PIC simulations, statistical closure for partial differential equations, the theoretical foundations of spectral balance in the presence of arbitrary noise sources, and the derivation of Kadomtsev-type equations from the general formalism.
Comparisons of Kinetic Electron Models in Gyrokinetic Particle Simulations
NASA Astrophysics Data System (ADS)
Wang, W. X.; Lin, Z.; Lewandowski, J. L. V.; Lee, W. W.
2001-10-01
Comparisons of the hybrid [1] and split-weight [2,3] schemes for the electron dynamics in gyrokinetic particle simulations has been carried out. The emphasis here is to understand the regions of validity for these schemes as well as their numerical properties with regard to noise, time step and accuracy. The numerical issues for the implementation of these schemes in our 3D global gyrokinetic particle code (GTC) in general geometry [4] will also be discussed. Work supported by US DoE. [1] Z. Lin and L. Chen, Phys. Plasmas <8>, 1447 (2001). [2] I. Manuilskiy and W. W. Lee, Phys. Plasmas <7>, 1381 (2000). [3] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm and Z. Lin, Phys. Plasmas (to appear). [4] Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang and R. White, Science <281>, 1835 (1998).
The nonlinear gyro-kinetic flux tube code GKW
NASA Astrophysics Data System (ADS)
Peeters, A. G.; Camenen, Y.; Casson, F. J.; Hornsby, W. A.; Snodin, A. P.; Strintzi, D.; Szepesi, G.
2009-12-01
A new nonlinear gyro-kinetic flux tube code (GKW) for the simulation of micro instabilities and turbulence in magnetic confinement plasmas is presented in this paper. The code incorporates all physics effects that can be expected from a state of the art gyro-kinetic simulation code in the local limit: kinetic electrons, electromagnetic effects, collisions, full general geometry with a coupling to a MHD equilibrium code, and E×B shearing. In addition the physics of plasma rotation has been implemented through a formulation of the gyro-kinetic equation in the co-moving system. The gyro-kinetic model is five-dimensional and requires a massive parallel approach. GKW has been parallelised using MPI and scales well up to 8192+ cores. The paper presents the set of equations solved, the numerical methods, the code structure, and the essential benchmarks. Program summaryProgram title: GKW Catalogue identifier: AEES_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEES_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 29 998 No. of bytes in distributed program, including test data, etc.: 206 943 Distribution format: tar.gz Programming language: Fortran 95 Computer: Not computer specific Operating system: Any for which a Fortran 95 compiler is available Has the code been vectorised or parallelised?: Yes. The program can efficiently utilise 8192+ processors, depending on problem and available computer. 128 processors is reasonable for a typical nonlinear kinetic run on the latest x86-64 machines. RAM:˜128 MB-1 GB for a linear run; 25 GB for typical nonlinear kinetic run (30 million grid points) Classification: 19.8, 19.9, 19.11 External routines: None required, although the functionality of the program is somewhat limited without a MPI implementation (preferably MPI-2) and the FFTW3 library. Nature of problem: Five
Gyrokinetic Particle Simulation of Microturbulence in Transport Time Scale
NASA Astrophysics Data System (ADS)
Lee, W. W.
2003-10-01
Recent investigations on Alfven waves in gyrokinetic plasmas and their relationship with those in the MHD theory have enabled us to extend the gyrokinetic particle simulation techniques into the kinetic-MHD regime when the finite-Larmor radius effects are important and the time step restrictions imposed by compressional Alfven waves are not desirable.[1,2] Some of the numerical schemes have already been devised based on their thermodynamic properties.[1,2] Here, we propose to use gyrokinetic particle simulation to study microturbulence in transport time scale. The procedures involve the use of finite-β microturbulence simulation as well as the use of transport coefficients in the steady state for predicting density,temperature and parallel current profile changes, along with the use of perpendicular current information for the establishment of equilibrium magnetic structure. Details will be given. [1] W. W. Lee and H. Qin, Phys. Plasmas, to appear (August 2003). [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Phys. Plasmas 8, 4435 (2001).
Nonlinear theory of drift-cyclotron kinetics and the possible breakdown of gyro-kinetics
Waltz, R. E.; Deng Zhao
2013-01-15
A nonlinear theory of drift-cyclotron kinetics (termed cyclo-kinetics here) is formulated to test the breakdown of the gyro-kinetic approximations. Six dimensional cyclo-kinetics can be regarded as an extension of five dimensional gyro-kinetics to include high-frequency cyclotron waves, which can interrupt the low-frequency gyro-averaging in the (sixth velocity grid) gyro-phase angle. Nonlinear cyclo-kinetics has no limit on the amplitude of the perturbations. Formally, there is no gyro-averaging when all cyclotron (gyro-phase angle) harmonics of the perturbed distribution function (delta-f) are retained. Retaining only the (low frequency) zeroth cyclotron harmonic in cyclo-kinetics recovers both linear and nonlinear gyro-kinetics. Simple recipes are given for converting continuum nonlinear delta-f gyro-kinetic transport simulation codes to cyclo-kinetics codes by retaining (at least some) higher cyclotron harmonics.
Center for Gyrokinetic Particle Simulations of Turbulent Transport. Final report
Parker, Scott; Chen, Yang
2011-05-02
This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of
Optimized Loading for Particle-in-cell Gyrokinetic Simulations
J.L.V. Lewandowski
2004-05-13
The problem of particle loading in particle-in-cell gyrokinetic simulations is addressed using a quadratic optimization algorithm. Optimized loading in configuration space dramatically reduces the short wavelength modes in the electrostatic potential that are partly responsible for the non-conservation of total energy; further, the long wavelength modes are resolved with good accuracy. As a result, the conservation of energy for the optimized loading is much better that the conservation of energy for the random loading. The method is valid for any geometry and can be coupled to optimization algorithms in velocity space.
Effects of Plasma Shaping on Nonlinear Gyrokinetic Turbulence
E. A. Belli; Hammett, G. W.; Dorland, W.
2008-08-01
The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B.N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus (JET) [P.H. Rebut and B.E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on both the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of χ ~ κ^{-1.5} or κ^{-2.0}, depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows.
Fluid electron, gyrokinetic ion simulations of linear internal kink and energetic particle modes
NASA Astrophysics Data System (ADS)
Cole, Michael; Mishchenko, Alexey; Könies, Axel; Kleiber, Ralf; Borchardt, Matthias
2014-07-01
The internal kink mode is an important plasma instability responsible for a broad class of undesirable phenomena in tokamaks, including the sawtooth cycle and fishbones. To predict and discover ways to mitigate this behaviour in current and future devices, numerical simulations are necessary. The internal kink mode can be modelled by reduced magnetohydrodynamics (MHD). Fishbone modes are an inherently kinetic and non-linear phenomenon based on the n = 1 Energetic Particle Mode (EPM), and have been studied using hybrid codes that combine a reduced MHD bulk plasma model with a kinetic treatment of fast ions. In this work, linear simulations are presented using a hybrid model which couples a fluid treatment of electrons with a gyrokinetic treatment of both bulk and fast ions. Studies of the internal kink mode in geometry relevant to large tokamak experiments are presented and the effect of gyrokinetic ions is considered. Interaction of the kink with gyrokinetic fast ions is also considered, including the destabilisation of the linear n = 1 EPM underlying the fishbone.
Fluid electron, gyrokinetic ion simulations of linear internal kink and energetic particle modes
Cole, Michael Mishchenko, Alexey; Könies, Axel; Kleiber, Ralf; Borchardt, Matthias
2014-07-15
The internal kink mode is an important plasma instability responsible for a broad class of undesirable phenomena in tokamaks, including the sawtooth cycle and fishbones. To predict and discover ways to mitigate this behaviour in current and future devices, numerical simulations are necessary. The internal kink mode can be modelled by reduced magnetohydrodynamics (MHD). Fishbone modes are an inherently kinetic and non-linear phenomenon based on the n = 1 Energetic Particle Mode (EPM), and have been studied using hybrid codes that combine a reduced MHD bulk plasma model with a kinetic treatment of fast ions. In this work, linear simulations are presented using a hybrid model which couples a fluid treatment of electrons with a gyrokinetic treatment of both bulk and fast ions. Studies of the internal kink mode in geometry relevant to large tokamak experiments are presented and the effect of gyrokinetic ions is considered. Interaction of the kink with gyrokinetic fast ions is also considered, including the destabilisation of the linear n = 1 EPM underlying the fishbone.
NASA Astrophysics Data System (ADS)
Howard, N. T.; Greenwald, M.; Mikkelsen, D. R.; White, A. E.; Reinke, M. L.; Ernst, D.; Podpaly, Y.; Candy, J.
2012-05-01
Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.
Howard, N. T.; Greenwald, M.; White, A. E.; Reinke, M. L.; Ernst, D.; Podpaly, Y.; Mikkelsen, D. R.; Candy, J.
2012-05-15
Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.
Linear and nonlinear verification of gyrokinetic microstability codes
Bravenec, R. V.; Candy, J.; Barnes, M.
2011-12-15
Verification of nonlinear microstability codes is a necessary step before comparisons or predictions of turbulent transport in toroidal devices can be justified. By verification we mean demonstrating that a code correctly solves the mathematical model upon which it is based. Some degree of verification can be accomplished indirectly from analytical instability threshold conditions, nonlinear saturation estimates, etc., for relatively simple plasmas. However, verification for experimentally relevant plasma conditions and physics is beyond the realm of analytical treatment and must rely on code-to-code comparisons, i.e., benchmarking. The premise is that the codes are verified for a given problem or set of parameters if they all agree within a specified tolerance. True verification requires comparisons for a number of plasma conditions, e.g., different devices, discharges, times, and radii. Running the codes and keeping track of linear and nonlinear inputs and results for all conditions could be prohibitive unless there was some degree of automation. We have written software to do just this and have formulated a metric for assessing agreement of nonlinear simulations. We present comparisons, both linear and nonlinear, between the gyrokinetic codes GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and GS2[W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. We do so at the mid-radius for the same discharge as in earlier work [C. Holland, A. E. White, G. R. McKee, M. W. Shafer, J. Candy, R. E. Waltz, L. Schmitz, and G. R. Tynan, Phys. Plasmas 16, 052301 (2009)]. The comparisons include electromagnetic fluctuations, passing and trapped electrons, plasma shaping, one kinetic impurity, and finite Debye-length effects. Results neglecting and including electron collisions (Lorentz model) are presented. We find that the linear frequencies with or without collisions agree well between codes, as do the time averages of
Linear and nonlinear verification of gyrokinetic microstability codes
NASA Astrophysics Data System (ADS)
Bravenec, R. V.; Candy, J.; Barnes, M.; Holland, C.
2011-12-01
Verification of nonlinear microstability codes is a necessary step before comparisons or predictions of turbulent transport in toroidal devices can be justified. By verification we mean demonstrating that a code correctly solves the mathematical model upon which it is based. Some degree of verification can be accomplished indirectly from analytical instability threshold conditions, nonlinear saturation estimates, etc., for relatively simple plasmas. However, verification for experimentally relevant plasma conditions and physics is beyond the realm of analytical treatment and must rely on code-to-code comparisons, i.e., benchmarking. The premise is that the codes are verified for a given problem or set of parameters if they all agree within a specified tolerance. True verification requires comparisons for a number of plasma conditions, e.g., different devices, discharges, times, and radii. Running the codes and keeping track of linear and nonlinear inputs and results for all conditions could be prohibitive unless there was some degree of automation. We have written software to do just this and have formulated a metric for assessing agreement of nonlinear simulations. We present comparisons, both linear and nonlinear, between the gyrokinetic codes GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and GS2 [W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. We do so at the mid-radius for the same discharge as in earlier work [C. Holland, A. E. White, G. R. McKee, M. W. Shafer, J. Candy, R. E. Waltz, L. Schmitz, and G. R. Tynan, Phys. Plasmas 16, 052301 (2009)]. The comparisons include electromagnetic fluctuations, passing and trapped electrons, plasma shaping, one kinetic impurity, and finite Debye-length effects. Results neglecting and including electron collisions (Lorentz model) are presented. We find that the linear frequencies with or without collisions agree well between codes, as do the time averages of
Gyrokinetic Particle Simulation of Fast Electron Driven Beta-induced Alfven Eigenmodes
NASA Astrophysics Data System (ADS)
Zhang, Wenlu; Cheng, Junyi; Lin, Zhihong
2016-10-01
The fast electron driven beta induced Alfven eigenmode (e-BAE) has been routinely observed in HL-2A tokamak. We study e-BAE for the first time using global gyrokinetic GTC simulation, where the fast electrons are described by the drift kinetic model. Frequency chirping is observed in nonlinear simulations in the absence of sources and sinks, which provide a new nonlinear paradigm beyond the standard ``bump-on-tail'' model. For weakly driven case, nonlinear frequency is observed to be in phase with particle flux, and nonlinear mode structure is almost the same as linear stage. In the strongly driven case, BAAE is also unstable and co-exists with BAE after the BAE saturation. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of the coherent structures in the fast electron phase space, where the dynamics of the coherent structure is controlled by the formation and destruction of phrase space islands in the canonical variables. Zonal fields are found to affect wave-particle resonance in the nonlinear e-BAE simulations.
Uncertainty estimation and a stopping rule in nonlinear gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Oberparleiter, Michael; Nordman, Hans; Verdoolaege, Geert; Jenko, Frank
2016-11-01
We present a method to estimate the mean and uncertainty of fluctuating quantities, such as spatially averaged density and temperature fluctuations or radial fluxes, from initial value simulations of the Eulerian gyrokinetic code GENE[1, 2]. Since the time series are autocorrelated in time, the data is grouped into batches based on the autocorrelation time and their means form the sample for further statistical treatment, such as calculating the standard error of the mean.Based on this uncertainty estimate we develop a stopping rule for a nonlinear simulation: First, regression tests ensure that it has reached a stationary (quasisteady) state and data before this point is discarded. Then the previously described estimate is calculated. If the estimated relative error is below a prescribed threshold, the simulation is stopped. This scheme is applied to several previously performed GENE simulations ranging from simple benchmarks to modelling of JET and ASDEX discharges. It can be demonstrated that a number of simulations could be around 30% shorter if a maximal statistical relative uncertainty of 5% is desired for all monitored quantities.
Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence
Angioni, C.; Candy, J.; Waltz, R. E.; Fable, E.; Maslov, M.; Weisen, H.; Peeters, A. G.
2009-06-15
The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor.
Nonlinear Gyrokinetics: A Powerful Tool for the Description of Microturbulence in Magnetized Plasmas
John E. Krommes
2010-09-27
Gyrokinetics is the description of low-frequency dynamics in magnetized plasmas. In magnetic-confinement fusion, it provides the most fundamental basis for numerical simulations of microturbulence; there are astrophysical applications as well. In this tutorial, a sketch of the derivation of the novel dynamical system comprising the nonlinear gyrokinetic (GK) equation (GKE) and the coupled electrostatic GK Poisson equation will be given by using modern Lagrangian and Lie perturbation methods. No background in plasma physics is required in order to appreciate the logical development. The GKE describes the evolution of an ensemble of gyrocenters moving in a weakly inhomogeneous background magnetic field and in the presence of electromagnetic perturbations with wavelength of the order of the ion gyroradius. Gyrocenters move with effective drifts, which may be obtained by an averaging procedure that systematically, order by order, removes gyrophase dependence. To that end, the use of the Lagrangian differential one-form as well as the content and advantages of Lie perturbation theory will be explained. The electromagnetic fields follow via Maxwell's equations from the charge and current density of the particles. Particle and gyrocenter densities differ by an important polarization effect. That is calculated formally by a "pull-back" (a concept from differential geometry) of the gyrocenter distribution to the laboratory coordinate system. A natural truncation then leads to the closed GK dynamical system. Important properties such as GK energy conservation and fluctuation noise will be mentioned briefly, as will the possibility (and diffculties) of deriving nonlinear gyro fluid equations suitable for rapid numerical solution -- although it is probably best to directly simulate the GKE. By the end of the tutorial, students should appreciate the GKE as an extremely powerful tool and will be prepared for later lectures describing its applications to physical problems.
Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes
NASA Astrophysics Data System (ADS)
Tronko, N.; Bottino, A.; Chandre, C.; Sonnendruecker, E.
2017-06-01
The reduced particle model is the central element for the systematic derivation of the gyrokinetic Vlasov-Maxwell equations from first principles. Coupled to the fields inside the gyrokinetic field-particle Lagrangian, the reduced particle model defines polarization and magnetization effects appearing in the gyrokinetic Maxwell equations. It is also used for the reconstruction of the gyrokinetic Vlasov equation from the particle characteristics. Various representations of reduced particle models are available according to the choice of the gyrokinetic phase space coordinates. In this paper, the Hamiltonian representation of the reduced particle dynamics at an order suitable for the implementation in particle-in-cell simulations is explicitly derived from the general reduction procedure. The second-order (with respect to the fluctuating electromagnetic fields), full finite Larmor radius (FLR) Hamiltonian gyrokinetic particle model as well as the second-order model suitable specifically for the long-wavelength approximation (i.e., containing up to the second-order FLR corrections), are derived and compared to the model recently implemented in the particle-in-cell code ORB5. We show that the same long-wavelength approximate equations can also be derived by taking the proper limit of the full FLR model.
White, A. E.; Schmitz, L.; Peebles, W. A.; Carter, T. A.; Doyle, E. J.; Rhodes, T. L.; Wang, G.; McKee, G. R.; Shafer, M. W.; Holland, C.; Tynan, G. R.; Austin, M. E.; Burrell, K. H.; Candy, J.; DeBoo, J. C.; Prater, R.; Staebler, G. M.; Waltz, R. E.; Makowski, M. A.
2008-05-15
For the first time, profiles (0.3<{rho}<0.9) of electron temperature and density fluctuations in a tokamak have been measured simultaneously and the results compared to nonlinear gyrokinetic simulations. Electron temperature and density fluctuations measured in neutral beam-heated, sawtooth-free low confinement mode (L-mode) plasmas in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] are found to be similar in frequency and normalized amplitude, with amplitude increasing with radius. The measured radial profile of two fluctuation fields allows for a new and rigorous comparison with gyrokinetic results. Nonlinear gyrokinetic flux-tube simulations predict that electron temperature and density fluctuations have similar normalized amplitudes in L-mode. At {rho}=0.5, simulation results match experimental heat diffusivities and density fluctuation amplitude, but overestimate electron temperature fluctuation amplitude and particle diffusivity. In contrast, simulations at {rho}=0.75 do not match either the experimentally derived transport properties or the measured fluctuation levels.
Fluid and gyrokinetic modelling of particle transport in plasmas with hollow density profiles
NASA Astrophysics Data System (ADS)
Tegnered, D.; Oberparleiter, M.; Nordman, H.; Strand, P.
2016-11-01
Hollow density profiles occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the fuelling scheme inefficient. In the present work, the particle transport driven by ITG/TE mode turbulence in regions of hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description, and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT , and magnetic shear are investigated. It is found that β in particular has a stabilizing effect in the negative R/Ln region, both nonlinear GENE and EDWM show a decrease in inward flux for negative R/Ln and a change of direction from inward to outward for positive R/Ln . This might have serious consequences for pellet fuelling of high β plasmas.
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-15
We present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory.
Hager, Robert; Chang, C. S.
2016-04-08
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Hager, Robert; Chang, C. S.
2016-04-08
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steepmore » edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.« less
NASA Astrophysics Data System (ADS)
Hager, Robert; Chang, C. S.
2016-04-01
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Hager, Robert Chang, C. S.
2016-04-15
As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Shear-Alfv'en Waves in Gyrokinetic Particle Simulation
NASA Astrophysics Data System (ADS)
Dickerson, Thomas D.; Startsev, Edward A.; Lee, W. W.
2012-10-01
Numerical properties of shear-Alfv'en waves in slab geometry have been studied using a Particle-in-Cell code implementing the recently developed double split-weight scheme [1]. This scheme separates the non-adiabatic response of the particles from both their adiabatic responses and the field-line bending effects arising from the background density and temperature gradients of both the electrons and the ions. This scheme is an improvement over the original split-weight scheme [2] in the presence of the zeroth-order inhomogeneities. The present studies consist of testing numerical restrictions on temporal resolution in the simulation of these waves in one and two dimensions, and on spatial resolutions on the formation of shear Alfv'en eigenmodes in two dimensional sheared slab simulations. For example, it is found that the correct behavior of ion temperature gradient modes in terms of frequencies and growth rates can be maintained with time steps larger than the limit imposed by the shear-Alfven waves. Details will be reported.[4pt] [1] E. A. Startsev and W. W. Lee, ``Finite-Beta Simulation of Microinstabilities,'' manuscript in preparation (2012). [0pt] [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm and Z. Lin, ``Shear-Alf'en Waves in Gyrokinetic Plasmas,'' Phys. Plasmas 10, 4435 (2001).
Finite-β Split-weight Gyrokinetic Particle Simulation of Microinstabilities
NASA Astrophysics Data System (ADS)
Jenkins, Thomas G.; Lee, W. W.; Lewandowski, J. L. V.
2003-10-01
The finite-β split-weight gyrokinetic particle simulation scheme [1] has been implemented in two-dimensional slab geometry for the purpose of studying the effects of high temperature electrons on microinstabilities. Drift wave instabilities and ion temperature gradient modes are studied in both shearless slab and sheared slab geometries. The linear and nonlinear evolution of these modes, as well as the physics of microtearing, is compared with the results of Reynders [2] and Cummings [3]. [1] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Phys. Plasmas 8, 4435 (2001). [2] J. V. W. Reynders, Ph.D. thesis, Princeton University (1992). [3] J. C. Cummings, Ph.D. thesis, Princeton University (1995).
Gyrokinetic particle simulation of beta-induced Alfvén eigenmode
NASA Astrophysics Data System (ADS)
Zhang, H. S.; Lin, Z.; Holod, I.; Wang, X.; Xiao, Y.; Zhang, W. L.
2010-11-01
The beta-induced Alfvén eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.
Impact of a hollow density profile on turbulent particle fluxes: Gyrokinetic and fluid simulations
NASA Astrophysics Data System (ADS)
Tegnered, D.; Oberparleiter, M.; Strand, P.; Nordman, H.
2017-07-01
Hollow density profiles may occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the pellet fuelling scheme inefficient. In the present work, the particle transport driven by Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence in hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT, and magnetic shear are investigated. In addition, the effects of a fast species are studied and global ITG simulations in a simplified physics description are performed in order to investigate nonlocal effects. It is found that β in particular, has a stabilizing effect in the negative R/Ln region. Both nonlinear GENE and EDWM simulations show a decrease in inward flux for negative R/Ln and a change in the direction from inward to outward for positive R/Ln. Moreover, the addition of fast particles was shown to decrease the inward main ion particle flux in the positive gradient region further. This might have serious consequences for pellet fuelling of high β plasmas. Additionally, the heat flux in global ITG turbulence simulations indicates that nonlocal effects can play a different role from usual in connection with pellet fuelling.
Split-Weight δ f Schemes for Gyrokinetic Particle Simulation
NASA Astrophysics Data System (ADS)
Lee, W. W.; Lewandowski, J. L. V.; Lin, Z.; Hahm, T. S.
2000-10-01
One of the most challenging problems in gyrokinetic particle simulation is the treatment of the electrons. A straightforward implementation of the electron dynamics has many pitfalls. The split weight scheme, (I. Manuilskiy and W. W. Lee, Phys. Plasmas 7), 1381 (2000) in which the perturbed distribution for the electrons, δ fe (≡ Fe - F_0e), is split into e (φ /T_e) F_0e and δ h_e, where Fe is the total distribution, F_0e is the equilibrium part, δ h is the non-adiabatic part, and φ is the electrostatic potential, can circumvent the parallel Courant condition of k_allel v_te Δ t < 1, and, thereby, increase the time steps. For finite-β plasmas, the schemes with φ replaced by ψ ≡ φ -(v_allel/c) A_allel or ψ ≡ φ -(ω/k_allel c) A_allel for the adiabatic response make it possible to produce shear-Alfven waves without the nonadiabatic response of the fast electrons. (W. W. Lee, J. L. V. Lewandowski and T. S. Hahm, in preparation.) The implementation the the schemes in the 3D global toroidal GTC code, (Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. White, Science), 281, 1835 (1998). and the associated numerical schemes for solving field equations involving time derivatives of the potentials and the use of the adiabatic field pusher to advance the electrons will be reported.
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.
Unlike-particle collision operator for gyrokinetic particle simulations
Kolesnikov, R.A.; Wang, W.X.; Hinton, F.L.
2010-08-01
Plasmas in modern tokamak experiments contain a significant fraction of impurity ion species in addition to main deuterium background. A new unlike-particle collision operator for {delta}f particle simulation has been developed to self-consistently study the non-local effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for simulation of cross-collisions between different ion species includes test-particle and conserving field-particle operators. The field-particle operator is designed to enforce conservation of number, momentum and energy. It was shown that the new operator correctly simulates the thermal equilibration of different plasma components. It was verified that the ambipolar radial electric field reaches steady state when the total radial guiding center particle current vanishes.
Bass, E. M.; Waltz, R. E.
2010-11-15
Energetic particle (EP) transport from local high-n toroidal Alfven eigenmodes (TAEs) and energetic particle modes (EPMs) is simulated with a gyrokinetic code. Linear and nonlinear simulations have identified a parameter range where the longwave TAE and EPM are unstable alongside the well-known ion-temperature-gradient (ITG) and trapped-electron-mode (TEM) instabilities. A new eigenvalue solver in GYRO facilitates this mode identification. States of nonlinearly saturated local TAE/EPM turbulent intensity are identified, showing a 'soft' transport threshold for enhanced energetic particle transport against the TAE/EPM drive from the EP pressure gradient. The very long-wavelength (mesoscale) TAE/EPM transport is saturated partially by nonlinear interaction with microturbulent ITG/TEM-driven zonal flows. Fixed-gradient-length, nonlinearly saturated states are accessible over a relatively narrow range of EP pressure gradient. Within this range, and in the local limit employed, TAE/EPM-driven transport more closely resembles drift-wave microturbulent transport than 'stiff' ideal MHD transport with a clamped critical total pressure gradient. At a higher, critical EP pressure gradient, fixed-gradient nonlinear saturation fails: EP transport increases without limit and background transport decreases. Presumably saturation is then obtained by relaxation of the EP pressure gradient to near this critical EP pressure gradient. If the background plasma gradients driving the ITG/TEM turbulence and zonal flows are weakened, the critical gradient collapses to the TAE/EPM linear stability threshold. Even at the critical EP pressure gradient there is no evidence that TAE/EPM instability significantly increases transport in the background plasma channels.
NASA Astrophysics Data System (ADS)
Zhao, Deng; Waltz, R. E.
2015-10-01
This paper presents the numerical methods for the nonlinear simulations of cyclokinetic [Waltz and Zhao Deng (2013)] equations in Fourier harmonics of the gyro-phase. A parallel processed, implicit time advanced, Eulerian (or continuum) code (rCYCLO) is developed. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantees accurate conservation of the incremental entropy. By comparing the cyclokinetic simulations with the corresponding gyrokinetics, we quantitatively test the breakdown of gyrokinetics at high turbulence levels over a range of large relative ion cyclotron frequency (10 <Ω∗ < 100 where Ω∗ = 1 /ρ∗, and ρ∗ is the relative ion gyroradius). As an important code verification, the rCYCLO gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω∗ ⩾ 50) and low turbulence levels. In the case of linearly stable ion cyclotron modes, the cyclokinetic transport is lower (not higher) than the gyrokinetic transport at high turbulence levels and low-Ω∗ values.
Gyrokinetic study of the role of {beta} on electron particle transport in tokamaks
Hein, T.; Angioni, C.; Fable, E.; Candy, J.
2010-10-15
Electromagnetic effects on the radial transport of electrons in the core of tokamak plasmas are studied by means of linear and nonlinear gyrokinetic simulations with the code GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and by an analytical derivation. The impact of a finite {beta}, that is, a finite ratio of the plasma pressure to the magnetic pressure, is considered on the fluctuations of the magnetic field through Ampere's law, as well as on the geometrical modification of the vertical drift produced by the Shafranov shift in the magnetic equilibrium, which, for realistic descriptions, has to be included in both electrostatic and electromagnetic modeling. The condition of turbulent particle flux at the null, which allows the determination of stationary logarithmic density gradients when neoclassical transport and particle sources are negligible, is investigated for increasing values of {beta}, in regimes of ion temperature gradient and trapped electron mode turbulence. The loss of adiabaticity of passing electrons produced by fluctuations in the magnetic vector potential produces an outward convection. When the magnetic equilibrium geometry is kept fixed, this induces a strong reduction of the stationary logarithmic density gradient with increasing {beta}. This effect is partly compensated by the geometrical effect on the vertical drift. This compensation effect, however, is significantly weaker in nonlinear simulations as compared to quasilinear calculations. A detailed comparison between quasilinear and nonlinear results reveals that the predicted value of the logarithmic density gradient is highly sensitive on the assumptions on the wave number spectrum applied in the quasilinear model. The qualitative consistency of the theoretical predictions with the experimental results obtained so far on the dependence of density peaking on {beta} is discussed by considering the additional impact, with increasing {beta}, of a particle source delivered
Gyrokinetics Simulation of Energetic Particle Turbulence and Transport
Diamond, Patrick H.
2011-09-21
Progress in research during this year elucidated the physics of precession resonance and its interaction with radial scattering to form phase space density granulations. Momentum theorems for drift wave-zonal flow systems involving precession resonance were derived. These are directly generalizable to energetic particle modes. A novel nonlinear, subcritical growth mechanism was identified, which has now been verified by simulation. These results strengthen the foundation of our understanding of transport in burning plasmas
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-30
Here, we present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory. (C) 2015 AIP Publishing LLC.
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-30
Here, we present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory. (C) 2015 AIP Publishing LLC.
Relevance of the parallel nonlinearity in gyrokinetic simulations of tokamak plasmas
Candy, J.; Waltz, R. E.; Parker, S. E.; Chen, Y.
2006-07-15
The influence of the parallel nonlinearity on transport in gyrokinetic simulations is assessed for values of {rho}{sub *} which are typical of current experiments. Here, {rho}{sub *}={rho}{sub s}/a is the ratio of gyroradius, {rho}{sub s}, to plasma minor radius, a. The conclusion, derived from simulations with both GYRO [J. Candy and R. E. Waltz, J. Comput. Phys., 186, 585 (2003)] and GEM [Y. Chen and S. E. Parker J. Comput. Phys., 189, 463 (2003)] is that no measurable effect of the parallel nonlinearity is apparent for {rho}{sub *}<0.012. This result is consistent with scaling arguments, which suggest that the parallel nonlinearity should be O({rho}{sub *}) smaller than the ExB nonlinearity. Indeed, for the plasma parameters under consideration, the magnitude of the parallel nonlinearity is a factor of 8{rho}{sub *} smaller (for 0.000 75<{rho}{sub *}<0.012) than the other retained terms in the nonlinear gyrokinetic equation.
Global gyrokinetic particle-in-cell simulations of internal kink instabilities
Mishchenko, Alexey; Zocco, Alessandro
2012-12-15
Internal kink instabilities have been studied in straight tokamak geometry employing an electromagnetic gyrokinetic particle-in-cell (PIC) code. The ideal-MHD internal kink mode and the collisionless m=1 tearing mode have been successfully simulated with the PIC code. Diamagnetic effects on the internal kink modes have also been investigated.
Gyrokinetic particle simulation of the beta-induced Alfven eigen mode
NASA Astrophysics Data System (ADS)
Zhang, Huasen; Lin, Zhihong; Holod, Ihor; Wang, Xin; Xiao, Yong; Zhang, Wenlu
2010-11-01
The beta-induced Alfven eigen mode (BAE) is studied using the global gyrokinetic particle code GTC. In our simulation, BAE is successfully excited by antenna and energetic particle density gradient. Through the antenna frequency scan, we can measure the BAE frequency and damping rate by numerical fitting the saturation amplitude. BAE excitation by energetic particles shows that the BAE propagates in the ion diamagnetic direction and the frequency has a little downshift, which is due to modification of the energetic particles. The frequency and growth rate in gyrokinetic simulation is a little different from drift kinetic simulation, which is expected due to the finite larmor radius effect. We also find that the BAE frequency is related to the wavelength and the plasma beta while the growth rate is sensitive to the energetic particle properties. Benchmarks between GTC and HMGC are also done through initial perturbation, antenna excitation and energetic particle excitation. The simulation results agree with each other very well.
Monte Carlo particle-in-cell methods for the simulation of the Vlasov-Maxwell gyrokinetic equations
NASA Astrophysics Data System (ADS)
Bottino, A.; Sonnendrücker, E.
2015-10-01
> The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov-Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations.
Astrophysical Gyrokinetics: Basic Equations and Linear Theory
NASA Astrophysics Data System (ADS)
Howes, Gregory G.; Cowley, Steven C.; Dorland, William; Hammett, Gregory W.; Quataert, Eliot; Schekochihin, Alexander A.
2006-11-01
Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.
Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
Frieman, E.A.; Chen, L.
1981-10-01
A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magentic field geometries. The specific case of axisymmetric tokamaks is then considered, and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating sceme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency.
Gyrokinetic Particle Simulation of Compressible Electromagnetic Turbulence in High-β Plasmas
Lin, Zhihong
2014-03-13
Supported by this award, the PI and his research group at the University of California, Irvine (UCI) have carried out computational and theoretical studies of instability, turbulence, and transport in laboratory and space plasmas. Several massively parallel, gyrokinetic particle simulation codes have been developed to study electromagnetic turbulence in space and laboratory plasmas. In space plasma projects, the simulation codes have been successfully applied to study the spectral cascade and plasma heating in kinetic Alfven wave turbulence, the linear and nonlinear properties of compressible modes including mirror instability and drift compressional mode, and the stability of the current sheet instabilities with finite guide field in the context of collisionless magnetic reconnection. The research results have been published in 25 journal papers and presented at many national and international conferences. Reprints of publications, source codes, and other research-related information are also available to general public on the PI’s webpage (http://phoenix.ps.uci.edu/zlin/). Two PhD theses in space plasma physics are highlighted in this report.
Gyrokinetic Simulation of Energetic Particles Turbulence and Transport in Fusion Plasmas
NASA Astrophysics Data System (ADS)
Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Xiao, Yong; Bierwage, Andreas; Spong, Donald; Chu, Ming
2009-05-01
The confinement of the energetic particles (EP) is a critical issue in the International Thermonuclear Experimental Reactor (ITER), since that ignition relies on the self-heating by the fusion products. Shear Alfven wave excitations by EP in toroidal systems, for example Toroidal Alfven Eigenmode (TAE) and Energetic Particle Mode (EPM) have been investigated as primary candidate for fluctuation-induced transport of EP in fusion plasma. In this work, TAE excitations by energetic particles are investigated in large scale first-principle simulations of fusion plasmas using the global gyrokinetic toroidal code (GTC) [Lin, Science 1998]. Comprehensive linear benchmarking results are reported between GTC, GYRO, fluid code TAEFL, and Magnetohydrodynamic-gyrokinetic hybrid code HMGC.
3D hybrid simulations with gyrokinetic particle ions and fluid electrons
Belova, E.V.; Park, W.; Fu, G.Y.; Strauss, H.R.; Sugiyama, L.E.
1998-12-31
The previous hybrid MHD/particle model (MH3D-K code) represented energetic ions as gyrokinetic (or drift-kinetic) particles coupled to MHD equations using the pressure or current coupling scheme. A small energetic to bulk ion density ratio was assumed, n{sub h}/n{sub b} {much_lt} 1, allowing the neglect of the energetic ion perpendicular inertia in the momentum equation and the use of MHD Ohm`s law E = {minus}v{sub b} {times} B. A generalization of this model in which all ions are treated as gyrokinetic/drift-kinetic particles and fluid description is used for the electron dynamics is considered in this paper.
NASA Astrophysics Data System (ADS)
Chen, Yang; Fu, Guo-Yong; Parker, Scott
2016-10-01
We report simulation of simultaneous excitation of multiple Reverse Shear Alfven eigenmodes in DIII-D plasmas (discharge #142111), using the gyrokinetic ion/fluid electron hybrid model of GEM. Thermal ions and beam ions are gyrokinetic, electrons are fluid with finite-mass correction in the Ohm's law. The vorticity equation is solved instead of the quasi-neutrality condition. This improves numerical stability. We extend previous single-n nonlinear simulation to simultaneous excitation of toroidal modes with n = 0 and 2 < n < 15 . Both the zonal n = 0 mode and the n = 8 mode are observed to be force driven by the linearly dominant n = 4 mode coupled to itself, with a growth rate twice that of the n = 4 mode. The zonal mode (including the surface averaged ϕ and A∥) significantly reduces the initial saturation level of the n = 4 mode. Evolution of all the other modes are also dominated by nonlinear coupling to the n = 4 mode. The mechanism of zonal structure generation will be examined by comparing various terms in the vorticity equation, including the Reynolds stress, the magnetic stress and the beam ion nonlinear effect.
Toroidal Electromagnetic Particle-in-Cell Code with Gyro-kinetic Electron and Fully-kinetic ion
NASA Astrophysics Data System (ADS)
Lin, Jingbo; Zhang, Wenlu; Liu, Pengfei; Li, Ding
2016-10-01
A kinetic simulation model has been developed using gyro-kinetic electron and fully-kinetic ion by removing fast gyro motion of electrons using the Lie-transform perturbation theory. A particle-in-cell kinetic code is developed based on this model in general magnetic flux coordinate systems, which is particularly suitable for simulations of toroidally confined plasma. Single particle motion and field solver are successfully verified respectively. Integrated electrostatic benchmark, for example the lower-hybrid wave (LHW) and ion Bernstein wave (IBW), shows a good agreement with theoretical results. Preliminary electromagnetic benchmark of fast wave at lower hybrid frequency range is also presented. This code can be a first-principal tool to investigate high frequency nonlinear phenomenon, such as parametric decay instability, during lower-hybrid current drive (LHCD) and ion cyclotron radio frequency heating (ICRF) with complex geometry effect included. Supported by National Special Research Program of China For ITER and National Natural Science Foundation of China.
Bernstein, I.B.; Catto, P.J.
1984-05-01
A nonlinear gyrokinetic formalism is developed which permits mean velocities comparable to thermal speeds in arbitrary magnetic field geometry. The theory is fully electromagnetic and does not employ an eikonal ansatz. The freedom in the theory is exploited to display simply the connection with ideal magnetohydrodynamics.
A finite element Poisson solver for gyrokinetic particle simulations in a global field aligned mesh
Nishimura, Y. . E-mail: nishimuy@uci.edu; Lin, Z.; Lewandowski, J.L.V.; Ethier, S.
2006-05-20
A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations.
NASA Astrophysics Data System (ADS)
White, Anne
2014-10-01
Understanding transport in high performance ELM-suppressed tokamak plasmas is of great interest for ITER and other future experiments. `I-mode' regime on Alcator C-Mod, also known as `improved L-mode' on ASDEX Upgrade, has several favorable characteristics: pedestals in electron and ion temperature, with ITER98y2 H-factors similar to and exceeding H-mode [Hubbard et al., Phys. Plasmas 18, 056115 (2011)], but without a density pedestal and without impurity accumulation and without ELMs. Most research on I-mode focuses on changes in edge and pedestal turbulence/transport and stability. In this work, transport in I-mode is probed by measuring changes in core turbulence across L-I transitions at Alcator C-Mod and comparing with nonlinear gyrokinetic simulations. Long wavelength (kθρs < 0.5) density fluctuation levels decrease from L-mode levels by up to 30% in I-mode, and long wavelength (kθρs < 0.3) electron temperature fluctuation levels decrease by up to 70%, reaching the instrumental sensitivity limit. Gyrokinetic simulation results suggest that ExB shear in the core of these intrinsically rotating plasmas can reduce the fluctuation amplitude in I-mode. As the pedestal temperature increases across slow L-I transitions, core density fluctuations (0.40 < ρ <0.95) are reduced prior to the onset of the edge-localized (0.99 < ρ < 1.0) weakly coherent mode (WCM) and prior to the reduction of low-frequency turbulence in the edge/pedestal region (0.99 < ρ < 1.0), which suggests that effects of profile stiffness across the radius can also lead to reduced core turbulence. By comparing experimental measurements from Alcator C-Mod to nonlinear gyrokinetic simulations and to different models of profile stiffness, this talk will explore the impact of core turbulence and transport on overall I-mode confinement and on the separation of particle and heat transport in I-mode. This work was supported by U.S. Department of Energy Contract DE-FC02-99ER54512-CMOD.
Multi-Channel Validation of Nonlinear Gyrokinetic Simulations in Alcator C-Mod I-mode Plasmas
NASA Astrophysics Data System (ADS)
Creely, A. J.
2016-10-01
New multi-channel validation of nonlinear gyrokinetic simulations (GYRO) is carried out for I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and density and temperature fluctuations. I-mode plasmas are characterized by high energy confinement, similar to H-mode, but with L-mode-like particle confinement, making them favorable for reactors due to natural absence of ELMs, but without impurity accumulation [Whyte NF 2010]. At C-Mod, I-mode plasmas have been obtained across a wide range of plasma currents (Ip = 0.55-1.2MA) and magnetic fields (Bt = 2.8-8.0T). I-mode is also actively studied at ASDEX Upgrade, DIII-D and other tokamaks [Hubbard NF 2016]. Open questions remain regarding core transport in I-mode compared to L and H-mode, making validation studies in I-mode of great interest. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale, cross-scale coupling effects [Howard PoP 2016] may be less important in I-mode than in L-mode. Adding the constraint of experimental perturbative heat diffusivity, however, revealed that ITG/TEM scale simulations do not adequately capture the high profile stiffness in I-mode [Creely NF 2016]. These results motivated more comprehensive comparisons of gyrokinetic simulations with I-mode plasmas. This talk expands upon past I-mode GYRO validation work to simultaneously constrain nonlinear gyrokinetic simulations with experimental electron and ion heat fluxes, electron temperature fluctuations measured with Correlation ECE, density fluctuations measured with Phase Contrast Imaging and reflectometry, and the temperature profile stiffness measured using partial sawtooth heat pulses. This work is supported by the US DOE under Grants DE-SC0006419 and DEFC02-99ER54512-CMOD.
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
NASA Astrophysics Data System (ADS)
Spong, D. A.; Holod, I.; Todo, Y.; Osakabe, M.
2017-08-01
Energetic particles are inherent to toroidal fusion systems and can drive instabilities in the Alfvén frequency range, leading to decreased heating efficiency, high heat fluxes on plasma-facing components, and decreased ignition margin. The applicability of global gyrokinetic simulation methods to macroscopic instabilities has now been demonstrated and it is natural to extend these methods to 3D configurations such as stellarators, tokamaks with 3D coils and reversed field pinch helical states. This has been achieved by coupling the GTC global gyrokinetic PIC model to the VMEC equilibrium model, including 3D effects in the field solvers and particle push. This paper demonstrates the application of this new capability to the linearized analysis of Alfvénic instabilities in the LHD stellarator. For normal shear iota profiles, toroidal Alfvén instabilities in the n = 1 and 2 toroidal mode families are unstable with frequencies in the 75 to 110 kHz range. Also, an LHD case with non-monotonic shear is considered, indicating reductions in growth rate for the same energetic particle drive. Since 3D magnetic fields will be present to some extent in all fusion devices, the extension of gyrokinetic models to 3D configurations is an important step for the simulation of future fusion systems. ).
Spong, Donald A.; Holod, Ihor; Todo, Y.; ...
2017-06-23
Energetic particles are inherent to toroidal fusion systems and can drive instabilities in the Alfvén frequency range, leading to decreased heating efficiency, high heat fluxes on plasma-facing components, and decreased ignition margin. The applicability of global gyrokinetic simulation methods to macroscopic instabilities has now been demonstrated and it is natural to extend these methods to 3D configurations such as stellarators, tokamaks with 3D coils and reversed field pinch helical states. This has been achieved by coupling the GTC global gyrokinetic PIC model to the VMEC equilibrium model, including 3D effects in the field solvers and particle push. Here, this papermore » demonstrates the application of this new capability to the linearized analysis of Alfvénic instabilities in the LHD stellarator. For normal shear iota profiles, toroidal Alfvén instabilities in the n = 1 and 2 toroidal mode families are unstable with frequencies in the 75 to 110 kHz range. Also, an LHD case with non-monotonic shear is considered, indicating reductions in growth rate for the same energetic particle drive. Finally, since 3D magnetic fields will be present to some extent in all fusion devices, the extension of gyrokinetic models to 3D configurations is an important step for the simulation of future fusion systems.« less
NASA Astrophysics Data System (ADS)
Bañón Navarro, A.; Bardóczi, L.; Carter, T. A.; Jenko, F.; Rhodes, T. L.
2017-03-01
Neoclassical tearing modes have deleterious effects on plasma confinement and, if they grow large enough, they can lead to discharge termination. Therefore, they impose a major barrier in the development of operating scenarios of present-day tokamaks. Gyrokinetics offers a path toward studying multi-scale interactions with turbulence and the effect on plasma confinement. As a first step toward this goal, we have implemented static magnetic islands in nonlinear gyrokinetic simulations with the GENE code. We investigate the effect of the islands on profiles, flows, turbulence and transport and the scaling of these effects with respect to island size. We find a clear threshold island width, below which the islands have little or no effect while beyond this point the islands significantly perturb flows, increase turbulence and transport. Additionally, we study the effect of radially asymmetric islands on shear flows for the first time. We find that island induced shear flows can regulate turbulent fluctuation levels in the vicinity of the island separatrices. Throughout this work, we focus on experimentally relevant quantities, such as rms levels of density and electron temperature fluctuations, as well as amplitude and phasing of turbulence modulation. These simulations aim to provide guidelines for interpreting experimental results by comparing qualitative trends in the simulations with those obtained in tokamak experiments.
Weir, G. M.; Faber, B. J.; Likin, K. M.; Talmadge, J. N.; Anderson, D. T.; Anderson, F. S. B.
2015-05-15
Stiffness measurements are presented in the quasi-helically symmetric experiment (HSX), in which the neoclassical transport is comparable to that in a tokamak and turbulent transport dominates throughout the plasma. Electron cyclotron emission is used to measure the local electron temperature response to modulated electron cyclotron resonant heating. The amplitude and phase of the heat wave through the steep electron temperature gradient (ETG) region of the plasma are used to determine a transient electron thermal diffusivity that is close to the steady-state diffusivity. The low stiffness in the region between 0.2 ≤ r/a ≤ 0.4 agrees with the scaling of the steady-state heat flux with temperature gradient in this region. These experimental results are compared to gyrokinetic calculations in a flux-tube geometry using the gyrokinetic electromagnetic numerical experiment code with two kinetic species. Linear simulations show that the ETG mode may be experimentally relevant within r/a ≤ 0.2, while the Trapped Electron Mode (TEM) is the dominant long-wavelength microturbulence instability across most of the plasma. The TEM is primarily driven by the density gradient. Non-linear calculations of the saturated heat flux driven by the TEM and ETG bracket the experimental heat flux.
NASA Astrophysics Data System (ADS)
Howard, N. T.; Greenwald, M.; Mikkelsen, D. R.; Reinke, M. L.; White, A. E.; Ernst, D.; Podpaly, Y.; Candy, J.
2012-06-01
Nonlinear gyrokinetic simulations of impurity transport are compared to experimental impurity transport for the first time. The GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) was used to perform global, nonlinear gyrokinetic simulations of impurity transport for a standard Alcator C-Mod, L-mode discharge. The laser blow-off technique was combined with soft x-ray measurements of a single charge state of calcium to provide time-evolving profiles of this non-intrinsic, non-recycling impurity over a radial range of 0.0 ⩽ r/a ⩽ 0.6. Experimental transport coefficient profiles and their uncertainties were extracted from the measurements using the impurity transport code STRAHL and rigorous Monte Carlo error analysis. To best assess the agreement of gyrokinetic simulations with the experimental profiles, the sensitivity of the GYRO predicted impurity transport to a wide range of turbulence-relevant plasma parameters was investigated. A direct comparison of nonlinear gyrokinetic simulation and experiment is presented with an in depth discussion of error sources and a new data analysis methodology.
NASA Astrophysics Data System (ADS)
Xu, Yingfeng; Ye, Lei; Dai, Zongliang; Xiao, Xiaotao; Wang, Shaojie
2017-08-01
The electrostatic gyrokinetic nonlinear turbulence code NLT, which is based on a numerical Lie-transform perturbation method, is developed. For improving the computational efficiency and avoiding the numerical instabilities, field-aligned coordinates and a Fourier filter are adopted in the NLT code. Nonlinear tests of the ion temperature gradient driven turbulence with adiabatic electrons are performed for verifying the NLT code by comparing with other gyrokinetic codes. The time evolution of the ion heat diffusivity and the relation between the ion heat diffusivity and the ion temperature gradient are compared in the nonlinear tests. Good agreements are achieved from the nonlinear benchmarks between the NLT code and other codes. The mode structures of the perturbed electric potential representing different phases have been simulated.
Center for Gyrokinetic Particle Simulations of Turbulent Transport in Burning Plasmas
Scott, Parker
2011-05-02
This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of
Global gyrokinetic models for energetic particle driven Alfvén instabilities in 3D equilibria
NASA Astrophysics Data System (ADS)
Spong, Don; Holod, Ihor
2015-11-01
The GTC global gyrokinetic PIC model has been adapted to 3D VMEC equilibria and provides a new method for the analysis of Alfvénic instabilities in stellarators, 3D tokamaks, and helical RFP states. The gyrokinetic orderings (k||/k⊥ << 1, ω/Ωci << 1, ρEP/L << 1) are applicable to a range of energetic particle driven instabilities that have been observed in 3D configurations. Applications of this model to stellarators have indicated that a variety of different Alfvén instabilities can be excited, depending on the toroidal mode number, fast ion average energy and fast ion density profile. Both an LHD discharge where bursting n = 1 Alfvén activity in the TAE gap was observed and a W7-X case have been examined. TAE,/EAE/GAE modes have been found in the simulations, depending on the mode family and fast ion profiles used. The dynamical evolution of the instabilities shows the field period coupling between n and n + Nfp expected for a stellarator. The development of gyrofluid reduced models that can capture relevant physics aspects of the gyrokinetic models will also be discussed. Research sponsored by the U.S. Department of Energy under Contract DE-AC05-00OR22725 with UT-Battelle, LLC and the GSEP SciDAC Center.
NASA Astrophysics Data System (ADS)
White, A. E.; Howard, N. T.; Mikkelsen, D. R.; Greenwald, M.; Candy, J.; Waltz, R. E.
2011-11-01
This paper describes the use of nonlinear gyrokinetic simulations to assess the feasibility of a new correlation electron cyclotron emission (CECE) diagnostic that has been proposed for the Alcator C-Mod tokamak (Marmar et al 2009 Nucl. Fusion 49 104014). This work is based on a series of simulations performed with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545). The simulations are used to predict ranges of fluctuation level, peak poloidal wavenumber and radial correlation length of electron temperature fluctuations in the core of the plasma. The impact of antenna pattern and poloidal viewing location on measurable turbulence characteristics is addressed using synthetic diagnostics. An upper limit on the CECE sample volume size is determined. The modeling results show that a CECE diagnostic capable of measuring transport-relevant, long-wavelength (kθρs < 0.5) electron temperature fluctuations is feasible at Alcator C-Mod.
Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas (GPS - TTBP) Final Report
Chame, Jacqueline
2011-05-27
The goal of this project is the development of the Gyrokinetic Toroidal Code (GTC) Framework and its applications to problems related to the physics of turbulence and turbulent transport in tokamaks,. The project involves physics studies, code development, noise effect mitigation, supporting computer science efforts, diagnostics and advanced visualizations, verification and validation. Its main scientific themes are mesoscale dynamics and non-locality effects on transport, the physics of secondary structures such as zonal flows, and strongly coherent wave-particle interaction phenomena at magnetic precession resonances. Special emphasis is placed on the implications of these themes for rho-star and current scalings and for the turbulent transport of momentum. GTC-TTBP also explores applications to electron thermal transport, particle transport; ITB formation and cross-cuts such as edge-core coupling, interaction of energetic particles with turbulence and neoclassical tearing mode trigger dynamics. Code development focuses on major initiatives in the development of full-f formulations and the capacity to simulate flux-driven transport. In addition to the full-f -formulation, the project includes the development of numerical collision models and methods for coarse graining in phase space. Verification is pursued by linear stability study comparisons with the FULL and HD7 codes and by benchmarking with the GKV, GYSELA and other gyrokinetic simulation codes. Validation of gyrokinetic models of ion and electron thermal transport is pursed by systematic stressing comparisons with fluctuation and transport data from the DIII-D and NSTX tokamaks. The physics and code development research programs are supported by complementary efforts in computer sciences, high performance computing, and data management.
Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode
NASA Astrophysics Data System (ADS)
Cheng, Junyi; Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Li, Ding; Chen, Yang; Cao, Jintao
2016-05-01
The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.
Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode
Cheng, Junyi; Chen, Yang; Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Li, Ding; Cao, Jintao
2016-05-15
The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.
Nonlinear saturation of trapped electron modes via perpendicular particle diffusion.
Merz, F; Jenko, F
2008-01-25
In magnetized fusion plasmas, trapped electron mode (TEM) turbulence constitutes, together with ion temperature gradient (ITG) turbulence, the dominant source of anomalous transport on ion scales. While ITG modes are known to saturate via nonlinear zonal flow generation, this mechanism is shown to be of little importance for TEM turbulence in the parameter regime explored here. Instead, a careful analysis of the statistical properties of the ExB nonlinearity in the context of gyrokinetic turbulence simulations reveals that perpendicular particle diffusion is the dominant saturation mechanism. These findings allow for the construction of a rather realistic quasilinear model of TEM induced transport.
Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode
Zhang, H. S.; Liu, Y. Q.; Lin, Z.; Zhang, W. L.
2016-04-15
The beta-induced Alfven-acoustic eigenmode (BAAE) in toroidal plasmas is verified and studied by global gyrokinetic particle simulations. When ion temperature is much lower than electron temperature, the existence of the weakly damped BAAE is verified in the simulations using initial perturbation, antenna excitation, and energetic particle excitation, respectively. When the ion temperature is comparable to the electron temperature, the unstable BAAE can be excited by realistic energetic particle density gradient, even though the stable BAAE (in the absence of energetic particles) is heavily damped by the thermal ions. In the simulations with reversed magnetic shear, BAAE frequency sweeping is observed and poloidal mode structure has a triangle shape with a poloidal direction similar to that observed in tokamak experiments. The triangle shape changes the poloidal direction, and no frequency sweeping is found in the simulations with normal magnetic shear.
Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas
Ma, Kwan-Liu
2011-12-21
In this project, we have developed techniques for visualizing large-scale time-varying multivariate particle and field data produced by the GPS_TTBP team. Our basic approach to particle data visualization is to provide the user with an intuitive interactive interface for exploring the data. We have designed a multivariate filtering interface for scientists to effortlessly isolate those particles of interest for revealing structures in densely packed particles as well as the temporal behaviors of selected particles. With such a visualization system, scientists on the GPS-TTBP project can validate known relationships and temporal trends, and possibly gain new insights in their simulations. We have tested the system using over several millions of particles on a single PC. We will also need to address the scalability of the system to handle billions of particles using a cluster of PCs. To visualize the field data, we choose to use direct volume rendering. Because the data provided by PPPL is on a curvilinear mesh, several processing steps have to be taken. The mesh is curvilinear in nature, following the shape of a deformed torus. Additionally, in order to properly interpolate between the given slices we cannot use simple linear interpolation in Cartesian space but instead have to interpolate along the magnetic field lines given to us by the scientists. With these limitations, building a system that can provide an accurate visualization of the dataset is quite a challenge to overcome. In the end we use a combination of deformation methods such as deformation textures in order to fit a normal torus into their deformed torus, allowing us to store the data in toroidal coordinates in order to take advantage of modern GPUs to perform the interpolation along the field lines for us. The resulting new rendering capability produces visualizations at a quality and detail level previously not available to the scientists at the PPPL. In summary, in this project we have
NASA Astrophysics Data System (ADS)
Zhang, Chenxi; Zhang, Wenlu; Lin, Zhihong; Li, Ding
2013-05-01
This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitation and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.
Zhang, Chenxi; Li, Ding; Zhang, Wenlu; Lin, Zhihong
2013-05-15
This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitation and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.
NASA Astrophysics Data System (ADS)
Teaca, Bogdan; Jenko, Frank; Told, Daniel
2017-04-01
Using large resolution numerical simulations of gyrokinetic (GK) turbulence, spanning an interval ranging from the end of the fluid scales to the electron gyroradius, we study the energy transfers in the perpendicular direction for a proton-electron plasma in a slab equilibrium magnetic geometry. The plasma parameters employed here are relevant to kinetic Alfvén wave turbulence in solar wind conditions. In addition, we use an idealized test representation for the energy transfers between two scales, to aid our understanding of the diagnostics applicable to the nonlinear cascade in an infinite inertial range. For GK turbulence, a detailed analysis of nonlinear energy transfers that account for the separation of energy exchanging scales is performed. Starting from the study of the energy cascade and the scale locality problem, we show that the general nonlocal nature of GK turbulence, captured via locality functions, contains a subset of interactions that are deemed local, are scale invariant (i.e. a sign of asymptotic locality) and possess a locality exponent that can be recovered directly from measurements on the energy cascade. It is the first time that GK turbulence is shown to possess an asymptotic local component, even if the overall locality of interactions is nonlocal. The results presented here and their implications are discussed from the perspective of previous findings reported in the literature and the idea of universality of GK turbulence.
Accuracy of momentum and gyrodensity transport in global gyrokinetic particle-in-cell simulations
McMillan, B. F.; Villard, L.
2014-05-15
Gyrokinetic Particle-In-Cell (PIC) simulations based on conservative Lagrangian formalisms admit transport equations for conserved quantities such as gyrodensity and toroidal momentum, and these can be derived for arbitrary wavelength, even though previous applications have used the long-wavelength approximation. In control-variate PIC simulations, a consequence of the different treatment of the background (f{sub 0}) and perturbed parts (δf), when a splitting f = f{sub 0} + δf is performed, is that analytical transport relations for the relevant fluxes and moments are only reproduced in the large marker number limit. The transport equations for f can be used to write the inconsistency in the perturbed quantities explicitly in terms of the sampling of the background distribution f{sub 0}. This immediately allows estimates of the error in consistency of momentum transport in control-variate PIC simulations. This inconsistency tends to accumulate secularly and is not directly affected by the sources and noise control in the system. Although physical tokamaks often rotate quite strongly, the standard gyrokinetic formalism assumes weak perpendicular flows, comparable to the drift speed. For systems with such weak flows, maintaining acceptably small relative errors requires that a number of markers scale with the fourth power of the linear system size to consistently resolve long-wavelength evolution. To avoid this unfavourable scaling, an algorithm for exact gyrodensity transport has been developed, and this is shown to allow accurate simulations with an order of magnitude fewer markers.
Combining electromagnetic gyro-kinetic particle-in-cell simulations with collisions
NASA Astrophysics Data System (ADS)
Slaby, Christoph; Kleiber, Ralf; Könies, Axel
2017-09-01
It has been an open question whether for electromagnetic gyro-kinetic particle-in-cell (PIC) simulations pitch-angle collisions and the recently introduced pullback transformation scheme (Mishchenko et al., 2014; Kleiber et al., 2016) are consistent. This question is positively answered by comparing the PIC code EUTERPE with an approach based on an expansion of the perturbed distribution function in eigenfunctions of the pitch-angle collision operator (Legendre polynomials) to solve the electromagnetic drift-kinetic equation with collisions in slab geometry. It is shown how both approaches yield the same results for the frequency and damping rate of a kinetic Alfvén wave and how the perturbed distribution function is substantially changed by the presence of pitch-angle collisions.
Chen, Yang
2012-03-07
At Colorado University-Boulder the primary task is to extend our gyrokinetic Particle-in-Cell simulation of tokamak micro-turbulence and transport to the area of energetic particle physics. We have implemented a gyrokinetic ion/massless fluid electron hybrid model in the global {delta} f-PIC code GEM, and benchmarked the code with analytic results on the thermal ion radiative damping rate of Toroidal Alfven Eigenmodes (TAE) and with mode frequency and spatial structure from eigenmode analysis. We also performed nonlinear simulations of both a single-n mode (n is the toroidal mode number) and multiple-n modes, and in the case of single-n, benchmarked the code on the saturation amplitude vs. particle collision rate with analytical theory. Most simulations use the f method for both ions species, but we have explored the full-f method for energetic particles in cases where the burst amplitude of the excited instabilities is large as to cause significant re-distribution or loss of the energetic particles. We used the hybrid model to study the stability of high-n TAEs in ITER. Our simulations show that the most unstable modes in ITER lie in the rage of 10 < n < 20. Thermal ion pressure effect and alpha particles non-perturbative effect are important in determining the mode radial location and stability threshold. The thermal ion Landau damping rate and radiative damping rate from the simulations are compared with analytical estimates. The thermal ion Landau damping is the dominant damping mechanism. Plasma elongation has a strong stabilizing effect on the alpha driven TAEs. The central alpha particle pressure threshold for the most unstable n=15 mode is about {beta}{sub {alpha}}(0) = 0.7% for the fully shaped ITER equilibrium. We also carried nonlinear simulations of the most unstable n = 15 mode and found that the saturation amplitude for the nominal ITER discharge is too low to cause large redistribution or loss of alpha particles. To include kinetic electron effects
Advances in stellarator gyrokinetics
NASA Astrophysics Data System (ADS)
Helander, P.; Bird, T.; Jenko, F.; Kleiber, R.; Plunk, G. G.; Proll, J. H. E.; Riemann, J.; Xanthopoulos, P.
2015-05-01
Recent progress in the gyrokinetic theory of stellarator microinstabilities and turbulence simulations is summarized. The simulations have been carried out using two different gyrokinetic codes, the global particle-in-cell code EUTERPE and the continuum code GENE, which operates in the geometry of a flux tube or a flux surface but is local in the radial direction. Ion-temperature-gradient (ITG) and trapped-electron modes are studied and compared with their counterparts in axisymmetric tokamak geometry. Several interesting differences emerge. Because of the more complicated structure of the magnetic field, the fluctuations are much less evenly distributed over each flux surface in stellarators than in tokamaks. Instead of covering the entire outboard side of the torus, ITG turbulence is localized to narrow bands along the magnetic field in regions of unfavourable curvature, and the resulting transport depends on the normalized gyroradius ρ* even in radially local simulations. Trapped-electron modes can be significantly more stable than in typical tokamaks, because of the spatial separation of regions with trapped particles from those with bad magnetic curvature. Preliminary non-linear simulations in flux-tube geometry suggest differences in the turbulence levels in Wendelstein 7-X and a typical tokamak.
Diagnosing collisionless energy transfer using field-particle correlations: gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Klein, Kristopher G.; Howes, Gregory G.; Tenbarge, Jason M.
2017-08-01
Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behaviour of a variety of space and astrophysical plasmas. Such a determination is complicated by the complex nature of the turbulence as well as observational constraints, chiefly that in situ measurements of such plasmas are typically only available at a single point in space. Recent work has shown that correlations between electric fields and particle velocity distributions constructed from single-point measurements produce a velocity-dependent signature of the collisionless damping mechanism. We extend this work by constructing field-particle correlations using data sets drawn from single points in strongly driven, turbulent, electromagnetic gyrokinetic simulations to demonstrate that this technique can identify the collisionless mechanisms operating in such systems. The velocity-space structure of the correlation between proton distributions and parallel electric fields agrees with expectations of resonant mechanisms transferring energy collisionlessly in turbulent systems. This work motivates the eventual application of field-particle correlations to spacecraft measurements in the solar wind, with the ultimate goal to determine the physical mechanisms that dissipate magnetized plasma turbulence.
NASA Astrophysics Data System (ADS)
Kraus, Michael; Kormann, Katharina; Sonnendrücker, Eric; Morrison, Philip
2016-10-01
In this talk we will describe recent work on the development of geometric particle-in-cell methods for the Vlasov-Maxwell system and gyrokinetics. We present a novel framework for particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive semi-discrete Poisson brackets which satisfy the Jacobi identity and apply Hamiltonian splitting schemes for time integration. Techniques from Finite Element Exterior Calculus and spline differential forms ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge-invariant, feature exact charge conservation show excellent long-time energy behaviour. The talk will be concluded with an outline of how to extend these techniques towards gyrokinetics.
Gyrokinetic particle-in-cell simulations of Alfvén eigenmodes in presence of continuum effects
Mishchenko, Alexey Könies, Axel; Hatzky, Roman
2014-05-15
First-principle gyrokinetic particle-in-cell simulations of a global Toroidal Alfvén Eigenmode (TAE) are undertaken in the presence of a strong coupling with the continuum. Effects of the bulk plasma temperature on the interplay between the TAE and Kinetic Alfvén Waves (KAWs) are investigated. A global TAE-KAW structure is identified which appears to be more unstable with respect to the fast ions than a simple (fluid-like) TAE mode.
Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasma
Viktor K. Decyk
2008-04-24
The UCLA work on this grant was to design and help implement an object-oriented version of the GTC code, which is written in Fortran90. The GTC code is the main global gyrokinetic code used in this project, and over the years multiple, incompatible versions have evolved. The reason for this effort is to allow multiple authors to work together on GTC and to simplify future enhancements to GTC. The effort was designed to proceed incrementally. Initially, an upper layer of classes (derived types and methods) was implemented which called the original GTC code 'under the hood.' The derived types pointed to data in the original GTC code, and the methods called the original GTC subroutines. The original GTC code was modified only very slightly. This allowed one to define (and refine) a set of classes which described the important features of the GTC code in a new, more abstract way, with a minimum of implementation. Furthermore, classes could be added one at a time, and at the end of the each day, the code continued to work correctly. This work was done in close collaboration with Y. Nishimura from UC Irvine and Stefan Ethier from PPPL. Ten classes were ultimately defined and implemented: gyrokinetic and drift kinetic particles, scalar and vector fields, a mesh, jacobian, FLR, equilibrium, interpolation, and particles species descriptors. In the second state of this development, some of the scaffolding was removed. The constructors in the class objects now allocated the data and the array data in the original GTC code was removed. This isolated the components and now allowed multiple instantiations of the objects to be created, in particular, multiple ion species. Again, the work was done incrementally, one class at a time, so that the code was always working properly. This work was done in close collaboration with Y. Nishimura and W. Zhang from UC Irvine and Stefan Ethier from PPPL. The third stage of this work was to integrate the capabilities of the various versions of
Hybrid simulations of the interaction of hot gyrokinetic particles with MHD waves
Belova, E.V.; Denton, R.E.; Hudson, M.K.; Chan, A.A.
1996-12-31
A self-consistent study of the interaction of energetic ions with low-frequency MHD waves is performed using hybrid MHD-gyrokinetic particle simulations. In particular, the excitation of magnetospheric hydromagnetic waves by magnetic drift-bounce resonance with energetic ring current ions is investigated. In the model, energetic ions are treated as gyrokinetic particles using fully electromagnetic gyro-center equations, while the cold background plasma is treated as a fluid. The particles are coupled to the fluid equations through their current which appear in the bulk plasma momentum equation: where {rho}{sub b}, V{sub b} and p{sub b} are bulk plasma density, velocity and pressure, n{sub h} and j{sub h} axe hot ion density and current density. Other equations for the bulk plasma axe that of the MHD equations including E = - V{sub b} x B/c. It is assumed that n{sub h} {much_lt} n{sub b}. Spatial gyroaveraging in the gyro-center equations of motion as well as transformation to physical space axe performed by using four or eight point gyroangle distribution, in order to include the finite Larmor radius effects. In test runs, good conservation of the total energy was obtained and the finite Larmor radius effects were well reproduced for k{sub {perpendicular}}{rho}{sub h} {approximately} 1. Since magnetic drift-bounce resonant instability is driven by radial pressure gradients and requires resonance between azimuthal ion drift motion and bounce motion along magnetic field line, 3-D simulations are necessary for its investigation. The use of a multiple spatial scale expansion method enables to separate the equilibrium spatial scale lengths from those of the perturbations. In this case the zero-order ion pressure and magnetic field gradients become input parameters for the 2-D simulation. The 2-D numerical model with fixed background inhomogeneity was developed and it is used to study the drift-bounce resonant instability in 2-D box geometry.
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.
Nonlinear particle simulation of ion cyclotron waves in toroidal geometry
NASA Astrophysics Data System (ADS)
Kuley, A.; Bao, J.; Lin, Z.; Wei, X. S.; Xiao, Y.
2015-12-01
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.
NASA Astrophysics Data System (ADS)
Dong, Ge; Bao, Jian; Bhattacharjee, Amitava; Brizard, Alain; Lin, Zhihong; Porazik, Peter
2017-08-01
The compressional component of magnetic perturbation δ B ∥ can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma β increases (β is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating δ B ∥ , and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when δ B ∥ is neglected for β e = 0.02 , and that δ B ∥ has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. The KBM growth rate decreases about 15% when equilibrium current is neglected.
NASA Astrophysics Data System (ADS)
Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team
2016-10-01
The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.
Particle-in-cell δf gyrokinetic simulations of the microtearing mode
Chowdhury, J.; Chen, Yang; Wan, Weigang; Parker, Scott E.; Guttenfelder, W.; Canik, J. M.
2016-01-15
The linear stability properties of the microtearing mode are investigated in the edge and core regimes of the National Spherical Torus Experiment (NSTX) using the particle-in-cell method based gyrokinetic code GEM. The dependence of the mode on various equilibrium quantities in both regions is compared. While the microtearing mode in the core depends upon the electron-ion collisions, in the edge region, it is found to be weakly dependent on the collisions and exists even when the collision frequency is zero. The electrostatic potential is non-negligible in each of the cases. It plays opposite roles in the core and edge of NSTX. While the microtearing mode is partially stabilized by the electrostatic potential in the core, it has substantial destabilizing effect in the edge. In addition to the spherical tokamak, we also study the microtearing mode for parameters relevant to the core of a standard tokamak. The fundamental characteristics of the mode remain the same; however, the electrostatic potential in this case is destabilizing as opposed to the core of NSTX. The velocity dependence of the collision frequency, which is crucial for the mode to grow in slab calculations, is not required to destabilize the mode in toroidal devices.
SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas
Lin, Zhihong
2013-12-18
During the first year of the SciDAC gyrokinetic particle simulation (GPS) project, the GPS team (Zhihong Lin, Liu Chen, Yasutaro Nishimura, and Igor Holod) at the University of California, Irvine (UCI) studied the tokamak electron transport driven by electron temperature gradient (ETG) turbulence, and by trapped electron mode (TEM) turbulence and ion temperature gradient (ITG) turbulence with kinetic electron effects, extended our studies of ITG turbulence spreading to core-edge coupling. We have developed and optimized an elliptic solver using finite element method (FEM), which enables the implementation of advanced kinetic electron models (split-weight scheme and hybrid model) in the SciDAC GPS production code GTC. The GTC code has been ported and optimized on both scalar and vector parallel computer architectures, and is being transformed into objected-oriented style to facilitate collaborative code development. During this period, the UCI team members presented 11 invited talks at major national and international conferences, published 22 papers in peer-reviewed journals and 10 papers in conference proceedings. The UCI hosted the annual SciDAC Workshop on Plasma Turbulence sponsored by the GPS Center, 2005-2007. The workshop was attended by about fifties US and foreign researchers and financially sponsored several gradual students from MIT, Princeton University, Germany, Switzerland, and Finland. A new SciDAC postdoc, Igor Holod, has arrived at UCI to initiate global particle simulation of magnetohydrodynamics turbulence driven by energetic particle modes. The PI, Z. Lin, has been promoted to the Associate Professor with tenure at UCI.
Modern gyrokinetic particle-in-cell simulation of fusion plasmas on top supercomputers
Wang, Bei; Ethier, Stephane; Tang, William; ...
2017-06-29
The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the petascale and beyond. Motivated by the goal of developing a modern code capable of dealing with the physics challenge of increasing problem size with sufficient resolution, new thread-level optimizations have been introduced as well as a key additional domain decomposition. GTC-P's multiple levels of parallelism, including inter-node 2D domain decomposition and particle decomposition, as well as intra-node shared memory partition and vectorization have enabled pushing the scalability ofmore » the PIC method to extreme computational scales. In this paper, we describe the methods developed to build a highly parallelized PIC code across a broad range of supercomputer designs. This particularly includes implementations on heterogeneous systems using NVIDIA GPU accelerators and Intel Xeon Phi (MIC) co-processors and performance comparisons with state-of-the-art homogeneous HPC systems such as Blue Gene/Q. New discovery science capabilities in the magnetic fusion energy application domain are enabled, including investigations of Ion-Temperature-Gradient (ITG) driven turbulence simulations with unprecedented spatial resolution and long temporal duration. Performance studies with realistic fusion experimental parameters are carried out on multiple supercomputing systems spanning a wide range of cache capacities, cache-sharing configurations, memory bandwidth, interconnects and network topologies. These performance comparisons using a realistic discovery-science-capable domain application code provide valuable insights on optimization techniques across one of the broadest sets of current high-end computing platforms worldwide.« less
Xu, Yingfeng Dai, Zongliang; Wang, Shaojie
2014-04-15
The nonlinear gyrokinetic theory in the tokamak configuration based on the two-step transform is developed; in the first step, we transform the magnetic potential perturbation to the Hamiltonian part, and in the second step, we transform away the gyroangle-dependent part of the perturbed Hamiltonian. Then the I-transform method is used to decoupled the perturbation part of the motion from the unperturbed motion. The application of the I-transform method to the computation of the guiding-center orbit and the guiding-center distribution function in tokamaks is presented. It is demonstrated that the I-transform method of the orbit computation which involves integrating only along the unperturbed orbit agrees with the conventional method which integrates along the full orbit. A numerical code based on the I-transform method is developed and two numerical examples are given to verify the new method.
White, A E; Schmitz, L; Peebles, W A; Carter, T A; Rhodes, T L; Doyle, E J; Gourdain, P A; Hillesheim, J C; Wang, G; Holland, C; Tynan, G R; Austin, M E; McKee, G R; Shafer, M W; Burrell, K H; Candy, J; DeBoo, J C; Prater, R; Staebler, G M; Waltz, R E; Makowski, M A
2008-10-01
A correlation electron cyclotron emission (CECE) diagnostic has been used to measure local, turbulent fluctuations of the electron temperature in the core of DIII-D plasmas. This paper describes the hardware and testing of the CECE diagnostic and highlights the importance of measurements of multifield fluctuation profiles for the testing and validation of nonlinear gyrokinetic codes. The process of testing and validating such codes is critical for extrapolation to next-step fusion devices. For the first time, the radial profiles of electron temperature and density fluctuations are compared to nonlinear gyrokinetic simulations. The CECE diagnostic at DIII-D uses correlation radiometry to measure the rms amplitude and spectrum of the electron temperature fluctuations. Gaussian optics are used to produce a poloidal spot size with w(o) approximately 1.75 cm in the plasma. The intermediate frequency filters and the natural linewidth of the EC emission determine the radial resolution of the CECE diagnostic, which can be less than 1 cm. Wavenumbers resolved by the CECE diagnostic are k(theta) < or = 1.8 cm(-1) and k(r) < or = 4 cm(-1), relevant for studies of long-wavelength turbulence associated with the trapped electron mode and the ion temperature gradient mode. In neutral beam heated L-mode plasmas, core electron temperature fluctuations in the region 0.5 < r/a < 0.9, increase with radius from approximately 0.5% to approximately 2%, similar to density fluctuations that are measured simultaneously with beam emission spectroscopy. After incorporating "synthetic diagnostics" to effectively filter the code output, the simulations reproduce the characteristics of the turbulence and transport at one radial location r/a = 0.5, but not at a second location, r/a = 0.75. These results illustrate that measurements of the profiles of multiple fluctuating fields can provide a significant constraint on the turbulence models employed by the code.
White, A. E.; Schmitz, L.; Peebles, W. A.; Carter, T. A.; Rhodes, T. L.; Doyle, E. J.; Gourdain, P. A.; Hillesheim, J. C.; Wang, G.; Holland, C.; Tynan, G. R.; Austin, M. E.; McKee, G. R.; Shafer, M. W.; Burrell, K. H.; Candy, J.; DeBoo, J. C.; Prater, R.; Staebler, G. M.; Waltz, R. E.
2008-10-15
A correlation electron cyclotron emission (CECE) diagnostic has been used to measure local, turbulent fluctuations of the electron temperature in the core of DIII-D plasmas. This paper describes the hardware and testing of the CECE diagnostic and highlights the importance of measurements of multifield fluctuation profiles for the testing and validation of nonlinear gyrokinetic codes. The process of testing and validating such codes is critical for extrapolation to next-step fusion devices. For the first time, the radial profiles of electron temperature and density fluctuations are compared to nonlinear gyrokinetic simulations. The CECE diagnostic at DIII-D uses correlation radiometry to measure the rms amplitude and spectrum of the electron temperature fluctuations. Gaussian optics are used to produce a poloidal spot size with w{sub o}{approx}1.75 cm in the plasma. The intermediate frequency filters and the natural linewidth of the EC emission determine the radial resolution of the CECE diagnostic, which can be less than 1 cm. Wavenumbers resolved by the CECE diagnostic are k{sub {theta}}{<=}1.8 cm{sup -1} and k{sub r}{<=}4 cm{sup -1}, relevant for studies of long-wavelength turbulence associated with the trapped electron mode and the ion temperature gradient mode. In neutral beam heated L-mode plasmas, core electron temperature fluctuations in the region 0.5
Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks
NASA Astrophysics Data System (ADS)
Biancalani, A.; Bottino, A.; Cole, M.; Di Troia, C.; Lauber, Ph; Mishchenko, A.; Scott, B.; Zonca, F.
2017-05-01
The confinement of energetic particles (EPs) is crucial in the efficient heating of tokamak plasmas. Plasma instabilities such as Alfvén eigenmodes (AEs) can redistribute the EP population, making the plasma heating less effective and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AEs (TAEs) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EPs due to the wave-particle nonlinearity is studied. In particular, we focus on the linear modification of the frequency, growth rate and radial structure of the TAE, caused by the nonlinear evolution of the EP distribution function. For the ITPA benchmark case, we find that the frequency increases when the growth rate decreases, and the mode shrinks radially. The theoretical interpretation is given in terms of a nonperturbative nonlinear evolution of the AE in relation to the Alfvén continuum.
Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics
Yu Lin; Xueyi Wang; Liu Chen; Zhihong Lin
2009-08-11
Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence test
NASA Astrophysics Data System (ADS)
Cheng, Junyi; Chen, Yang; Zhang, Wenlu; Lin, Zhihong; Chen, Wei; Yu, Limin; Ding, Xuantong
2015-11-01
A verification and validation study is carried out for a sequence of fast electron driven beta-induced Alfven eigenmodes in HL-2A tokamak plasma. The fast electron driven beta induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electrons are described by the drift kinetic model. The phase space structure shows that only the processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels such as transit, drift-bounce, and processional resonance. For weakly nonlinear driven case, frequency is observed to be in phase with the particle energy flux, and mode structure is almost the same as linear stage . While in the strongly driven nonlinear case, BAAE is excited after the BAE mode saturated. The simulation of e-BAE with the HL-2A tokamak parameters is taken. Three modes n/m = 1/2 , 2/5 ,1/3 in HL-2A can be excited in our simulations.
Geometric Gyrokinetic Theory for Edge Plasma
Qin, H; Cohen, R H; Nevins, W M; Xu, X Q
2007-01-18
It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the
NASA Astrophysics Data System (ADS)
Ohana, N.; Jocksch, A.; Lanti, E.; Tran, T. M.; Brunner, S.; Gheller, C.; Hariri, F.; Villard, L.
2016-11-01
With the aim of enabling state-of-the-art gyrokinetic PIC codes to benefit from the performance of recent multithreaded devices, we developed an application from a platform called the “PIC-engine” [1, 2, 3] embedding simplified basic features of the PIC method. The application solves the gyrokinetic equations in a sheared plasma slab using B-spline finite elements up to fourth order to represent the self-consistent electrostatic field. Preliminary studies of the so-called Particle-In-Fourier (PIF) approach, which uses Fourier modes as basis functions in the periodic dimensions of the system instead of the real-space grid, show that this method can be faster than PIC for simulations with a small number of Fourier modes. Similarly to the PIC-engine, multiple levels of parallelism have been implemented using MPI+OpenMP [2] and MPI+OpenACC [1], the latter exploiting the computational power of GPUs without requiring complete code rewriting. It is shown that sorting particles [3] can lead to performance improvement by increasing data locality and vectorizing grid memory access. Weak scalability tests have been successfully run on the GPU-equipped Cray XC30 Piz Daint (at CSCS) up to 4,096 nodes. The reduced time-to-solution will enable more realistic and thus more computationally intensive simulations of turbulent transport in magnetic fusion devices.
Continuum Edge Gyrokinetic Theory and Simulations
Xu, X Q; Xiong, Z; Dorr, M R; Hittinger, J A; Bodi, K; Candy, J; Cohen, B I; Cohen, R H; Colella, P; Kerbel, G D; Krasheninnikov, S; Nevins, W M; Qin, H; Rognlien, T D; Snyder, P B; Umansky, M V
2007-01-09
The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential, and mirror ratio; and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the banana regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL. (5) Our 5D gyrokinetic formulation yields a set of nonlinear electrostatic gyrokinetic equations that are for both neoclassical and turbulence simulations.
Generalized Covariant Gyrokinetic Dynamics of Magnetoplasmas
Cremaschini, C.; Tessarotto, M.; Nicolini, P.; Beklemishev, A.
2008-12-31
A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurring typically in the vicinity of massive stellar objects (black holes, neutron stars, active galactic nuclei, etc.), is the accurate description of single-particle covariant dynamics, based on gyrokinetic theory (Beklemishev et al., 1999-2005). Provided radiation-reaction effects are negligible, this is usually based on the assumption that both the space-time metric and the EM fields (in particular the magnetic field) are suitably prescribed and are considered independent of single-particle dynamics, while allowing for the possible presence of gravitational/EM perturbations driven by plasma collective interactions which may naturally arise in such systems. The purpose of this work is the formulation of a generalized gyrokinetic theory based on the synchronous variational principle recently pointed out (Tessarotto et al., 2007) which permits to satisfy exactly the physical realizability condition for the four-velocity. The theory here developed includes the treatment of nonlinear perturbations (gravitational and/or EM) characterized locally, i.e., in the rest frame of a test particle, by short wavelength and high frequency. Basic feature of the approach is to ensure the validity of the theory both for large and vanishing parallel electric field. It is shown that the correct treatment of EM perturbations occurring in the presence of an intense background magnetic field generally implies the appearance of appropriate four-velocity corrections, which are essential for the description of single-particle gyrokinetic dynamics.
Validation of nonlinear gyrokinetic simulations of L- and I-mode plasmas on Alcator C-Mod
NASA Astrophysics Data System (ADS)
Creely, A. J.; Howard, N. T.; Rodriguez-Fernandez, P.; Cao, N.; Hubbard, A. E.; Hughes, J. W.; Rice, J. E.; White, A. E.; Candy, J.; Staebler, G. M.; Conway, G. D.; Freethy, S. J.; Sung, C.
2017-05-01
New validation of global, nonlinear, ion-scale gyrokinetic simulations (GYRO) is carried out for L- and I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and temperature fluctuations. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale (cross-scale coupling) effects [Howard PoP 2016] may be less important in I-mode than in L-mode. New results presented here, however, show that global, nonlinear, ion-scale GYRO simulations are able to match the experimental ion heat flux, but underpredict electron heat flux (at most radii), electron temperature fluctuations, and perturbative thermal diffusivity in both L- and I-mode. Linear addition of electron heat flux from electron scale runs does not resolve this discrepancy. These results indicate that single-scale simulations do not sufficiently describe the I-mode core transport, and that multi-scale (coupled electron- and ion-scale) transport models are needed. A preliminary investigation with multi-scale TGLF, however, was unable to resolve the discrepancy between ion-scale GYRO and experimental electron heat fluxes and perturbative diffusivity, motivating further work with multi-scale GYRO simulations and a more comprehensive study with multi-scale TGLF.
NASA Astrophysics Data System (ADS)
Leboeuf, Jean-Noel; Decyk, Viktor; Newman, David; Sanchez, Raul
2013-10-01
The massively parallel, 2D domain-decomposed, nonlinear, 3D, toroidal, electrostatic, gyrokinetic, Particle in Cell (PIC), Cartesian geometry UCAN2 code, with particle ions and adiabatic electrons, has been ported to two emerging mainframes. These two computers, one at NERSC in the US built by Cray named Edison and the other at the Barcelona Supercomputer Center (BSC) in Spain built by IBM named MareNostrum III (MNIII) just happen to share the same Intel ``Sandy Bridge'' processors. The successful port of UCAN2 to MNIII which came online first has enabled us to be up and running efficiently in record time on Edison. Overall, the performance of UCAN2 on Edison is superior to that on MNIII, particularly at large numbers of processors (>1024) for the same Intel IFORT compiler. This appears to be due to different MPI modules (OpenMPI on MNIII and MPICH2 on Edison) and different interconnection networks (Infiniband on MNIII and Cray's Aries on Edison) on the two mainframes. Details of these ports and comparative benchmarks are presented. Work supported by OFES, USDOE, under contract no. DE-FG02-04ER54741 with the University of Alaska at Fairbanks.
NASA Astrophysics Data System (ADS)
Sung, C.; White, A. E.; Mikkelsen, D. R.; Greenwald, M.; Holland, C.; Howard, N. T.; Churchill, R.; Theiler, C.
2016-04-01
Long wavelength turbulent electron temperature fluctuations (kyρs < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (kyρs ≲ 1.7) performed at r/a ˜ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the "Transport Shortfall" [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
Sung, C.; White, A. E.; Greenwald, M.; Howard, N. T.; Mikkelsen, D. R.; Churchill, R.; Holland, C.; Theiler, C.
2016-04-15
Long wavelength turbulent electron temperature fluctuations (k{sub y}ρ{sub s} < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (k{sub y}ρ{sub s} ≲ 1.7) performed at r/a ∼ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
Gyrokinetic Simulation of TAE in Fusion plasmas
NASA Astrophysics Data System (ADS)
Wang, Zhixuan
Linear gyrokinetic simulation of fusion plasmas finds a radial localization of the toroidal Alfvén eigenmodes (TAE) due to the non-perturbative energetic particles (EP) contribution. The EP-driven TAE has a radial mode width much smaller than that predicted by the magnetohydrodynamic (MHD) theory. The TAE radial position stays around the strongest EP pressure gradients when the EP profile evolves. The non-perturbative EP contribution is also the main cause for the breaking of the radial symmetry of the ballooning mode structure and for the dependence of the TAE frequency on the toroidal mode number. These phenomena are beyond the picture of the conventional MHD theory. Linear gyrokinetic simulation of the electron cyclotron heating (ECH) experiments on DIII-D successfully recover the TAE and RSAE. The EP profile, rather than the electron temperature, is found to be the key factor determining whether TAE or RSAE is the dominant mode in the system in our simulation. Investigation on the nonlinear gyrokinetic simulation model reveals a missing nonlinear term which has important contributions to the zonal magnetic fields. A new fluid-electron hybrid model is proposed to keep this nonlinear term in the lowest order fluid part. Nonlinear simulation of TAE using DIII-D parameters confirms the importance of this new term for the zonal magnetic fields. It is also found that zonal structures dominated by zonal electric fields are forced driven at about twice the linear growth rate of TAE in the linear phase. The zonal flows then limit the nonlinear saturation level by tearing the eigenmode structures apart. In the nonlinear phase of the simulation, the major frequency in the system chirps down by about 30% and stays there.
Global Gyrokinetic Simulation Model for Laboratory Magnetosphere
NASA Astrophysics Data System (ADS)
Xie, Hua-Sheng; Ou, Wei-Ke; Zhang, Yi; Du, Shi-Kang; Huang, Zi-Cong; Li, Bo
2016-10-01
A global gyro-kinetic particle-in-cell code (GKD) is developed to study the micro-instabilties driven turbulent transport for magnetic dipole configuration. This configuration is relevant to several experiment devices, such as LDX at MIT, CTX at Columbia University and HDX at Harbin Institute of Technology. The major electrostatic drift instability in this system is entropy mode, which can be unstable even when ideal interchange mode is stable. For comparison, we also show the nonlinear results in Z-pinch and linear results with benchmark to linear eigenvalue solution.
Bass, E. M.; Waltz, R. E.
2013-01-15
The unstable spectrum of Alfven eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfven eigenmode (RSAE) at toroidal mode number n=3 is mapped. The RSAE second harmonic and an unstable beta-induced Alfven eigenmode (BAE) are simultaneously tracked alongside the primary RSAE. An observed twist in the eigenmode pattern, caused mostly by shear in the driving EP profile, is shown through artificially varying the E Multiplication-Sign B rotational velocity shear to depend generally on shear in the local wave phase velocity. Coupling to the BAE and to the toroidal Alfven eigenmode limit the RSAE frequency sweeps at the lower and upper end, respectively. While the present fully gyrokinetic model (including thermal ions and electrons) constitutes the best treatment of compressibility physics available, the BAE frequency is overpredicted by about 20% against experiment here and is found to be sensitive to energetic beam ion pressure. The RSAE frequency is more accurately matched except when it is limited by the BAE. Simulations suggest that the experiment is very close to marginal AE stability at points of RSAE-BAE coupling. A recipe for comparing the radial profile of quasilinear transport flux from local modes to that from global modes paves the way for the development of a stiff (critical gradient) local AE transport model based on local mode stability thresholds.
Gyrokinetic simulation of current-driven instabilities
NASA Astrophysics Data System (ADS)
McClenaghan, Joseph
The gyrokinetic toroidal code(GTC) capability has been extended for simulating current-driven instabilities in magnetized plasmas such as kink and resistive tearing modes with kinetic effects. This new gyrokinetic capability enables first-principles, integrated simulations of macroscopic magnetohydrodynamic(MHD) modes, which limit the performance of burning plasmas and threaten the integrity of fusion devices. The excitation and evolution of macroscopic MHD modes often depend on the kinetic effects at microscopic scales and the nonlinear coupling of multiple physical processes. GTC simulation in the fluid limit of the internal kink modes in cylindrical geometry has been verified by benchmarking with an MHD eigenvalue code. The global simulation domain covers the magnetic axis which is necessary for simulating the macroscopic MHD modes. Gyrokinetic simulations of the internal kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface. This new GTC capability for current-driven instability has now been extended to simulate fishbone instabilities excited by energetic particles and resistive tearing modes. GTC has also been applied to study the internal kink modes in astrophysical jets that are formed around supermassive black holes. Linear simulations find that the internal kink modes in astrophysical jets are unstable with a broad eigenmode. Nonlinear saturation amplitude of these kink modes is observed to be small, suggesting that the jets can remain collimated even in the presence of the internal kink modes. Generation of a mean parallel electric field by the nonlinear dynamics of internal kink modes and the potential implication of this field on particle acceleration in jets has been examined.
Gyrokinetic Studies of Magnetic Reconnection
NASA Astrophysics Data System (ADS)
Pueschel, Moritz J.; Jenko, Frank; Told, Daniel; Buechner, Joerg
2011-10-01
Collisionless magnetic reconnection constitutes an effective mechanism for particle acceleration in astrophysical plasmas, in particular the solar corona. In addition, it is also of relevance to fusion experiments. Gyrokinetic simulations with the GENE code are performed to explore the temporal evolution of current sheets in two-dimensional slab geometry with a strong guide field. After successful code-code benchmarking, Extensive parameter studies are performed, covering a wide range of physical scenarios. In particular, differing findings regarding the influence of the ion temperature are explained. In its nonlinear phase, the characteristics of the reconnection process depend on whether the system is driven or decaying. Decaying turbulence sees an inverse cascade, and all energy is ultimately transferred to the largest radial scale. If driven by a Krook-type term, the system develops into a turbulent, quasi-stationary state. An important quantity to investigate in nonlinear simulations is the parallel electric field which is able to accelerate particles along the background magnetic field. The spatial structure of this field is studied for the different nonlinear cases, and its amplitude reported as a function of the drive frequency.
Lauber, Ph. Guenter, S.; Koenies, A.; Pinches, S.D.
2007-09-10
In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfven physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU Muenchen, 2003; Ph. Lauber, S. Guenter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D. Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfven regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects. Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles' trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction. Successful benchmarks for toroidal Alfven
Gyrokinetic simulation of internal kink modes
Naitou, Hiroshi; Tsuda, Kenji; Lee, W.W.; Sydora, R.D.
1995-05-01
Internal disruption in a tokamak has been simulated using a three-dimensional magneto-inductive gyrokinetic particle code. The code operates in both the standard gyrokinetic mode (total-f code) and the fully nonlinear characteristic mode ({delta}f code). The latter, a recent addition, is a quiet low noise algorithm. The computational model represents a straight tokamak with periodic boundary conditions in the toroidal direction. The plasma is initially uniformly distributed in a square cross section with perfectly conducting walls. The linear mode structure of an unstable m = 1 (poloidal) and n = 1 (toroidal) kinetic internal kink mode is clearly observed, especially in the {delta}f code. The width of the current layer around the x-point, where magnetic reconnection occurs, is found to be close to the collisionless electron skin depth. This is consistent with the theory in which electron inertia has a dominant role. The nonlinear behavior of the mode is found to be quite similar for both codes. Full reconnection in the Alfven time scale is observed along with the electrostatic potential structures created during the full reconnection phase. The E x B drift due to this electrostatic potential dominates the nonlinear phase of the development after the full reconnection.
Bao, J.; Lin, Z. Kuley, A.; Wang, Z. X.
2016-06-15
An electromagnetic particle simulation model has been formulated and verified for nonlinear processes of lower hybrid (LH) waves in fusion plasmas. Electron dynamics are described by the drift kinetic equation using either kinetic momentum or canonical momentum. Ion dynamics are treated as the fluid system or by the Vlasov equation. Compressible magnetic perturbation is retained to simulate both the fast and slow LH waves. Numerical properties are greatly improved by using the electron continuity equation to enforce the consistency between electrostatic potential and vector potential, and by using the importance sampling scheme. The simulation model has been implemented in the gyrokinetic toroidal code (GTC), and verified for the dispersion relation and nonlinear particle trapping of the electromagnetic LH waves.
Gyrokinetic simulations of ion and impurity transport
Estrada-Mila, C.; Candy, J.; Waltz, R.E.
2005-02-01
A systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas 4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple D-v (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 50-50 deuterium-tritium plasma, where a symmetry breaking is observed indicating the potential for fuel separation in a burning plasma. Quasilinear theory together with linear simulations shows that the symmetry breaking which enhances the tritium confinement arises largely from finite-Larmor-radius effects. To justify the numerical methods used in the paper, a variety of linear benchmarks and nonlinear grid refinement studies are detailed.
Gyrokinetic simulations of ion and impurity transport
NASA Astrophysics Data System (ADS)
Estrada-Mila, C.; Candy, J.; Waltz, R. E.
2005-02-01
A systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas 4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple D-v (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 50-50 deuterium-tritium plasma, where a symmetry breaking is observed indicating the potential for fuel separation in a burning plasma. Quasilinear theory together with linear simulations shows that the symmetry breaking which enhances the tritium confinement arises largely from finite-Larmor-radius effects. To justify the numerical methods used in the paper, a variety of linear benchmarks and nonlinear grid refinement studies are detailed.
Transport, noise, and conservation properties in gyrokinetic plasmas
NASA Astrophysics Data System (ADS)
Jenkins, Thomas
2005-10-01
The relationship between various transport properties (such as particle and heat flux, entropy production, heating, and collisional dissipation) [1] is examined in electrostatic gyrokinetic simulations of ITG modes in simple geometry. The effect of the parallel velocity nonlinearity on the achievement of steady-state solutions and the transport properties of these solutions is examined; the effects of nonadiabatic electrons are also considered. We also examine the effectiveness of the electromagnetic split-weight scheme [2] in reducing the noise and improving the conservation properties (energy, momentum, particle number, etc.) of gyrokinetic plasmas. [1] W. W. Lee and W. M. Tang, Phys. Fluids 31, 612 (1988). [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z.Lin, Phys. Plasmas 8, 4435 (2001).
NASA Astrophysics Data System (ADS)
Parra, Felix I.; Catto, Peter J.
2009-06-01
We compare two different derivations of the gyrokinetic equation: the Hamiltonian approach in Dubin D H E et al (1983 Phys. Fluids 26 3524) and the recursive methodology in Parra F I and Catto P J (2008 Plasma Phys. Control. Fusion 50 065014). We prove that both approaches yield the same result at least to second order in a Larmor radius over macroscopic length expansion. There are subtle differences in the definitions of some of the functions that need to be taken into account to prove the equivalence.
Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks
NASA Astrophysics Data System (ADS)
Qin, Hong
A general gyrokinetic formalism and appropriate computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both magnetohydrodynamic (MHD) instabilities and electromagnetic drift waves. The gyrokinetic system of equation is derived by phase- space Lagrangian Lie perturbation methods which enable applications to modes with arbitrary wavelength. An important component missing from previous electromagnetic gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed in the present analysis. This is accomplished by introducing a new ``distribution function'' and an associated governing gyrokinetic equation. Consequently, the compressional Alfvén waves and cyclotron waves can be systematically treated. The new insights into the gyrokinetic perpendicular dynamics uncovered here clarify the understanding of the gyrokinetic approach-the real spirit of the gyrokinetic reduction is to decouple the gyromotion from the guiding center orbital motion, instead of averaging it out. The gyrokinetic perpendicular dynamics is in fact essential to the recovery of the MHD model from a fully kinetic derivation. In particular, it serves to generalize, in gyrokinetic framework, Spitzer's solution of the fluid/particle paradox to a broader regime of applicability. The gyrokinetic system is also shown to be reducible to a simpler form to deal with shear Alfvén waves. This consists of an appropriate form of the gyrokinetic equation governing the distribution function, the gyrokinetic Poisson equation, and a newly derived gyrokinetic moment equation. If all of the kinetic effects are neglected, the gyrokinetic moment equation is shown to recover the ideal MHD equation for shear Alfvén modes. In addition, a gyrokinetic Ohm's law, including both the perpendicular and the parallel components, is
McClenaghan, J.; Lin, Z.; Holod, I.; Deng, W.; Wang, Z.
2014-12-15
The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynamic eigenvalue code. Gyrokinetic simulations of the kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface.
Simulation of neoclassical transport with the continuum gyrokinetic code COGENT
Dorf, M. A.; Cohen, R. H.; Dorr, M.; Rognlien, T.; Hittinger, J.; Compton, J.; Colella, P.; Martin, D.; McCorquodale, P.
2013-01-25
The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.
Simulation of neoclassical transport with the continuum gyrokinetic code COGENT
Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...
2013-01-25
The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy.more » Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.« less
Muñoz, P. A. Kilian, P.; Büchner, J.; Told, D.; Jenko, F.
2015-08-15
In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (b{sub g}). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (β{sub i} = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (b{sub g} ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (b{sub g} ≳ 5). Kinetic PIC simulations using guide fields b{sub g} ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (β{sub i} = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (b{sub g} ≲ 3)
NASA Astrophysics Data System (ADS)
Wang, Xin; Briguglio, Sergio; Chen, Liu; Fogaccia, Giuliana; Vlad, Gregorio; Zonca, Fulvio
2013-10-01
The extended version of nonlinear hybrid magnetohydrodynamic (MHD)-Gyrokinetic code HMGC (XHMGC) is used to investigate the reversed shear Alfvén eigenmodes (RSAE)/energetic particle modes (EPM) driven by an anisotropic Maxwellian energetic particles with reversed shear q profiles. In the region near the minimum-q surface, EPM are shown to exist inside the kinetic low-frequency shear Alfvén continuum gap. Fast non-adiabatic down-ward chirping frequency is found for given equilibrium profiles, which is understood as consequence of nonlinear wave particle dynamics. In our current case, the mode structure is dominated by two neighbor poloidal components, while wave energetic particle interaction is dominated by the sidebands of the dominant transit resonance. S. Briguglio et al., Phys. Plasmas 2, 3711 (1995).
Byers, J.A.; Williams, T.J.; Cohen, B.I.; Dimits, A.M.
1994-04-27
One of the programs of the Magnetic fusion Energy (MFE) Theory and computations Program is studying the anomalous transport of thermal energy across the field lines in the core of a tokamak. We use the method of gyrokinetic particle-in-cell simulation in this study. For this LDRD project we employed massively parallel processing, new algorithms, and new algorithms, and new formal techniques to improve this research. Specifically, we sought to take steps toward: researching experimentally-relevant parameters in our simulations, learning parallel computing to have as a resource for our group, and achieving a 100 {times} speedup over our starting-point Cray2 simulation code`s performance.
Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations
Brizard, Alain J.; Tronko, Natalia
2011-08-15
The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas 7, 4816 (2000)]. From the gyrokinetic Noether canonical-momentum equation derived by the Noether method, the gyrokinetic parallel momentum equation and other gyrokinetic Vlasov-moment equations are obtained. In addition, an exact gyrokinetic toroidal angular-momentum conservation law is derived in axisymmetric tokamak geometry, where the transport of parallel-toroidal momentum is related to the radial gyrocenter polarization, which includes contributions from the guiding-center and gyrocenter transformations.
Gyrokinetic Simulation of Low-n Tearing Modes
NASA Astrophysics Data System (ADS)
Chen, Yang
2015-11-01
-collisional linear growth rate, as well as the nonlinear scaling of particle trapping frequency with linear growth rate in the collisionless regime. Nonlinear results including collisions show that the mode initially saturates at low amplitude, followed by an algebraic growth period (the Rutherford regime). Current progress on simulating the low-n toroidal tearing mode in toroidal geometry will be reported.
Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence
NASA Astrophysics Data System (ADS)
Belli, Emily Ann
Advanced numerical algorithms for gyrokinetic simulations are explored for more effective studies of plasma turbulent transport. The gyrokinetic equations describe the dynamics of particles in 5-dimensional phase space, averaging over the fast gyromotion, and provide a foundation for studying plasma microturbulence in fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/continuum gyrokinetic solvers are compared. An iterative implicit scheme based on numerical approximations of the plasma response is developed. This method reduces the long time needed to set-up implicit arrays, yet still has larger time step advantages similar to a fully implicit method. Various model preconditioners and iteration schemes, including Krylov-based solvers, are explored. An Alternating Direction Implicit algorithm is also studied and is surprisingly found to yield a severe stability restriction on the time step. Overall, an iterative Krylov algorithm might be the best approach for extensions of core tokamak gyrokinetic simulations to edge kinetic formulations and may be particularly useful for studies of large-scale ExB shear effects. The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic equilibria based on interpolations of representative JET-like shapes. High shaping is found to be a stabilizing influence on both the linear ITG instability and nonlinear ITG turbulence. A scaling of the heat flux with elongation of chi ˜ kappa-1.5 or kappa-2 (depending on the triangularity) is observed, which is consistent with previous gyrofluid simulations. Thus, the GS2 turbulence simulations are explaining a significant fraction, but not all, of the empirical elongation scaling. The remainder of the scaling may come from (1) the edge boundary conditions for core turbulence, and (2) the larger Dimits nonlinear critical temperature gradient shift due to the
Gyrokinetic simulation of isotope scaling in tokamak plasmas
Lee, W.W.; Santoro, R.A.
1995-07-01
A three-dimensional global gyrokinetic particle code in toroidal geometry has been used for investigating the transport properties of ion temperature gradient (ITG) drift instabilities in tokamak plasmas. Using the isotopes of hydrogen (H{sup +}), deuterium (D{sup +}) and tritium (T{sup +}), we have found that, under otherwise identical conditions, there exists a favorable isotope scaling for the ion thermal diffusivity, i.e., Xi decreases with mass. Such a scaling, which exists both at the saturation of the instability and also at the nonlinear steady state, can be understood from the resulting wavenumber and frequency spectra.
Hinton, F. L.; Waltz, R. E.
2006-10-15
Expressions for particle and energy fluxes and heating rates due to turbulence are derived. These fluxes and heating rates are identified from moments of an extended drift-kinetic equation for the equilibrium distribution function. These include neoclassical as well as turbulent diffusion and heating. Phase-space conservation is demonstrated, allowing the drift-kinetic equation to be expressed in conservative form. This facilitates taking moments with few approximations, mainly those consistent with drift kinetics for the equilibrium distribution function and the relative smallness of the fluctuations. The turbulent heating is uniquely defined by choosing the standard gyrokinetic definition for the energy flux. With this definition, most of the heating can be expressed in the form of ohmic heating from turbulent parallel and perpendicular current density perturbations. The latter current is identified with grad-B and curvature drifts, plus terms involving magnetic perturbations (which are smaller for low beta). A small contribution to the heating comes from the divergence of an energy flux that is dependent on the finite gyroradius of the ions. The fluxes and heating rates are expressed in a form that can be easily evaluated from gyrokinetic turbulence simulations.
Gyrokinetic Simulation of Reverse Shear Alfven Eigenmodes in DIII-D Plasmas
NASA Astrophysics Data System (ADS)
Chen, Yang; Parker, Scott; Fu, Guo-Yong
2012-03-01
We present simulation results of the beam driven Reverse Shear Alfven Eigenmodes (RSAE) observed in DIII-D discharge 142111 using the Particle-in-Cell gyrokinetic code GEM [1]. Bulk ions and energetic particles are gyrokinetic, but electrons are described by a mass-less fluid model. Two schemes for obtaining the electric potential are implemented, one by solving the gyrokinetic Poisson equation for φ directly, the other by solving the gyrokinetic moment (GKM) equation for φ/t and then integrating in time. The GKM approach is found to be more robust for linear simulations (allowing larger time steps) but less robust for nonlinear simulations. Previous simulations reproduced the chirping in frequency as seen in the experiment. Recently it has been reported by other simulation codes (GTC, GYRO and TAEFL) that the shearing direction of the mode structure in the poloidal plane disagrees with observation. We found that the mode structure, including the shearing in the poloidal plane, is in general sensitive to the beam distribution. By changing the radial profile of the beam density while keeping the velocity dependence fixed, both shearing directions can be produced in the simulation. [4pt] [1] Y. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007)
Liu, Dongjian; Bao, Jian; Han, Tao; Wang, Jiaqi; Lin, Zhihong
2016-02-15
A finite-mass electron fluid model for low frequency electromagnetic fluctuations, particularly the collisionless tearing mode, has been implemented in the gyrokinetic toroidal code. Using this fluid model, linear properties of the collisionless tearing mode have been verified. Simulations verify that the linear growth rate of the single collisionless tearing mode is proportional to D{sub e}{sup 2}, where D{sub e} is the electron skin depth. On the other hand, the growth rate of a double tearing mode is proportional to D{sub e} in the parameter regime of fusion plasmas.
Micah Beck
2008-09-14
This project focused on the use of Logistical Networking technology to address the challenges involved in rapid sharing of data from the the Center's gyrokinetic particle simulations, which can be on the order of terabytes per time step, among researchers at a number of geographically distributed locations. There is a great need to manage data on this scale in a flexible manner, with simulation code, file system, database and visualization functions requiring access. The project used distributed data management infrastructure based on Logistical Networking technology to address these issues in a way that maximized interoperability and achieved the levels of performance the required by the Center's application community. The work focused on the development and deployment of software tools and infrastructure for the storage and distribution of terascale datasets generated by simulations running at the National Center for Computational Science at Oak Ridge National Laboratory.
Nonlinear collisionless plasma wakes of small particles
Hutchinson, I. H.
2011-03-15
The wake behind a spherical particle smaller than the Debye length ({lambda}{sub De}) in flowing plasma is calculated using a particle-in-cell code. The results with different magnitudes of charge reveal substantial nonlinear effects down to values that for a floating particle would correspond to a particle radius {approx}10{sup -2{lambda}}{sub De}. The peak potential in the oscillatory wake structure is strongly suppressed by nonlinearity, never exceeding {approx}0.4 times the unperturbed ion energy. By contrast, the density peak arising from ion focusing can be many times the ambient. Strong heating of the ions occurs in the nonlinear regime. Direct ion absorption by the particle is not important for the far wake unless the radius exceeds 10{sup -1{lambda}}{sub De}, and is therefore never significant (for the far wake) in the linear regime. Reasonable agreement with full-scale linear response calculations are obtained in the linear regime. The wake wavelength is confirmed and an explanation, in terms of the conical potential structure, is proposed for experimentally-observed oblique alignment of different-sized grains.
A Short Introduction to General Gyrokinetic Theory
H. Qin
2005-02-14
Interesting plasmas in the laboratory and space are magnetized. General gyrokinetic theory is about a symmetry, gyro-symmetry, in the Vlasov-Maxwell system for magnetized plasmas. The most general gyrokinetic theory can be geometrically formulated. First, the coordinate-free, geometric Vlasov-Maxwell equations are developed in the 7-D phase space, which is defined as a fiber bundle over the space-time. The Poincar{copyright}-Cartan-Einstein 1-form pullbacked onto the 7-D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinite small generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincar{copyright}-Cartan-Einstein 1-form, which also generates the most relaxed condition under which the gyro-symmetry still exists. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Since the general gyrokinetic system-developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and Liouville volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfven wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered. Three examples of applications of the general gyrokinetic theory developed in the areas of plasma equilibrium and plasma waves are
Nonlinear Particle Acceleration and Thermal Particles in GRB Afterglows
NASA Astrophysics Data System (ADS)
Warren, Donald C.; Ellison, Donald C.; Barkov, Maxim V.; Nagataki, Shigehiro
2017-02-01
The standard model for GRB afterglow emission treats the accelerated electron population as a simple power law, N(E)\\propto {E}-p for p≳ 2. However, in standard Fermi shock acceleration, a substantial fraction of the swept-up particles do not enter the acceleration process at all. Additionally, if acceleration is efficient, then the nonlinear back-reaction of accelerated particles on the shock structure modifies the shape of the nonthermal tail of the particle spectra. Both of these modifications to the standard synchrotron afterglow impact the luminosity, spectra, and temporal variation of the afterglow. To examine the effects of including thermal particles and nonlinear particle acceleration on afterglow emission, we follow a hydrodynamical model for an afterglow jet and simulate acceleration at numerous points during the evolution. When thermal particles are included, we find that the electron population is at no time well fitted by a single power law, though the highest-energy electrons are; if the acceleration is efficient, then the power-law region is even smaller. Our model predicts hard–soft–hard spectral evolution at X-ray energies, as well as an uncoupled X-ray and optical light curve. Additionally, we show that including emission from thermal particles has drastic effects (increases by factors of 100 and 30, respectively) on the observed flux at optical and GeV energies. This enhancement of GeV emission makes afterglow detections by future γ-ray observatories, such as CTA, very likely.
NASA Astrophysics Data System (ADS)
Brizard, Alain J.
2017-08-01
The nonlinear (full-f) electromagnetic gyrokinetic Vlasov-Maxwell equations are derived in the parallel-symplectic representation from an Eulerian gyrokinetic variational principle. The gyrokinetic Vlasov-Maxwell equations are shown to possess an exact energy conservation law, which is derived by the Noether method from the gyrokinetic variational principle. Here, the gyrocenter Poisson bracket and the gyrocenter Jacobian contain contributions from the perturbed magnetic field. In the full-f formulation of the gyrokinetic Vlasov-Maxwell theory presented here, the gyrocenter parallel-Ampère equation contains a second-order contribution to the gyrocenter current density that is derived from the second-order gyrocenter ponderomotive Hamiltonian.
NASA Astrophysics Data System (ADS)
Bass, E. M.; Waltz, R. E.
2013-01-01
The unstable spectrum of Alfvén eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfvén eigenmode (RSAE) at toroidal mode number n =3 is mapped. The RSAE second harmonic and an unstable beta-induced Alfvén eigenmode (BAE) are simultaneously tracked alongside the primary RSAE. An observed twist in the eigenmode pattern, caused mostly by shear in the driving EP profile, is shown through artificially varying the E ×B rotational velocity shear to depend generally on shear in the local wave phase velocity. Coupling to the BAE and to the toroidal Alfvén eigenmode limit the RSAE frequency sweeps at the lower and upper end, respectively. While the present fully gyrokinetic model (including thermal ions and electrons) constitutes the best treatment of compressibility physics available, the BAE frequency is overpredicted by about 20% against experiment here and is found to be sensitive to energetic beam ion pressure. The RSAE frequency is more accurately matched except when it is limited by the BAE. Simulations suggest that the experiment is very close to marginal AE stability at points of RSAE-BAE coupling. A recipe for comparing the radial profile of quasilinear transport flux from local modes to that from global modes paves the way for the development of a stiff (critical gradient) local AE transport model based on local mode stability thresholds.
Nonlinear effects near the particle resonance
NASA Astrophysics Data System (ADS)
Palous, J.
1980-07-01
The nonlinear behavior of stellar orbits near the particle resonance is described. For the rotation speed of the spiral structure the value of 20 km/s per kpc is used which was derived elsewhere (Palous et al., 1977). This new value draws attention to the orbits approaching the corotation from the distant peripheries of the stellar system. These orbits exhibit near the damped particle resonance a leap-frogging motion. The maximum of the response density is near the points L1 and L2 and it is slightly shifted in the direction opposite to that of galactic rotation.
Nonlinear electrophoresis of ideally polarizable particles
NASA Astrophysics Data System (ADS)
Figliuzzi, Bruno; Chan, Wai Hong Ronald; Buie, Cullen R.
2013-11-01
We focus in this presentation on the nonlinear electrophoresis of ideally polarizable particles. At high applied voltages, significant ionic exchanges occur between the EDL which surrounders the particle and the bulk solution. In this situation, the velocity field, the electric potential and the ionic concentration at the immediate vicinity of the particle are described by a complicated set of coupled nonlinear partial differential equations. These equations are classically considered in the limit of a weak applied field, which enables further analytical progress (Khair and Squires, Phys. Fluids, 2010). However, in the general case, the equation governing the electrophoretic motion of the particle must be solved numerically. In this study, we rely on a numerical approach to determine the electric potential, ionic concentration and velocity field in the bulk solution surrounding the particle. The numerical simulations use a pseudo-spectral which was used successfully by Chu and Bazant to determine the electric potential and the ionic concentration around an ideally polarizable metallic sphere (Physical Review E, 2006). Our numerical model also incorporates the steric model developed by Kilic et al. in 2007 to account for crowding effects in the electric double layer.
NASA Astrophysics Data System (ADS)
Sonnino, G.
2011-03-01
Fully ionized L-mode tokamak plasmas in the fully collisional (Pfirsch-Schlüter) and in the low-collisional (banana) nonlinear transport regimes are analyzed. We derive the expressions for particles and heat losses together with the steady-state particle distribution functions in the several collisional transport regimes. The validity of the nonlinear closure equations, previously derived, has been indirectly tested by checking that the obtained particle distribution functions are indeed solutions of the nonlinear, steady-state, Vlasov-Landau gyro-kinetic equations. A quite encouraging result is the fact that, for L-mode tokamak plasmas a dissymmetry appears between the ion and electron transport coefficients: the latter submits to a nonlinear correction, which makes the radial electron coefficients much larger than the former. In particular we show that when the L-mode JET plasma is out of the linear region, the Pfirsch-Schlüter electron transport coefficients are corrected by an amplification factor, which may reach values of order 102. Such a correction is absent for ions. On the contrary, in the banana regime, the ion transport coefficients are increased by a factor 2 and the nonlinear corrections for electrons are negligible. These results are in line with experiments.
Optical nonlinearities in carbon black particles
NASA Astrophysics Data System (ADS)
Mansour, Kamjou; Van Stryland, Eric W.; Soileau, M. J.
1990-10-01
We have characterized the nonlinear optical properties of carbon black particles in liquids and layers deposited on glass. We find that the limiting is dependent on the energy density (fluence) and that the material changes from a linear absorber to a nonlinear scatterer for fluence levels 0.2 J/cm2 and 0.38 J/cm2 for 0.532 jim, 14 ns and 1.064 pm, 20 ns laser pulses respectively. In this paper, we will discuss the possible mechanisms that have been proposed to explain the nonlinear scattering. These mechanisms are plasma formation, micro-bubble formation and change in index of refraction of the liquid surrounding the particles. We will show through a series of experiments that plasma formation is consistent with all of the experimental results while bubble formation may influence the limiting behavior at fluence levels substantially above the limiting threshold. In this model, the microscopic carbon particles are heated by linear absorption to a temperature at which a plasma can be created by the optical field. These microplasmas rapidly expand, thus scattering the incident light and limiting the transmittance.
NASA Astrophysics Data System (ADS)
Ku, S.; Chang, C.-S.; Adams, M.; Cummings, J.; Hinton, F.; Keyes, D.; Klasky, S.; Lee, W.; Lin, Z.; Parker, S.; CPES Team
2006-09-01
A gyrokinetic neoclassical solution for a diverted tokamak edge plasma has been obtained for the first time using the massively parallel Jaguar XT3 computer at Oak Ridge National Laboratory. The solutions show similar characteristics to the experimental observations: electric potential is positive in the scrape-off layer and negative in the H-mode layer, and the parallel rotation is positive in the scrape-off layer and at the inside boundary of the H-mode layer. However, the solution also makes a new physical discovery that there is a strong ExB convective flow in the scrape-off plasma. A general introduction to the edge simulation problem is also presented.
Adams, Mark; Chang, C. S.; Cummings, J.; Hinton, F.; Keyes, David E; Klasky, Scott A; Ku, S.; Lee, W. W.; Lin, Z.; Parker, Scott; CPES Team, the
2006-01-01
A gyrokinetic neoclassical solution for a diverted tokamak edge plasma has been obtained for the first time using the massively parallel Jaguar XT3 computer at Oak Ridge National Laboratory. The solutions show similar characteristics to the experimental observations: electric potential is positive in the scrape-off layer and negative in the H-mode layer, and the parallel rotation is positive in the scrape-off layer and at the inside boundary of the H-mode layer. However, the solution also makes a new physical discovery that there is a strong ExB convective flow in the scrape-off plasma. A general introduction to the edge simulation problem is also presented.
Free Energy Cascade in Gyrokinetic Turbulence
Banon Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-02-04
In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.
Shear-Alfven waves in gyrokinetic plasmas
Lee, W. W.; Lewandowski, J. L. V.; Hahm, T. S.; Lin, Z.
2001-10-01
It is found that the thermal fluctuation level of the shear-Alfven waves in a gyrokinetic plasma is dependent on plasma {beta}((equivalent to)c{sub s}{sup 2}/v{sub A}{sup 2}), where c{sub s} is the ion acoustic speed and v{sub A} is the Alfven velocity. This unique thermodynamic property based on the fluctuation--dissipation theorem is verified in this paper using a new gyrokinetic particle simulation scheme, which splits the particle distribution function into the equilibrium part as well as the adiabatic and nonadiabatic parts. The numerical implication of this property is discussed.
Nonlinear Frequency Chirping of β-induced Alfven Eigenmode
NASA Astrophysics Data System (ADS)
Zhang, Huasen
2012-03-01
The β-induced Alfven eigenmode (BAE) have been observed in many tokamaks. The BAE oscillates with the GAM frequency φ0, and therefore, has strong interactions with both thermal and energetic particles. In this work, linear gyrokinetic particle simulations show that nonperturbative contributions by energetic particles and kinetic effects of thermal particles modify BAE mode structure and frequency relative to the MHD theory. Gyrokinetic simulations have been verified by theory-simulation comparison and by benchmark with MHD-gyrokinetic hybrid simulation. Nonlinear simulations show that the unstable BAE saturates due to nonlinear wave-particle interactions with thermal and energetic particles. Wavelet analysis shows that the mode frequency chirping occurs in the absence of sources and sinks, thus it complements the standard ``bump-on-tail'' paradigm for the frequency chirping of Alfven eigenmodes. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of coherent structures in the energetic particle phase space of (ζ,φd) with toroidal angle ζ and precessional frequency φd. The dynamics of the coherent structures is controlled by the formation and destruction of phase space islands of energetic particles in the canonical variables of (ζ,Pζ) with canonical angular momentum Pζ. Our studies use the gyrokinetic toroidal code (GTC) recently upgraded with a comprehensive formulation for simulating kinetic-MHD processes. In collaborations with GTC team and SciDAC GSEP Center.
Continuum Gyrokinetic Edge New Technology
Dorr, M. R.; Hittinger, J. A.; Dorf, M.; Cohen, R.; Ghosh, D.; Lee, W.; Reynolds, C.
2016-05-02
COGENT is a simulation code that models the plasma evolution in the edge region of a tokamak fusion reactor, from the open field line scrape-off layer, across the separatrix, and into the core. The model is based on the 4D gyrokinetic closure of the kinetic equations for a plasma coupled to an electrostatic potential field. The background magnetic field is prescribed either analytically or generated from experimental data, and the grid is aligned with magnetic flux surfaces. Multiple collision operator options are provided, from Krook to fully nonlinear Fokker-Planck.
Linear and nonlinear dynamics of Alfven modes driven by energetic particles
Vlad, G.; Briguglio, S.; Romanelli, F.; Zonca, F.
1996-12-31
The understanding of the stability of global Alfven eigenmodes in the presence of energetic particles has been recognized to be very important in evaluating the success of the next step generation of thermonuclear fusion devices. The mode stability depends strongly on the spatial localization of the mode, being typically damped in the internal part of the discharge by Ion Landau Damping and being driven unstable if the mode is localized around 9 the maximum value of the pressure gradient of the energetic particles. Thus, the fully 2-D structure of the eigenmode is required in order to properly assess the issue of global Alfven modes stability, as, e.g., the Toroidal Alfven Eigenmodes (TAE). Furthermore, for realistic parameters, the effect of the drive and damping terms, as well as finite orbit widths of energetic particles and bulk-ions finite Larmor radius effects, cannot be treated perturbatively but should be considered at the same order as that at which toroidicity enters. The linear stability of TAE, Kinetic TAE (KTAE), and Energetic Particle continuum Mode (EPM) is studied using a code which solves the two-dimensional mode structure and global stability, in the limit of high toroidal mode number n, using a two spatial-scale WKBJ formalism treating drive and damping terms non-perturbatively. The nonlinear dynamics of these modes is studied by means a hybrid MHD-gyrokinetic particle simulation code. The code is able to treat low and moderately low toroidal mode number n. Nonperturbative treatment of the finite drift-orbit effects has been found to be crucial. It has been found that for typical parameters, the KTAE is indeed more unstable than the TAR In particular, in the nonlinear phase, the EPM is found to be particularly dangerous, leading to the expulsion of the energetic particles from the plasma column.
Gyrokinetic Turbulence Simulations for Stellarators
NASA Astrophysics Data System (ADS)
Merz, F.; Xanthopoulos, P.; Gorler, T.; Jenko, F.; Mikkelsen, D.
2007-11-01
While there is an abundance of publications on plasma microturbulence in tokamaks, not much is presently known about its character in nonaxisymmetric devices. The present work constitutes the first attempt to investigate turbulent transport in modern stellarators, using the gyrokinetic turbulence code Gene and realistic magnetic equilibria. First, linear and nonlinear gyrokinetic simulations of ion-temperature-gradient (ITG) and trapped electron modes are presented for the optimized stellarator Wendelstein 7-X which is currently under construction at Greifswald, Germany. The newly developed code Tracer -- based on field line tracing -- is employed to extract the required geometric information from the MHD equilibria [Phys. Plasmas 13, 092301 (2006)]. Extensive linear studies reveal substantial differences with respect to axisymmetric geometry [Phys. Plasmas 14, 042501 (2007)]. Nonlinear ITG simulations are also presented [Phys. Rev. Lett., in print]. Several fundamental features are discussed, including the role of zonal flows for turbulence saturation, the resulting flux-gradient relationship and the co-existence of ITG modes with trapped ion modes in the saturated state. Similar studies will be presented for the stellarator experiment NCSX at PPPL with the aim to comprehend the effects of quasi-axisymmetric geometry on the properties - both linear and nonlinear - of various microinstabilities.
Nonlinear electrophoresis of ideally polarizable particles
NASA Astrophysics Data System (ADS)
Figliuzzi, B.; Chan, W. H. R.; Moran, J. L.; Buie, C. R.
2014-10-01
We focus in this paper on the nonlinear electrophoresis of ideally polarizable particles. At high applied voltages, significant ionic exchange occurs between the electric double layer, which surrounds the particle, and the bulk solution. In addition, steric effects due to the finite size of ions drastically modify the electric potential distribution in the electric double layer. In this situation, the velocity field, the electric potential, and the ionic concentration in the immediate vicinity of the particle are described by a complicated set of coupled nonlinear partial differential equations. In the general case, these equations must be solved numerically. In this study, we rely on a numerical approach to determine the electric potential, the ionic concentration, and the velocity field in the bulk solution surrounding the particle. The numerical simulations rely on a pseudo-spectral method which was used successfully by Chu and Bazant [J. Colloid Interface Sci. 315(1), 319-329 (2007)] to determine the electric potential and the ionic concentration around an ideally polarizable metallic sphere. Our numerical simulations also incorporate the steric model developed by Kilic et al. [Phys. Rev. E 75, 021502 (2007)] to account for crowding effects in the electric double layer, advective transport, and for the presence of a body force in the bulk electrolyte. The simulations demonstrate that surface conduction significantly decreases the electrophoretic mobility of polarizable particles at high zeta potential and at high applied electric field. Advective transport in the electric double layer and in the bulk solution is also shown to significantly impact surface conduction.
Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments
Wang, W.X.; Lin, Z.; Tang, W.M.; Lee, W.W.; Ethier, S.; Lewandowski, J.L.V.; Rewoldt, G.; Hahm, T.S.; Manickam, J.
2006-01-01
A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Predictive Gyrokinetic Transport Simulations and Application of Synthetic Diagnostics
NASA Astrophysics Data System (ADS)
Candy, J.
2009-11-01
In this work we make use of the gyrokinetic transport solver TGYRO [1] to predict kinetic plasma profiles consistent with energy and particle fluxes in the DIII-D tokamak. TGYRO uses direct nonlinear and neoclassical fluxes calculated by the GYRO and NEO codes, respectively, to solve for global, self-consistent temperature and density profiles via Newton iteration. Previous work has shown that gyrokinetic simulation results for DIII-D discharge 128913 match experimental data rather well in the plasma core, but with a discrepancy in both fluxes and fluctuation levels emerging closer to the edge (r/a > 0.8). The present work will expand on previous results by generating model predictions across the entire plasma core, rather than at isolated test radii. We show that TGYRO predicts temperature and density profiles in good agreement with experimental observations which simultaneously yield near-exact (to within experimental uncertainties) agreement with power balance calculations of the particle and energy fluxes for r/a <=0.8. Moreover, we use recently developed synthetic diagnostic algorithms [2] to show that TGYRO also predicts density and electron temperature fluctuation levels in close agreement with experimental measurements across the simulated plasma volume. 8pt [1] J. Candy, C. Holland, R.E. Waltz, M.R. Fahey, and E. Belli, ``Tokamak profile prediction using direct gyrokinetic and neoclassical simulation," Phys. Plasmas 16, 060704 (2009). [2] C. Holland, A.E. White, G.R. McKee, M.W. Shafer, J. Candy, R.E. Waltz, L. Schmitz, and G.R. Tynan, ``Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence," Phys. Plasmas 16, 052301 (2009).
Observational signatures of nonlinear magnetotail particle dynamics
NASA Technical Reports Server (NTRS)
Chen, James; Burkhart, Grant R.; Huang, Cheryl Y.
1990-01-01
It has been predicted that the nonlinear particle dynamics in the magnetotail leads to a class of resonance structures in the quiet-time ion distribution functions in the central plasma sheet (CPS). These structures exhibit a scaling law of H to the 1/4 power. The first identification of such a scaling law in quiet-time CPS distribution functions obtained aboard ISEE 1 is reported. A method is proposed which uses the observed resonance structures to determine the quiet-time current sheet thickness based on a measurement of the distribution function and magnetic field obtained by one satellite.
Particle systems and nonlinear Landau damping
Villani, Cédric
2014-03-15
Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov–Arnold–Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.
Particle systems and nonlinear Landau dampinga)
NASA Astrophysics Data System (ADS)
Villani, Cédric
2014-03-01
Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov-Arnold-Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.
Intercode comparison of gyrokinetic global electromagnetic modes
Görler, T. Tronko, N.; Hornsby, W. A.; Bottino, A.; Sonnendrücker, E.; Kleiber, R.; Norscini, C.; Grandgirard, V.; Jenko, F.
2016-07-15
Aiming to fill a corresponding lack of sophisticated test cases for global electromagnetic gyrokinetic codes, a new hierarchical benchmark is proposed. Starting from established test sets with adiabatic electrons, fully gyrokinetic electrons, and electrostatic fluctuations are taken into account before finally studying the global electromagnetic micro-instabilities. Results from up to five codes involving representatives from different numerical approaches as particle-in-cell methods, Eulerian and Semi-Lagrangian are shown. By means of spectrally resolved growth rates and frequencies and mode structure comparisons, agreement can be confirmed on ion-gyro-radius scales, thus providing confidence in the correct implementation of the underlying equations.
Gyrokinetic modelling of stationary electron and impurity profiles in tokamaks
Skyman, A. Tegnered, D. Nordman, H. Strand, P.
2014-09-15
Particle transport due to Ion Temperature Gradient (ITG)/Trapped Electron Mode (TEM) turbulence is investigated using the gyrokinetic code GENE. Both a reduced quasilinear treatment and nonlinear simulations are performed for typical tokamak parameters corresponding to ITG dominated turbulence. The gyrokinetic results are compared and contrasted with results from a computationally efficient fluid model. A selfconsistent treatment is used, where the stationary local profiles are calculated corresponding to zero particle flux simultaneously for electrons and trace impurities. The scaling of the stationary profiles with magnetic shear, safety factor, electron-to-ion temperature ratio, collisionality, toroidal sheared rotation, plasma β, triangularity, and elongation is investigated. In addition, the effect of different main ion mass on the zero flux condition is discussed. The electron density gradient can significantly affect the stationary impurity profile scaling. It is therefore expected that a selfconsistent treatment will yield results more comparable to experimental results for parameter scans where the stationary background density profile is sensitive. This is shown to be the case in scans over magnetic shear, collisionality, elongation, and temperature ratio, for which the simultaneous zero flux electron and impurity profiles are calculated. A slight asymmetry between hydrogen, deuterium, and tritium with respect to profile peaking is obtained, in particular, for scans in collisionality and temperature ratio.
Gyrokinetic simulation of microturbulence in EAST tokamak
NASA Astrophysics Data System (ADS)
Xiao, Yong; Zhang, Taige; Zhao, Chen
2014-10-01
A complete understanding of anomalous transport is critical for designing future magnetic fusion reactors. It is generally accepted that the micro-scale turbulence leads to anomalous transport. For low beta toroidal plasmas, the electrostatic modes may dominate and ion temperature gradient (ITG) mode and trapped electron mode (TEM) are two very important candidates accounting for ion and electron turbulent transport respectively. Recently the massively parallel gyrokinetic simulation has emerged as a major tool to investigate the nonlinear physics of the turbulent transport. The newly-developed capabilities enable the gyrokinetic code GTC to simulate the turbulent transport for real tokamak plasma shape and profiles. These capabilities include a new gyrokinetic Poisson solver and zonal flow solver suitable for general plasma shape and profiles, improvements on the conventional four-point gyroaverage and newly-developed nonuniform initial marker loading. The GTC code is now able to import experimental plasma profiles and equilibrium magnetic field that come from the EFIT or TRANSP equilibrium reconstruction. Linear and nonlinear gyrokinetic simulations are carried out with the new capabilities in GTC for the electron coherent mode (ECM) recently observed in the EAST tokamak (EAST shot # 38300). We found that in the pedestal region with strong electron temperature gradient, the unstable waves propagate in the electron diamagnetic direction, showing a trapped electron mode (TEM) feature. It is also found in the collisionless limit, the linear mode frequency is higher than that from the experiment.
Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.
Xu, X Q
2008-07-01
We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.
T.S. Hahm; Z. Lin; P.H. Diamond; G. Rewoldt; W.X. Wang; S. Ethier; O. Gurcan; W.W. Lee; W.M. Tang
2004-12-21
An integrated program of gyrokinetic particle simulation and theory has been developed to investigate several outstanding issues in both turbulence and neoclassical physics. Gyrokinetic particle simulations of toroidal ion temperature gradient (ITG) turbulence spreading using the GTC code and its related dynamical model have been extended to the case with radially increasing ion temperature gradient, to study the inward spreading of edge turbulence toward the core. Due to turbulence spreading from the edge, the turbulence intensity in the core region is significantly enhanced over the value obtained from simulations of the core region only. Even when the core gradient is within the Dimits shift regime (i.e., self-generated zonal flows reduce the transport to a negligible value), a significant level of turbulence and transport is observed in the core due to spreading from the edge. The scaling of the turbulent front propagation speed is closer to the prediction from our nonlinear diffusion model than one based on linear toroidal coupling. A calculation of ion poloidal rotation in the presence of sharp density and toroidal angular rotation frequency gradients from the GTC-Neo particle simulation code shows that the results are significantly different from the conventional neoclassical theory predictions. An energy conserving set of a fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to edge turbulence, is being derived via the phase-space action variational Lie perturbation method. Our generalized ordering takes the ion poloidal gyroradius to be on the order of the radial electric field gradient length.
Linear gyrokinetic theory for kinetic magnetohydrodynamic eigenmodes in tokamak plasmas
NASA Astrophysics Data System (ADS)
Qin, H.; Tang, W. M.; Rewoldt, G.
1999-06-01
A two-dimensional (2D) numerical solution method is developed for the recently derived linear gyrokinetic system which describes arbitrary wavelength electromagnetic perturbations in tokamak plasmas. The system consists of the gyrokinetic equation, the gyrokinetic Poisson equation, and the gyrokinetic moment equation. Since familiar magnetohydrodynamic (MHD) results can be recovered entirely from this gyrokinetic model, and all interesting kinetic effects are intrinsically included, this gyrokinetic system offers an approach for kinetic MHD phenomena which is more rigorous, self-consistent, and comprehensive than the previous hybrid models. Meanwhile, drift type microinstabilities can be also investigated systematically in this theoretical framework. The linear gyrokinetic equation is solved for the distribution function in terms of the perturbed fields by integrating along unperturbed particle orbits. The solution is substituted back into the gyrokinetic moment equation and the gyrokinetic Poisson equation. When the boundary conditions are incorporated, an eigenvalue problem is formed. The resulting numerical code, KIN-2DEM, is applied to kinetic ballooning modes, internal kink modes, and toroidal Alfvén eigenmodes (TAEs). The numerical results are benchmarked against the well-established FULL code [G. Rewoldt, W. M. Tang, and M. S. Chance, Phys. Fluids 25, 480 (1982)], the PEST code [J. Manickam, Nucl. Fusion 24, 595 (1984)], and the NOVA-K code [C. Z. Cheng, Phys. Rep. 211, No. 1 (1992)]. More importantly, kinetic effects on MHD modes can be investigated nonperturbatively. In particular, the kinetic effects of the background plasma on internal kink modes and the hot particle destabilization of TAEs are studied numerically.
Analysis and gyrokinetic simulation of MHD Alfven wave interactions
NASA Astrophysics Data System (ADS)
Nielson, Kevin Derek
The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the
Free energy balance in gyrokinetic turbulence
Banon Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-09-15
Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.
Free energy balance in gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Bañón Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Görler, T.; Jenko, F.
2011-09-01
Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.
Global full-f gyrokinetic simulations of plasma turbulence
NASA Astrophysics Data System (ADS)
Grandgirard, V.; Sarazin, Y.; Angelino, P.; Bottino, A.; Crouseilles, N.; Darmet, G.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, Ph; Jolliet, S.; Latu, G.; Sonnendrücker, E.; Villard, L.
2007-12-01
Critical physical issues can be specifically tackled with the global full-f gyrokinetic code GYSELA. Three main results are presented. First, the self-consistent treatment of equilibrium and fluctuations highlights the competition between two compensation mechanisms for the curvature driven vertical charge separation, namely, parallel flow and polarization. The impact of the latter on the turbulent transport is discussed. In the non-linear regime, the benchmark with the Particle-In-Cell code ORB5 looks satisfactory. Second, the transport scaling with ρ* is found to depend both on ρ* itself and on the distance to the linear threshold. Finally, a statistical steady-state turbulent regime is achieved in a reduced version of GYSELA by prescribing a constant heat source.
NONLINEAR EFFECTS IN PARTICLE TRANSPORT IN STOCHASTIC MAGNETIC FIELDS
Vlad, M.; Spineanu, F.; Croitoru, A.
2015-12-10
Collisional particle transport in stochastic magnetic fields is studied using a semi-analytical method. The aim is to determine the influence of the nonlinear effects that occur in the magnetic field line random walk on particle transport. We show that particle transport coefficients can be strongly influenced by the magnetic line trapping. The conditions that correspond to these nonlinear regimes are determined. We also analyze the effects produced by the space variation of the large-scale magnetic field. We show that an average drift is generated by the gradient of the magnetic field, which strongly increases and reverses its orientation in the nonlinear regime.
Gyrokinetic turbulence simulations at high plasma beta
Pueschel, M. J.; Kammerer, M.; Jenko, F.
2008-10-15
Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for {beta} values up to and beyond the kinetic ballooning threshold. The {beta} scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of {beta} values just below the respective ideal limit. The magnetic transport scales like {beta}{sup 2} and is well described by a Rechester-Rosenbluth-type ansatz.
Beyond linear gyrocenter polarization in gyrokinetic theory
Brizard, Alain J.
2013-09-15
The concept of polarization in gyrokinetic theory is clarified and generalized to include contributions from the guiding-center (zeroth-order) polarization as well as the nonlinear (second-order) gyrocenter polarization. The guiding-center polarization, which appears as the antecedent (zeroth-order) of the standard linear (first-order) gyrocenter polarization, is obtained from a modified guiding-center transformation. The nonlinear gyrocenter polarization is derived either variationally from the third-order gyrocenter Hamiltonian or directly by gyrocenter push-forward method.
Neoclassical physics in full distribution function gyrokinetics
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Diamond, P. H.; Grandgirard, V.; Sarazin, Y.; Abiteboul, J.; Garbet, X.; Ghendrih, Ph.; Latu, G.; Strugarek, A.; Ku, S.; Chang, C. S.
2011-06-01
Treatment of binary Coulomb collisions when the full gyrokinetic distribution function is evolved is discussed here. A spectrum of different collision operators is presented, differing through both the physics that can be addressed and the numerics they are based on. Eulerian-like (semi-Lagrangian) and particle in cell (PIC) (Monte-Carlo) schemes are successfully cross-compared, and a detailed confrontation to neoclassical theory is shown.
Status of Continuum Edge Gyrokinetic Code Physics Development
Xu, X Q; Xiong, Z; Dorr, M R; Hittinger, J A; Kerbel, G D; Nevins, W M; Cohen, B I; Cohen, R H
2005-05-31
We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D ({psi}, {theta}, {epsilon}, {mu}) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in ({nu}{sub {parallel}},{nu}{sub {perpendicular}}) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt|{sub coll} to/from ({epsilon}, {mu}) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassical theory for core plasma parameters; and we study the transition from collisional to collisionless end-loss. In the real X-point geometry, we find that the particles are trapped near outside midplane and in the X-point regions due to the magnetic configurations. The sizes of banana orbits are comparable to the pedestal width and/or the SOL width for energetic trapped particles. The effect of the real X-point geometry and edge plasma conditions on standard neoclassical theory will be evaluated, including a comparison of our 4D code with other kinetic
Higher-order energy-conserving gyrokinetic theory
Mishchenko, Alexey; Brizard, Alain J.
2011-02-15
A higher-order self-consistent energy-conserving gyrokinetic system of equations is derived. It is shown that additional terms appear in the quasineutrality condition. These terms are nonlinear in the electric field. The derivation includes higher-order terms in the gyrokinetic Hamiltonian (needed for the energy conservation) and employs a variational principle that automatically provides all the conservation laws through the Noether theorem. The equations derived here can be applied in certain transition layers such as the stellarator transport barriers caused by the transition between the electron and ion root regimes. The theory may also be of interest for the edge plasma, where the nonlinear terms in the quasineutrality equation could be relevant. The equations derived are simple enough and can readily be used in gyrokinetic codes.
Dispersion of sound in dilute suspensions with nonlinear particle relaxation.
Kandula, Max
2010-03-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of omegatau(d), where omega is the circular frequency and tau(d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction.
Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
NASA Technical Reports Server (NTRS)
Kandula, Max
2010-01-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction
Monte-Carlo finite elements gyrokinetic simulations of Alfven modes in tokamaks
NASA Astrophysics Data System (ADS)
Bottino, Alberto; Biancalani, Alessandro; Palermo, Francesco; Tronko, Natalia
2016-10-01
The global gyrokinetic code ORB5 can simultaneously include electromagnetic perturbations, general ideal MHD axisymmetric equilibria, zonal-flow preserving sources, collisions, and the ability to solve the full core plasma including the magnetic axis. In this work, a Monte Carlo Particle In Cell Finite Element model, starting from a gyrokinetic discrete Lagrangian, is derived and implemented into the ORB5 code. The variations of the Lagrangian are used to obtain the time continuous equations of motion for the particles and the Finite Element approximation of the field equations. The Noether theorem for the semi-discretised system, implies a certain number of conservation properties for the final set of equation. Linear and nonlinear results, concerning Alfvén instabilities, in the presence of an energetic particle population, and microinstabilities, such as electromagnetic ion temperature gradient (ITG) driven modes and kinetic ballooning modes (KBM), will be presented and discussed. Due to losses of energetic particles, Alfvén instabilities can not only affect plasma stability and damage the walls, but also strongly impact the heating efficiency of a fusion reactor and ultimately the possibility of reaching ignition.
Benchmarking finite- β ITG gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Nevins, W. M.; Dimits, A. M.; Candy, J.; Holland, C.; Howard, N.
2016-10-01
We report the results of an electromagnetic gyrokinetic-simulation benchmarking study based on a well-diagnosed ion-temperature-gradient (ITG)-turbulence dominated experimental plasma. We compare the 4x3 matrix of transport/transfer quantities for each plasma species; namely the (a) particle flux, Γa, (b) momentum flux, Πa, (c) energy flux, Qa, and (d) anomalous heat exchange, Sa, with each transport coefficient broken down into: (1) electrostatic (δφ) (2) transverse electromagnetic (δA∥) , and (3) compressional electromagnetic, (δB∥) contributions. We compare realization-independent quantities (correlation functions, spectral densities, etc.), which characterize the fluctuating fields from various gyrokinetic simulation codes. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and by GA under Contract DE-FG03-95ER54309. This work was supported by the U.S. DOE, Office of Science, Fusion Energy Sciences.
Particle flow for nonlinear filters with log-homotopy
NASA Astrophysics Data System (ADS)
Daum, Fred; Huang, Jim
2008-04-01
We describe a new nonlinear filter that is vastly superior to the classic particle filter. In particular, the computational complexity of the new filter is many orders of magnitude less than the classic particle filter with optimal estimation accuracy for problems with dimension greater than 2 or 3. We consider nonlinear estimation problems with dimensions varying from 1 to 20 that are smooth and fully coupled (i.e. dense not sparse). The new filter implements Bayes' rule using particle flow rather than with a pointwise multiplication of two functions; this avoids one of the fundamental and well known problems in particle filters, namely "particle collapse" as a result of Bayes' rule. We use a log-homotopy to derive the ODE that describes particle flow. This paper was written for normal engineers, who do not have homotopy for breakfast.
Global gyrokinetic ion temperature gradient turbulence simulations of ITER
NASA Astrophysics Data System (ADS)
Villard, L.; Angelino, P.; Bottino, A.; Brunner, S.; Jolliet, S.; McMillan, B. F.; Tran, T. M.; Vernay, T.
2013-07-01
Global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence in an ideal MHD ITER equilibrium plasma are performed with the ORB5 code. The noise control and field-aligned Fourier filtering procedures implemented in ORB5 are essential in obtaining numerically healthy results with a reasonable amount of computational effort: typical simulations require 109 grid points, 109 particles and, despite a particle per cell ratio of unity, achieve a signal to noise ratio larger than 50. As compared with a circular concentric configuration with otherwise similar parameters (same ρ* = 1/720), the effective heat diffusivity is considerably reduced for the ITER MHD equilibrium. A self-organized radial structure appears, with long-lived zonal flows (ZF), modulating turbulence heat transport and resulting in a corrugated temperature gradient profile. The ratio of long-lived ZF to the fluctuating ZF is markedly higher for the ITER MHD equilibrium as compared with circular configurations, thereby producing a more effective ITG turbulence suppression, in spite of a higher linear growth rate. As a result, the nonlinear critical temperature gradient, R/LTcrit,NL, is about twice the linear critical temperature gradient, R/LTcrit,lin. Moreover, the heat transport stiffness above the nonlinear threshold is considerably reduced as compared with circular cases. Plasma elongation is probably one of the essential causes of this behaviour: indeed, undamped ZF residual levels and geodesic acoustic mode damping are both increasing with elongation. Other possible causes of the difference, such as magnetic shear profile effects, are also investigated.
Discrete particle noise in a nonlinearly saturated plasma
NASA Astrophysics Data System (ADS)
Jenkins, Thomas; Lee, W. W.
2006-04-01
Understanding discrete particle noise in an equilibrium plasma has been an important topic since the early days of particle-in- cell (PIC) simulation [1]. In this paper, particle noise in a nonlinearly saturated system is investigated. We investigate the usefulness of the fluctuation-dissipation theorem (FDT) in a regime where drift instabilities are nonlinearly saturated. We obtain excellent agreement between the simulation results and our theoretical predictions of the noise properties. It is found that discrete particle noise always enhances the particle and thermal transport in the plasma, in agreement with the second law of thermodynamics. [1] C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation, McGraw-Hill, New York (1985).
Effects of collisions on conservation laws in gyrokinetic field theory
NASA Astrophysics Data System (ADS)
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2014-10-01
In gyrokinetic field theory, the gyrokinetic Vlasov equation, Poisson's equation, and Ampere's law are all obtained from the Lagrangian formulation, and conservation laws of energy and momentum for collisionless magnetized plasmas are derived by applying the Noether's theorem. In this work, effects of collisions on conservation laws are investigated by using the gyrokinetic Boltzmann equation which includes Landau's collision operator represented in the gyrocenter coordinates. Particle, energy, and momentum transport equations including collisional transport fluxes are systematically derived by modifying Noether's theorem. Then, the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include both collisional and turbulent transport fluxes which agree with those derived from the conventional recursive formulation with the WKB representation.
Nonlinearly interacting trapped particle solitons in collisionless plasmas
NASA Astrophysics Data System (ADS)
Mandal, Debraj; Sharma, Devendra
2016-02-01
The formulation of collective waves in collisionless plasmas is complicated by the kinetic effects produced by the resonant particles, capable of responding to the smallest of the amplitude disturbance. The dispersive plasma manifests this response by generating coherent nonlinear structures associated with phase-space vortices, or holes, at very small amplitudes. The nonlinear interaction between solitary electron phase-space holes is studied in the electron acoustic regime of a collisionless plasma using Vlasov simulations. Evolution of the analytic trapped particle solitary solutions is examined, observing them propagate stably, preserve their identity across strong mutual interactions in adiabatic processes, and display close correspondence with observable processes in nature.
Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments
Wang, W. X.; Lin, Z.; Tang, W. M.; Lee, W. W.; Ethier, S.; Lewandowski, J. L. V.; Rewoldt, G.; Hahm, T. S.; Manickam, J.
2006-09-15
A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Probabilistic approach to nonlinear wave-particle resonant interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2017-02-01
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution. In this equation, effects of charged-particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
Generalized nonlinear Proca equation and its free-particle solutions
NASA Astrophysics Data System (ADS)
Nobre, F. D.; Plastino, A. R.
2016-06-01
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schrödinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ ^{μ }(ěc {x},t), involves an additional field Φ ^{μ }(ěc {x},t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E2 = p2c2 + m2c4 for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed.
Gyrokinetic simulations of momentum transport and fluctuation spectra for ICRF-heated L-Mode plasmas
NASA Astrophysics Data System (ADS)
Sierchio, J. M.; White, A. E.; Howard, N. T.; Sung, C.; Ennever, P.; Porkolab, M.; Candy, J.
2014-10-01
We examine ICRF-heated L-mode plasmas in Alcator C-Mod, with differing momentum transport (hollow vs. peaked radial profiles of intrinsic toroidal rotation) but similar heat and particle transport. Nonlinear gyrokinetic simulations of heat and particle transport with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] have previously been compared with these experiments [White et al., Phys. Plasmas 20, 056106 (2013); Howard et al. PPCF submitted (2014)] as part of an effort to validate the gyrokinetic model for core turbulent transport in C-Mod plasmas. To further test the model for these plasmas, predicted core turbulence characteristics such as fluctuation spectra will be compared with experiment. Using synthetic diagnostics for the CECE, reflectometry, and PCI systems at C-Mod, synthetic spectra and, when applicable, fluctuation amplitudes, are generated. We compare these generated results with fluctuation measurements from the experiment. We also report the momentum transport results from simulations of these plasmas and compare them to experiment. Supported by USDoE award DE-FC02-99ER54512.
On the Existence of Canonical Gyrokinetic Variables for Chaotic Magnetic Fields
Nicolini, Piero; Tessarotto, Massimo
2008-12-31
The gyrokinetic description of particle dynamics faces a basic difficulty when a special type of canonical variables is sought, i.e., the so-called gyrokinetic canonical variables. These are defined in such a way that two of them are respectively identified with the gyrophase-angle, describing the fast particle gyration motion around magnetic field lines, and its canonically conjugate momentum. In this paper we intend to discuss the conditions of existence for these variables.
Nonlinear dynamics of beta-induced Alfven eigenmode in tokamak
Zhang, H. S.; Lin, Z.; Deng, W.; Holod, I.; Wang, Z. X.; Xiao, Y.; Zhang, W. L.
2013-01-15
The beta-induced Alfven eigenmode (BAE) excited by energetic particles in toroidal plasmas is studied in the global gyrokinetic simulations. It is found that the nonlinear BAE dynamics depends on the deviation from the marginality. In the strongly driven case, the mode exhibits a bursting state with fast and repetitive chirping. The nonlinear saturation is determined by the thermal ion nonlinearity and has no clear dependence on the linear growth rate. In the weakly driven case, the mode reaches a nearly steady state with small frequency chirping. The nonlinear dynamics is dominated by the energetic particle nonlinearity. In both cases, the nonlinear intensity oscillation and frequency chirping are correlated with the evolution of the coherent structures in the energetic particle phase space. Due to the radial variation of the mode amplitude and the radially asymmetric guiding center dynamics, the wave-particle interaction in the toroidal geometry is much more complex than the conventional one-dimensional wave-particle interaction paradigm.
Hager, Robert; Lang, Jianying; Chang, C. S.; ...
2017-05-24
As an alternative option to kinetic electrons, the gyrokinetic total-f particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons. Here, two representative long wavelength modes, shear Alfven waves and resistive tearing modes, are verified in cylindrical and toroidal magnetic field geometries.
Highly nonlinear solitary waves in chains of ellipsoidal particles.
Ngo, Duc; Khatri, Devvrath; Daraio, Chiara
2011-08-01
We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated.
The theory of gyrokinetic turbulence: A multiple-scales approach
NASA Astrophysics Data System (ADS)
Plunk, Gabriel Galad
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics -- such as turbulence, universality, self-organization and dynamic criticality -- which are found in physical systems that are driven far from thermodynamic equilibrium. One such system is of particular importance, as it is central in the development of fusion energy -- this system is the turbulent plasma found in magnetically confined fusion device. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in magnetized plasmas. I present three projects, based on the work of me and my collaborators, which take a tour of different aspects and approaches to the gyrokinetic turbulence problem. I begin with the fundamental theory of gyrokinetics, and a novel formulation of its extension to the equations for mean-scale transport -- the equations which must be solved to determine the performance of Magnetically confined fusion devices. The results of this work include (1) the equations of evolution for the mean scale (equilibrium) density, temperature and magnetic field of the plasma, (2) a detailed Poynting's theorem for the energy balance and (3) the entropy balance equations. The second project presents gyrokinetic secondary instability theory as a mechanism to bring about saturation of the basic instabilities that drive gyrokinetic turbulence. Emphasis is put on the ability for this analytic theory to predict basic properties of the nonlinear state, which can be applied to a mixing length phenomenology of transport. The results of this work include (1) an integral equation for the calculation of the growth rate of the fully gyrokinetic secondary instability with finite Larmor radius (FLR) affects included exactly, (2) the demonstration of the robustness of the secondary instability at fine scales (krhoi for ion temperature gradient (ITG) turbulence and krhoe ≪ 1 for electron temperature
Report of the working group on single-particle nonlinear dynamics
NASA Astrophysics Data System (ADS)
Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.
1999-04-01
The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of acclerators. (AIP)
Weakly nonlinear electrophoresis of a highly charged colloidal particle
NASA Astrophysics Data System (ADS)
Schnitzer, Ory; Zeyde, Roman; Yavneh, Irad; Yariv, Ehud
2013-05-01
At large zeta potentials, surface conduction becomes appreciable in thin-double-layer electrokinetic transport. In the linear weak-field regime, where this effect is quantified by the Dukhin number, it is manifested in non-Smoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv ["Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction," Phys. Rev. E 86, 021503 (2012), 10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of spherical-particle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the far-field conditions, representing a non-uniformity of the weak-field approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using inner-outer asymptotic expansions in the spirit of Acrivos and Taylor ["Heat and mass transfer from single spheres in Stokes flow," Phys. Fluids 5, 387 (1962), 10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zeta-potential inhomogeneity, animated by concentration polarization, on electro-osmosis and diffuso-osmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particle-layer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.
Particle swarm optimization for complex nonlinear optimization problems
NASA Astrophysics Data System (ADS)
Alexandridis, Alex; Famelis, Ioannis Th.; Tsitouras, Charalambos
2016-06-01
This work presents the application of a technique belonging to evolutionary computation, namely particle swarm optimization (PSO), to complex nonlinear optimization problems. To be more specific, a PSO optimizer is setup and applied to the derivation of Runge-Kutta pairs for the numerical solution of initial value problems. The effect of critical PSO operational parameters on the performance of the proposed scheme is thoroughly investigated.
Sideband growth in nonlinear Landau wave-particle interaction.
NASA Technical Reports Server (NTRS)
Brinca, A. L.
1972-01-01
The distortion of the electron velocity distribution caused by a large amplitude Landau wave is determined analytically for the initial-value problem. The resulting stability of electrostatic perturbations impressed on the evolving plasma is studied. Narrow sidebands of the applied frequency experience consecutive growths of large magnitude during the early stages of the nonlinear wave-particle interaction. The significance of the derived results to both wave propagation experiments and triggered VLF emissions in the magnetosphere is discussed.
Nonlinear Statistical Signal Processing: A Particle Filtering Approach
Candy, J
2007-09-19
A introduction to particle filtering is discussed starting with an overview of Bayesian inference from batch to sequential processors. Once the evolving Bayesian paradigm is established, simulation-based methods using sampling theory and Monte Carlo realizations are discussed. Here the usual limitations of nonlinear approximations and non-gaussian processes prevalent in classical nonlinear processing algorithms (e.g. Kalman filters) are no longer a restriction to perform Bayesian inference. It is shown how the underlying hidden or state variables are easily assimilated into this Bayesian construct. Importance sampling methods are then discussed and shown how they can be extended to sequential solutions implemented using Markovian state-space models as a natural evolution. With this in mind, the idea of a particle filter, which is a discrete representation of a probability distribution, is developed and shown how it can be implemented using sequential importance sampling/resampling methods. Finally, an application is briefly discussed comparing the performance of the particle filter designs with classical nonlinear filter implementations.
Benchmarking of the Gyrokinetic Microstability Codes GYRO, GS2, and GEM
NASA Astrophysics Data System (ADS)
Bravenec, Ronald; Chen, Yang; Wan, Weigang; Parker, Scott; Candy, Jeff; Barnes, Michael; Howard, Nathan; Holland, Christopher; Wang, Eric
2012-10-01
The physics capabilities of modern gyrokinetic microstability codes are now so extensive that they cannot be verified fully for realistic tokamak plasmas using purely analytic approaches. Instead, verification (demonstrating that the codes correctly solve the gyrokinetic-Maxwell equations) must rely on benchmarking (comparing code results for identical plasmas and physics). Benchmarking exercises for a low-power DIII-D discharge at the mid-radius have been presented recently for the Eulerian codes GYRO and GS2 [R.V. Bravenec, J. Candy, M. Barnes, C. Holland, Phys. Plasmas 18, 122505 (2011)]. This work omitted ExB flow shear, but we include it here. We also present GYRO/GS2 comparisons for a high-power Alcator C-Mod discharge. To add further confidence to the verification exercises, we have recently added the particle-in-cell (PIC) code GEM to the efforts. We find good agreement of linear frequencies between GEM and GYRO/GS2 for the DIII-D plasma. We also present preliminary nonlinear comparisons. This benchmarking includes electromagnetic effects, plasma shaping, kinetic electrons and one impurity. In addition, we compare linear results among the three codes for the steep-gradient edge region of a DIII-D plasma between edge-localized modes.
A verification of the gyrokinetic microstability codes GEM, GYRO, and GS2
Bravenec, R. V.; Chen, Y.; Wan, W.; Parker, S.; Candy, J.
2013-10-15
A previous publication [R. V. Bravenec et al., Phys. Plasmas 18, 122505 (2011)] presented favorable comparisons of linear frequencies and nonlinear fluxes from the Eulerian gyrokinetic codes gyro[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and gs2[W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)]. The motivation was to verify the codes, i.e., demonstrate that they correctly solve the gyrokinetic-Maxwell equations. The premise was that it is highly unlikely for both codes to yield the same incorrect results. In this work, we add the Lagrangian particle-in-cell code gem[Y. Chen and S. Parker, J. Comput. Phys. 220, 839 (2007)] to the comparisons, not simply to add another code, but also to demonstrate that the codes' algorithms do not matter. We find good agreement of gem with gyro and gs2 for the plasma conditions considered earlier, thus establishing confidence that the codes are verified and that ongoing validation efforts for these plasma parameters are warranted.
A verification of the gyrokinetic microstability codes GEM, GYRO, and GS2
NASA Astrophysics Data System (ADS)
Bravenec, R. V.; Chen, Y.; Candy, J.; Wan, W.; Parker, S.
2013-10-01
A previous publication [R. V. Bravenec et al., Phys. Plasmas 18, 122505 (2011)] presented favorable comparisons of linear frequencies and nonlinear fluxes from the Eulerian gyrokinetic codes gyro [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and gs2 [W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)]. The motivation was to verify the codes, i.e., demonstrate that they correctly solve the gyrokinetic-Maxwell equations. The premise was that it is highly unlikely for both codes to yield the same incorrect results. In this work, we add the Lagrangian particle-in-cell code gem [Y. Chen and S. Parker, J. Comput. Phys. 220, 839 (2007)] to the comparisons, not simply to add another code, but also to demonstrate that the codes' algorithms do not matter. We find good agreement of gem with gyro and gs2 for the plasma conditions considered earlier, thus establishing confidence that the codes are verified and that ongoing validation efforts for these plasma parameters are warranted.
Comparison of Implicit Multiscale Full Kinetics to Gyrokinetics
NASA Astrophysics Data System (ADS)
Parker, Scott; Sturdevant, Benjamin; Chen, Yang
2016-10-01
Recent progress has been made developing full kinetic Lorentz force ion dynamics using implicit multiscale techniques. It is now possible to capture low-frequency physics along with finite Larmor radius (FLR) effects with a fully kinetic multiscale delta-f particle simulation. The utility of such a model is to be able to verify gyrokinetics in situations where the smallness of the ordering parameters are under question. Additionally, such a model can help identify what higher order terms in gyrokinetics might be important. Orbit averaging and sub-cycling are utilized with an implicit particle time advance based on variational principles. This produces stable and accurate ion trajectories on long time scales. Excellent agreement with the gyrokinetic dispersion relation is obtained including full FLR effects. Ion Bernstein waves are easily suppressed with the implicit time advance. We have developed a global toroidal electrostatic adiabatic electron Lorentz ion code. We will report our linear results benchmarking Lorentz ions with gyrokinetics for the Cyclone base case. We will also present our progress on ion including drift-kinetic electrons and electromagnetic perturbations.
Testing gyrokinetic simulations of electron turbulence
NASA Astrophysics Data System (ADS)
Holland, C.; DeBoo, J. C.; Rhodes, T. L.; Schmitz, L.; Hillesheim, J. C.; Wang, G.; White, A. E.; Austin, M. E.; Doyle, E. J.; Peebles, W. A.; Petty, C. C.; Zeng, L.; Candy, J.
2012-06-01
An extensive set of tests comparing gyrokinetic predictions of temperature-gradient driven electron turbulence to power balance transport analyses and fluctuation measurements are presented. These tests use data from an L-mode validation study on the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614) in which the local value of a/L_{T_e } =-(a/T_e )(dT_e /dr) is varied by modulated electron cyclotron heating; the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) is used to make the gyrokinetic predictions. Using a variety of novel measures, both local and global nonlinear simulations are shown to predict key characteristics of the electron energy flux Qe and long-wavelength (low-k) Te fluctuations, but systematically underpredict (by roughly a factor of two) the ion energy flux Qi. A new synthetic diagnostic for comparison to intermediate wavelength Doppler backscattering measurements is presented, and used to compare simulation predictions against experiment. In contrast to the agreement observed in the low-k Te fluctuation comparisons, little agreement is found between the predicted and measured intermediate-k density fluctuation responses. The results presented in this paper significantly expand upon those previously reported in DeBoo et al (2010 Phys. Plasmas 17 056105), comparing transport and multiple turbulence predictions from numerically converged local and global simulations for all four experimental heating configurations (instead of only fluxes and low-k Te fluctuations for one condition) to measurements and power balance analyses.
Ding, Bo; Fang, Huajing
2017-03-31
This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system.
A very general electromagnetic gyrokinetic formalism
NASA Astrophysics Data System (ADS)
McMillan, B. F.; Sharma, A.
2016-09-01
We derive a gyrokinetic formalism which is very generally valid: the ordering allows both large inhomogeneities in plasma flow and magnetic field at long wavelength, such as typical drift-kinetic theories, as well as fluctuations at the gyro-scale. The underlying approach is to order the vorticity to be small, and to assert that the timescales in the local plasma frame are long compared to the gyrofrequency. Unlike most other derivations, we do not treat the long and short wavelength components of the fluctuating fields separately; the single-field description defines the particle motion and their interaction with the electromagnetic field at small-scale, the system-scale, and intermediate length scales in a unified fashion. As in earlier literature, the work consists of identifying a coordinate system where the gyroangle-dependent terms are small, and using a near-unity transform to systematically find a set of coordinates where the gyroangle dependence vanishes. We derive a gyrokinetic Lagrangian which is valid where the vorticity | ∇ × ( E × B / B ) | is small compared to the gyrofrequency Ω, and the magnetic field scale length is long compared to the gyroradius; we also require that time variation be slow in an appropriately chosen reference frame. This appears to be a minimum set of constraints on a gyrokinetic theory and is substantially more general than earlier approaches. It is the general-geometry electromagnetic extension of Dimits, Phys. Plasmas 17, 055901 (2010) (which is an electrostatic formalism with a homogeneous background magnetic field). This approach also does not require a separate treatment of fluctuating and background components of the magnetic field, unlike much of the previous literature. As a consequence, the "cross terms" due to a combination of long- and short-wavelength variation, which were ignored in the earlier work (but derived in a more restrictive ordering in Parra and Calvo, Plasma Phys. Controlled Fusion 53, 045001 (2011
Nonlinear particle-wave kinetics in weakly unstable plasmas
Breizman, B.N.; Berk, H.L.; Pekker, M.S.
1996-12-31
With the motivation to address the behavior of the fusion produced alpha particles in a thermonuclear reactor, a theory is developed for predicting the wave saturation levels and particle transport in weakly unstable systems with a discrete number of modes in the presence of energetic particle sources and sinks. Conditions are established for either steady state or bursting nonlinear scenarios when several modes are excited for cases where there is and there is not resonance overlap. Depending on parameters, the particles can undergo benign relaxation, with only a small fraction of the available free energy released to waves and with no global transport, or the particles can experience rapid global transport caused by a substantial conversion of their free energy into wave energy. When the resonance condition of the particle-wave interaction is varied adiabatically, the particles trapped in a wave are found to form phase space holes or clumps that enhance the particle-wave energy exchange. This mechanism, which has been experimentally observed when there is frequency chirping, causes increased saturation levels of instabilities. If resonance sweeping is imposed externally, the particle free energy can even be tapped in stable systems where background dissipation suppresses linear instability. Externally applied resonance sweeping can be important for alpha particle energy channeling, as well as for understanding fishbone and some Alfven wave instability experiments. Near instability threshold, that is when the destabilizing drive just exceeds the background dissipation, a more sophisticated analysis is developed to predict the correct saturation. To leading order, this problem reduces to an integral equation for the wave amplitude with a temporally non local cubic term. This equation has a self-similar solution that blows-up in a finite time.
Gyrokinetic simulations of ETG Turbulence*
NASA Astrophysics Data System (ADS)
Nevins, William
2005-10-01
Recent gyrokinetic simulations of electron temperature gradient (ETG) turbulence [1,2] produced different results despite similar plasma parameters. Ref.[1] differs from Ref.[2] in that [1] eliminates magnetically trapped particles ( r/R=0 ), while [2] retains magnetically trapped particles ( r/R 0.18 ). Differences between [1] and [2] have been attributed to insufficient phase-space resolution and novel physics associated with toroidicity and/or global simulations[2]. We have reproduced the results reported in [2] using a flux-tube, particle-in-cell (PIC) code, PG3EQ[3], thereby eliminating global effects as the cause of the discrepancy. We observe late-time decay of ETG turbulence and the steady-state heat transport in agreement with [2], and show this results from discrete particle noise. Discrete particle noise is a numerical artifact, so both the PG3EQ simulations reported here and those reported in Ref.[2] have little to say about steady-state ETG turbulence and the associated anomalous electron heat transport. Our attempts to benchmark PIC and continuum[4] codes at the plasma parameters used in Ref.[2] produced very large, intermittent transport. We will present an alternate benchmark point for ETG turbulence, where several codes reproduce the same transport levels. Parameter scans about this new benchmark point will be used to investigate the parameter dependence of ETG transport and to elucidate saturation mechanisms proposed in Refs.[1,2] and elsewhere[5-7].*In collaboration with A. Dimits (LLNL), J. Candy, C. Estrada-Mila (GA), W. Dorland (U of MD), F. Jenko, T. Dannert (Max-Planck Institut), and G. Hammett (PPPL). Work at LLNL performed for US DOE under Contract W7405-ENG-48.[1] F. Jenko and W. Dorland, PRL 89, 225001 (2002).[2] Z. Lin et al, 2004 Sherwood Mtg.; 2004 TTF Mtg.; Fusion Energy 2004 (IAEA, Vienna, 2005); Bull. Am. Phys. Soc. (November, 2004); 2005 TTF Mtg.; 2005 Sherwood Mtg.; Z. Lin, et al, Phys. Plasmas 12, 056125 (2005). [3] A.M. Dimits
Physical dynamics of quasi-particles in nonlinear wave equations
NASA Astrophysics Data System (ADS)
Christov, Ivan; Christov, C. I.
2008-02-01
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.
Speech enhancement based on nonlinear models using particle filters.
Mustière, Frédéric; Bolić, Miodrag; Bouchard, Martin
2009-12-01
Motivated by the reportedly strong performance of particle filters (PFs) for noise reduction on essentially linear speech production models, and the mounting evidence that the introduction of nonlinearities can lead to a refined speech model, this paper presents a study of PF solutions to the problem of speech enhancement in the context of nonlinear, neural-type speech models. Several variations of a global model are presented (single/multiple neurons; bias/no bias), and corresponding PF solutions are derived. Different importance functions are given when beneficial, Rao-Blackwellization is proposed when possible, and dual/nondual versions of each algorithms are presented. The method shown can handle both white and colored noise. Using a variety of speech and noise signals and different objective quality measures, the performance of these algorithms are evaluated against other PF solutions running on linear models, as well as some traditional enhancement algorithms. A certain hierarchy in performance is established between each algorithm in the paper. Depending on the experimental conditions, the best-performing algorithms are a classical Rao-Blackwellized particle filter (RBPF) running on a linear model, and a proposed PF employing a nondual, nonlinear model with multiple neurons and no biases. With consistence, the neural-network-based PF outperforms RBPF at low signal-to-noise ratio (SNR).
Alfvén Waves in Gyrokinetic Plasmas
NASA Astrophysics Data System (ADS)
Lee, W. W.; Qin, H.; Lewandowski, J. L. V.
2002-11-01
The ordering that ρi << L_eq enables us to use the gyrokinetic description for a magnetically-confined plasma,^1-3 by seperating the fast gyromotion of the particle from its slow gyrocenter motion and the associated polarization effects. In this paper, we present a brief comparison of the properties of the Alfvén waves based on the conventional MHD descriptions with those under the gyrokinetic approximation, and show that the unique treatment of the polarization effects in the gyrokinetic formalism makes it possible to eliminate the compressional Alfvén waves without resorting to geometric simplification for the reduced gyrokinetic-MHD equations. Thus, one may use the existing gyrokinetic particle simulation techniques^1,4-5 together with the elliptic multigrid solver^6 on the modern day massively parallel computers to study the effects of neoclassical and microturbulence transport on the global (MHD) problems based on the realistic MHD equilibria. This work is supported by the US DoE SciDAC project. ^1W. W. Lee, Phys. Fluids 26, 556 ('83); J. Comp. Phys. 72, 243 ('87). 2T. S. Hahm, W. W. Lee and A. Brizard, Phys. Fluids 31, 1940 ('88). ^3H. Qin, W. M. Tang and W. W. Lee, Phys. Plasmas 7, 4433 ('00). 4I. Manuilskiy and W. W. Lee, Phys. Plasmas 7, 1381 ('00). ^5W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Phys. Plasmas 8, 4435 ('01). \\$^6J. L. V. Lewandowski, manuscript in preparation.
Gyrokinetic Theory and Computational Methods for Electromagnetic Perturbations in Tokamaks
NASA Astrophysics Data System (ADS)
Qin, H.; Tang, W. M.; Rewoldt, G.
1998-11-01
A general gyrokinetic formalism and computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and the associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both MHD instabilities and electromagnetic drift waves(H. Qin, W. M. Tang, and G. Rewoldt, Phys. Plasmas 5), 1035 (1998). The gyrokinetic system of equations is derived by phase-space Lagrangian Lie perturbation methods. An important component missing from previous gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed. The corresponding numerical code, KIN-2DEM, has been systematically benchmarked against the high-n FULL code, the PEST code, and the NOVA-K code for kinetic ballooning modes, internal kink modes, and TAEs, respectively. For the internal kink mode, it is found that kinetic effects due to trapped ions can significantly modify the γ vs. q0 curve. For the destabilization of the TAEs by energetic particles, comparisons have been made between the non-perturbative, fully kinetic KIN-2DEM results and the perturbative hybrid NOVA-K results.
Beyond linear polarization in gyrokinetic theory
NASA Astrophysics Data System (ADS)
Brizard, Alain
2012-10-01
The concept of linear gyrocenter polarization in gyrokinetic theory is generalized to include contributions from guiding-center polarization as well as nonlinear (quadratic) gyrocenter polarization. The former polarization is obtained from Hamiltonian guiding-center theory in which higher-order corrections due to magnetic-field nonuniformity are retained [1]. The latter polarization can be derived either variationally from the cubic gyrocenter Hamiltonian [2] or directly by push-forward construction [3]. [4pt] [1] A.J. Brizard and N. Tronko, submitted for publication (2012).[0pt] [2] A. Mishchenko and A.J. Brizard, Phys. Plasmas 18, 022305 (2011).[0pt] [3] A.J. Brizard, Comm. Nonlin. Sci. Num. Sim. 13, 24 (2008).
Single particle dynamics and nonlinear resonances in circular accelerators
Ruth, R.D.
1985-11-01
The purpose of this paper is to introduce the reader to single particle dynamics in circular accelerators with an emphasis on nonlinear resonances. We begin with the Hamiltonian and the equations of motion in the neighborhood of the design orbit. In the linear theory this yields linear betatron oscillations about a closed orbit. It is useful then to introduce the action-angle variables of the linear problem. Next we discuss the nonlinear terms which are present in an actual accelerator, and in particular, we motivate the inclusion of sextupoles to cure chromatic effects. To study the effects of the nonlinear terms, we next discuss canonical perturbation theory which leads us to nonlinear resonances. After showing a few examples of perturbation theory, we abandon it when very close to a resonance. This leads to the study of an isolated resonance in one degree of freedom with a 'time'-dependent Hamiltonian. We see the familiar resonance structure in phase space which is simply closed islands when the nonlinear amplitude dependence of the frequency or 'tune' is included. To show the limits of the validity of the isolated resonance approximation, we discuss two criteria for the onset of chaotic motion. Finally, we study an isolated coupling resonance in two degrees of freedom with a 'time'-dependent Hamiltonian and calculate the two invariants in this case. This leads to a surface of section which is a 2-torus in 4-dimensional phase space. However, we show that it remains a 2-torus when projected into particular 3-dimensional subspaces, and thus can be viewed in perspective.
NASA Astrophysics Data System (ADS)
Medvedev, M. V.
1998-11-01
The magnetic field fluctuations frequently observed in the Solar Wind and Interstellar Medium are likely to be nonlinear Alfvén waves, in which the ponderomotive coupling of Alfvénic magnetic energy to ion-acoustic quasi-modes has modified the phase velocity vA and caused wave-front steepening. In the warm, collisionless Solar Wind plasma the resonant particle-wave interactions result in relatively rapid (compared to the particle bounce time) formation of quasi-stationary Alfvénic Rotational Discontinuities, (M.V. Medvedev, P.H. Diamond, V.I. Shevchenko, and V.L. Galinsky, Phys. Rev. Lett. 78), 4934 (1997) and references therein. which have been the subject of intense satellite observations and theoretical investigations, and whose emergence and dynamics has not been previously understood. These discontinuities are shown to be quasi-stationary wave-form remnants of nonlinearly evolved coherent Alfvén waves. In long-time asymptotics, however, the particle distribution function (PDF) is affected by wave magnetic fields. Indeed, the resonant particles are trapped in the quasi-stationary Alfvénic discontinuities by mirroring forces giving rise to the nonlinear Landau damping and, ultimately, to a formation of a plateau on the PDF, so that the linear collisionless damping vanishes. Using Virial theorem for trapped particles, it is analytically demonstrated (M.V. Medvedev, P.H. Diamond, M.N. Rosenbluth, and V.I. Shevchenko, Submitted to Phys. Rev. Lett. (1998).) that their effect on the nonlinear dynamics of such discontinuities is highly non-trivial and forces a significant departure of the theory from the conventional paradigm. Considering the strongly compressible MHD (Alfvénic) Solar Wind turbulence as an ensemble of randomly interacting Alfvénic discontinuities and nonlinear waves, it is also shown (M.V. Medvedev and P.H. Diamond, Phys. Rev. E 56), R2371 (1997). that there exist two different phases of turbulence which are due to the collisionless (Landau
NASA Astrophysics Data System (ADS)
Bierwage, Andreas; Spong, Donald A.
2009-05-01
Hybrid-MHD-Gyrokinetic Code (HMGC) [1] and the gyrofluid code TAEFL [2,3] are used for nonlinear simulation of Alfven Eigenmodes in Tokamak plasma. We compare results obtained in two cases: (I) a case designed for cross-code benchmark of TAE excitation; (II) a case based on a dedicated DIII-D shot #132707 where RSAE and TAE activity is observed. Differences between the numerical simulation results are discussed and future directions are outlined. [1] S. Briguglio, G. Vlad, F. Zonca and C. Kar, Phys. Plasmas 2 (1995) 3711. [2] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Fluids B4 (1992) 3316. [3] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Plasmas 1 (1994) 1503.
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles
Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A.; Wuite, Gijs J. L.; Roos, Wouter H.; Barsegov, Valeri
2016-01-01
The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.
Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A; Wuite, Gijs J L; Roos, Wouter H; Barsegov, Valeri
2016-01-01
The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.
Discoveries from the exploration of gyrokinetic momentum transporta)
NASA Astrophysics Data System (ADS)
Staebler, G. M.; Waltz, R. E.; Kinsey, J. E.
2011-05-01
The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.
Discoveries from the exploration of gyrokinetic momentum transport
Staebler, G.M.; Waltz, R. E.; Kinsey, J. E.
2011-05-15
The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.
The energetic coupling of scales in gyrokinetic plasma turbulence
Teaca, Bogdan; Jenko, Frank
2014-07-15
In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into a series of scale structures, while accounting separately for contributions made by modes possessing special symmetries (e.g., the zonal flow modes). The interaction of these scales is analyzed using the energy transfer functions, including a forward and backward decomposition, scale fluxes, and locality functions. The comparison between the ITG and ETG cases shows that ETG turbulence has a more pronounced classical turbulent behavior, exhibiting a stronger energy cascade, with implications for gyrokinetic turbulence modeling.
The energetic coupling of scales in gyrokinetic plasma turbulence
NASA Astrophysics Data System (ADS)
Teaca, Bogdan; Navarro, Alejandro Bañón; Jenko, Frank
2014-07-01
In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into a series of scale structures, while accounting separately for contributions made by modes possessing special symmetries (e.g., the zonal flow modes). The interaction of these scales is analyzed using the energy transfer functions, including a forward and backward decomposition, scale fluxes, and locality functions. The comparison between the ITG and ETG cases shows that ETG turbulence has a more pronounced classical turbulent behavior, exhibiting a stronger energy cascade, with implications for gyrokinetic turbulence modeling.
Gyrokinetic investigation of ITG modes in helical RFPs
NASA Astrophysics Data System (ADS)
Predebon, I.; Xanthopoulos, P.; Terranova, D.
2013-10-01
Micro-instabilities in the RFP have been investigated in the last years from several viewpoints and with various numerical tools. The strongest underlying assumption for all of these approaches is that the magnetic equilibrium does not deviate significantly from axisymmetry. Contrary to this, in RFX-mod, the physical conditions more favorable for the onset of electrostatic/electromagnetic turbulence emerge when magnetic surfaces are helical, i.e., during the single helicity states of the RFP. In general, we wish to systematically revisit the existing gyrokinetic studies of microturbulence focusing on the novel 3D feature. The RFP equilibria are now derived using the VMEC code and subsequently applied to the nonlinear gyrokinetic code GENE with the aid of the GIST interface code. The physical problem we address here is the occurrence of ITG instability in single helicity plasmas, and its distinct properties compared to the axisymmetric geometry.
Graphics Processing Unit Acceleration of Gyrokinetic Turbulence Simulations
NASA Astrophysics Data System (ADS)
Hause, Benjamin; Parker, Scott
2012-10-01
We find a substantial increase in on-node performance using Graphics Processing Unit (GPU) acceleration in gyrokinetic delta-f particle-in-cell simulation. Optimization is performed on a two-dimensional slab gyrokinetic particle simulation using the Portland Group Fortran compiler with the GPU accelerator compiler directives. We have implemented the GPU acceleration on a Core I7 gaming PC with a NVIDIA GTX 580 GPU. We find comparable, or better, acceleration relative to the NERSC DIRAC cluster with the NVIDIA Tesla C2050 computing processor. The Tesla C 2050 is about 2.6 times more expensive than the GTX 580 gaming GPU. Optimization strategies and comparisons between DIRAC and the gaming PC will be presented. We will also discuss progress on optimizing the comprehensive three dimensional general geometry GEM code.
Gyrokinetic simulations of the tearing instability
Numata, Ryusuke; Dorland, William; Howes, Gregory G.; Loureiro, Nuno F.; Tatsuno, Tomoya
2011-11-15
Linear gyrokinetic simulations covering the collisional-collisionless transitional regime of the tearing instability are performed. It is shown that the growth rate scaling with collisionality agrees well with that predicted by a two-fluid theory for a low plasma beta case in which ion kinetic dynamics are negligible. Electron wave-particle interactions (Landau damping), finite Larmor radius, and other kinetic effects invalidate the fluid theory in the collisionless regime, in which a general non-polytropic equation of state for pressure (temperature) perturbations should be considered. We also vary the ratio of the background ion to electron temperatures and show that the scalings expected from existing calculations can be recovered, but only in the limit of very low beta.
Simulations of energetic particles interacting with nonlinear anisotropic dynamical turbulence
NASA Astrophysics Data System (ADS)
Heusen, M.; Shalchi, A.
2016-09-01
We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bendover scales and a magnetic field ratio of δ B / B0 = 0.75.
The particle resonance in spiral galaxies - Nonlinear effects.
NASA Technical Reports Server (NTRS)
Contopoulos, G.
1973-01-01
A theory is developed to account for the nonlinear effects, near the particle resonance, found by numerical integration. There are four equilibrium points in the rotating frame of reference: two of them unstable, at the minima of potential (L1, L2), and two stable, at the maxima of potential (L4, L5). Many particles are trapped in librating orbits around L4, L5. Using the lowest-order terms of a 'third integral' of motion near L4, L5, the behavior of the trapped orbits is determined, and the approximate theoretical results are compared with the orbits found numerically by computer. An estimate of the trapped mass is given. It amounts to about 30% of the total mass between 9 and 11 kpc when the particle resonance is at r sub s = 10 kpc and the maximum force due to the spiral is 4% of the axisymmetric force. Some effects due to these mass concentrations are found numerically and theoretically.
Wave-particle interaction and the nonlinear saturation of the electron temperature gradient mode
NASA Astrophysics Data System (ADS)
Vadlamani, Srinath; Parker, Scott E.; Chen, Yang; Howard, James E.
2004-11-01
It has been proposed that the electron temperature gradient (ETG) driven turbulence is responsible for experimentally relevant electron thermal transport in tokamak plasmas. Significant transport levels are possible by the creation of radially elongated vortices or ``streamers" [1,2], which are sustained by the nonlinear saturation of the instability and are not susceptible to shear flow destruction, as is the case with the ion temperature gradient (ITG) mode. We present a dynamical system to explore the dependence of saturation level due to E × B and E_\\| motion, as well as the effect of radial elongation. With this model, we can predict the nonlinear saturation level of the ETG streamers. We compare our theoretical predictions with a 2D shear-less slab gyrokinetic electron code that includes the E_\\| nonlinearity. [1]F. Jenko, W. Dorland, M Kotschenreuther, and B.N. Rogers, Phys. Plasmas 7, 1904 (2000). [2]C. Holland, and P.H. Diamond, Phys. Plasmas 9, 3857 (2002). [3]W. M. Manheimer, Phys. Fluids 14, 579 (1971). [4]R. A. Smith, John A. Krommes, and W. W. Lee, Phys. Fluids 28, 1069 (1985).
NASA Astrophysics Data System (ADS)
Deng, Zhao
2014-10-01
Gyrokinetic simulations of L-mode near edge tokamak plasmas with the GYRO code underpredict both the transport and the turbulence levels by 5 to 10 fold, which suggest either some important mechanism is missing from current gyrokinetic codes like GYRO or the gyrokinetic approximation itself is breaking down. It is known that GYRO drift-kinetic simulations with gyro-averaging suppressed recover most of the missing transport. With these motivations, we developed a flux tube nonlinear cyclokinetic code rCYCLO with the parallel motion and variation suppressed. rCYCLO dynamically follows the high frequency ion gyro-phase motion (with no averaging) which is nonlinearly coupled into the low frequency drift-waves thereby interrupting and possibly suppressing the gyro-averaging. By comparison with the corresponding gyrokinetic simulations, we can test the conditions for the breakdown of gyrokinetics. rCYCLO nonlinearly couples ∇B driven ion temperature gradient (ITG) modes and collisional fluid electron drift modes to ion cyclotron (IC) modes. As required, rCYCLO cyclokinetic transport recovers gyrokinetics at high relative ion cyclotron frequency (Ω*) and low turbulence levels. However, because the IC modes are stable and act as a turbulence sink, we have found that at high turbulence levels and low-Ω* cyclokinetic transport is lower (not higher) than gyrokinetic transport. Work is in progress with unstable IC modes to explore the possibility of driving cyclokinetic transport higher than gyrokinetic transport. Supported by the CSC, NSFC No. 1126114032, No. 10975012 ITER-CN No. 2013GB112006 and the US DOE under DE-FG02-95ER54309.
A Numerical Instability in an ADI Algorithm for Gyrokinetics
E.A. Belli; G.W. Hammett
2004-12-17
We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.
Gyrokinetic treatment of GAE modes in cylindrical geometry
Eremin, D.
2006-11-30
Global Alfven eigenmodes (GAEs) are investigated in cylindrical geometry both analytically and numerically. These modes are of particular importance in low-shear magnetic configurations, such as modern stellarators. Analytical treatment starts from the linearised equations of gyrokinetics and yields a generalized dispersion relation for GAE with FLR and kinetic effects taken into account, which is demonstrated to reduce to the well-known MHD counterpart in the appropriate limit. An eigenvalue code is developed to solve the dispersion relation, which is used to investigate the kinetic analogs of GAE modes in various regimes with different beta. On the other hand, GAE modes are simulated with global linear particle-in-cell (PIC) electromagnetic gyrokinetic code following self-consistent time evolution of electromagnetic fields and plasma. GAE modes are observed and their damping rate agrees with predictions made by the eigenvalue code.
Low dimensional gyrokinetic PIC simulation by δf method
NASA Astrophysics Data System (ADS)
Chen, C. M.; Nishimura, Yasutaro; Cheng, C. Z.
2015-11-01
A step by step development of our low dimensional gyrokinetic Particle-in-Cell (PIC) simulation is reported. One dimensional PIC simulation of Langmuir wave dynamics is benchmarked. We then take temporal plasma echo as a test problem to incorporate the δf method. Electrostatic driftwave simulation in one dimensional slab geometry is resumed in the presence of finite density gradients. By carefully diagnosing contour plots of the δf values in the phase space, we discuss the saturation mechanism of the driftwave instabilities. A v∥ formulation is employed in our new electromagnetic gyrokinetic method by solving Helmholtz equation for time derivative of the vector potential. Electron and ion momentum balance equations are employed in the time derivative of the Ampere's law. This work is supported by Ministry of Science and Technology of Taiwan, MOST 103-2112-M-006-007 and MOST 104-2112-M-006-019.
Alternate treatment of the polarization drift for gyrokinetic PIC simulations
NASA Astrophysics Data System (ADS)
Lodestro, L. L.; Dimits, A. M.; Nevins, W. M.
2003-10-01
Tokamak edge turbulence is characterized by a range of spatial scales up through k_⊥ρ_pol ˜ 1, and can involve fluctuation amplitudes of order unity. To apply gyrokinetic methods to the study of such turbulence, an extension of the usual formulation is therefore required. A promising route appears to have been developed in Ref. 1footnotetextA.M. Dimits, L.L. LoDestro, and D.H.E. Dubin, Phys. Fluids B 4, 277 (1992)., where it is shown that with the use of expansion parameter ɛ=tilde v/v_th i ˜ k_⊥ρ_ie(φ-A_\\|/c)/T≪1, the nonlinear gyrokinetic equations span the usual drift-kinetic and gyrokinetic regimes. However, there remain technical difficulties with the numerical implementation of the polarization drift in Poisson's equation when the fluctuations are large. In this paper we present our progress assessing the various methods that have been proposed for treating the polarization drift.
Testing Gyrokinetics on C-Mod and NSTX
M.H. Redi; W. Dorland; C.L. Fiore; D. Stutman; J.A. Baumgaertel; B. Davis; S.M. Kaye; D.C. McCune; J. Menard; G. Rewoldt
2005-06-20
Quantitative benchmarks of computational physics codes against experiment are essential for the credible application of such codes. Fluctuation measurements can provide necessary critical tests of nonlinear gyrokinetic simulations, but such require extraordinary computational resources. Linear micro-stability calculations with the GS2 [1] gyrokinetic code have been carried out for tokamak and ST experiments which exhibit internal transport barriers (ITB) and good plasma confinement. Qualitative correlation is found for improved confinement before and during ITB plasmas on Alcator C-Mod [2] and NSTX [3], with weaker long wavelength micro-instabilities in the plasma core regions. Mixing length transport models are discussed. The NSTX L-mode is found to be near marginal stability for kinetic ballooning modes. Fully electromagnetic, linear, gyrokinetic calculations of the Alcator C-Mod ITB during off-axis rf heating, following four plasma species and including the complete electron response show ITG/TEM microturbulence is suppressed in the plasma core and in the barrier region before barrier formation, without recourse to the usual requirements of velocity shear or reversed magnetic shear [4-5]. No strongly growing long or short wavelength drift modes are found in the plasma core but strong ITG/TEM and ETG drift wave turbulence is found outside the barrier region. Linear microstability analysis is qualitatively consistent with the experimental transport analysis, showing low transport inside and high transport outside the ITB region before barrier formation, without consideration of ExB shear stabilization.
Tokamak profile prediction using direct gyrokinetic and neoclassical simulation
Candy, J.; Waltz, R. E.; Belli, E.; Holland, C.; Fahey, M. R.
2009-06-15
Tokamak transport modeling scenarios, including ITER [ITER Physics Basis Editors, Nucl. Fusion 39, 2137 (1999)] performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes (local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles). Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] code, for turbulent transport, and the NEO[E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 (2008)] code, for kinetic neoclassical transport. Results for DIII-D L-mode discharge 128913 are given, with computational and experimental results consistent in the region 0{<=}r/a{<=}0.8.
Tokamak profile prediction using direct gyrokinetic and neoclassical simulation
Candy, Jeff; Holland, Chris; Waltz, R. E.; Fahey, Mark R; Belli, E
2009-01-01
okamak transport modeling scenarios, including ITER ITER Physics Basis Editors, Nucl. Fusion 39, 2137 1999 performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles . Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D J. L. Luxon, Nucl. Fusion 42, 614 2002 plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 2003 code, for turbulent transport, and the NEO E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 2008 code, for kinetic neoclassical transport. Results for DIII-D L-mode discharge 128913 are given, with computational and experimental results consistent in the region 0 <= r/a <= 0.8.
Effects of collisions on conservation laws in gyrokinetic field theory
Sugama, H.; Nunami, M.; Watanabe, T.-H.
2015-08-15
Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.
Effects of collisions on conservation laws in gyrokinetic field theory
NASA Astrophysics Data System (ADS)
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2015-08-01
Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.
On push-forward representations in the standard gyrokinetic model
Miyato, N. Yagi, M.; Scott, B. D.
2015-01-15
Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This is true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.
Nonlinear Generation of Zonal Fields by the Beta-Induced Alfvén Eigenmode in Tokamak
NASA Astrophysics Data System (ADS)
Zhang, Huasen; Lin, Zhihong
2013-10-01
The zonal fields effect on the beta-induced Alfvén eigenmode (BAE) destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations. It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE. In the weakly driven case, the zonal fields with a strong geodesic acoustic mode (GAM) component have weak effects on the nonlinear BAE evolution. In the strongly driven case, the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.
Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model
NASA Technical Reports Server (NTRS)
Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.
2009-01-01
Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.
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.
NASA Astrophysics Data System (ADS)
Hager, Robert; Lang, Jianying; Chang, C. S.; Ku, S.; Chen, Y.; Parker, S. E.; Adams, M. F.
2017-05-01
As an alternative option to kinetic electrons, the gyrokinetic total-f particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons analogous to Chen and Parker [Phys. Plasmas 8, 441 (2001)]. Two representative long wavelength modes, shear Alfvén waves and resistive tearing modes, are verified in cylindrical and toroidal magnetic field geometries.
A multi-species collisional operator for full-F gyrokinetics
Estève, D.; Garbet, X.; Sarazin, Y.; Grandgirard, V.; Cartier-Michaud, T.; Dif-Pradalier, G.; Ghendrih, P.; Latu, G.; Norscini, C.
2015-12-15
A linearized multi-species collision operator has been developed for an efficient implementation in gyrokinetic codes. This operator satisfies the main expected properties: particle, momentum, and energy conservation, and existence of an H-theorem. A gyrokinetic version is then calculated, which involves derivatives with respect to the gyrocenter position, parallel velocity, and magnetic momentum. An isotropic version in the velocity space can be constructed for the specific problem of trace impurities colliding with a main species. A simpler version that involves derivatives with parallel velocity only has been developed. This reduced version has been implemented in the GYSELA gyrokinetic code, and is shown to comply with particle, momentum, and energy conservation laws. Moreover, the interspecies relaxation rates for momentum and energy agree very well with the theoretical values.
A multi-species collisional operator for full-F gyrokinetics
NASA Astrophysics Data System (ADS)
Estève, D.; Garbet, X.; Sarazin, Y.; Grandgirard, V.; Cartier-Michaud, T.; Dif-Pradalier, G.; Ghendrih, P.; Latu, G.; Norscini, C.
2015-12-01
A linearized multi-species collision operator has been developed for an efficient implementation in gyrokinetic codes. This operator satisfies the main expected properties: particle, momentum, and energy conservation, and existence of an H-theorem. A gyrokinetic version is then calculated, which involves derivatives with respect to the gyrocenter position, parallel velocity, and magnetic momentum. An isotropic version in the velocity space can be constructed for the specific problem of trace impurities colliding with a main species. A simpler version that involves derivatives with parallel velocity only has been developed. This reduced version has been implemented in the GYSELA gyrokinetic code, and is shown to comply with particle, momentum, and energy conservation laws. Moreover, the interspecies relaxation rates for momentum and energy agree very well with the theoretical values.
Applications of large eddy simulation methods to gyrokinetic turbulence
Bañón Navarro, A. Happel, T.; Teaca, B. [Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB; Max-Planck für Sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau; Max-Planck Jenko, F. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching; Max-Planck Hammett, G. W. [Max-Planck Collaboration: ASDEX Upgrade Team
2014-03-15
The large eddy simulation (LES) approach—solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model—is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system.
NASA Astrophysics Data System (ADS)
Artemyev, Anton; Agapitov, Oleksiy; Krasnoselskikh, Vladimir; Mourenas, Didier; Vasiliev, Alexei
Wave-particle resonant interaction is the main mechanism responsible for electron acceleration and scattering in the radiation belts. There are two approaches describing this interaction - quasi-linear theory describes particle diffusion in momentum space, while nonlinear trapping of particles by high-amplitude waves can describe fast particle acceleration. The diffusion approach is more developed and widely used now. However, many modern observations in the radiation belts suggest the presence of significant population of large amplitude waves which can be responsible for nonlinear wave-particle interaction. We show that such nonlinear wave-particle resonant interaction corresponds to the fast transport of particles in phase space. We show that the general approach for the description of the evolution of the particle velocity distribution based on the Fokker-Plank equation can be modified to consider the process of nonlinear wave-particle interaction, including particle trapping. Such a modification consists in one additional operator describing fast particle jumps in phase space. The proposed approach is illustrated by considering the acceleration of relativistic electrons by strongly oblique whistler waves. We determine the typical variation of electron phase-density due to nonlinear wave-particle interaction and compare this variation with pitch-angle/energy diffusion due to quasi-linear electron scattering. We show that relation between nonlinear and quasi-linear effects is controlled by the distribution of wave-amplitudes. When this distribution has a heavy tail, nonlinear effects can become dominant in the formation of the electron energy distribution. We compare effectiveness of quasi-linear diffusion and nonlinear trapping for conditions typical for Earth radiation belts.
Deng, Zhao; Waltz, R. E.
2015-05-15
This paper presents numerical simulations of the nonlinear cyclokinetic equations in the cyclotron harmonic representation [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Simulations are done with a local flux-tube geometry and with the parallel motion and variation suppressed using a newly developed rCYCLO code. Cyclokinetic simulations dynamically follow the high-frequency ion gyro-phase motion which is nonlinearly coupled into the low-frequency drift-waves possibly interrupting and suppressing gyro-averaging and increasing the transport over gyrokinetic levels. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the breakdown of gyrokinetics at high turbulence levels is quantitatively tested over a range of relative ion cyclotron frequency 10 < Ω*{sup }< 100 where Ω*{sup }= 1/ρ*, and ρ* is the relative ion gyroradius. The gyrokinetic linear mode rates closely match the cyclokinetic low-frequency rates for Ω*{sup }> 5. Gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω*{sup }≥ 50) and low turbulence level as required. Cyclokinetic transport is found to be lower than gyrokinetic transport at high turbulence levels and low-Ω* values with stable ion cyclotron (IC) modes. The gyrokinetic approximation is found to break down when the density perturbations exceed 20%. For cyclokinetic simulations with sufficiently unstable IC modes and sufficiently low Ω*{sup }∼ 10, the high-frequency component of cyclokinetic transport level can exceed the gyrokinetic transport level. However, the low-frequency component of the cyclokinetic transport and turbulence level does not exceed that of gyrokinetics. At higher and more physically relevant Ω*{sup }≥ 50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport and turbulence level is still smaller than that of
Plasma Simulation Using Gyrokinetic-Gyrofluid Hybrid Models
Scott Parker
2009-04-09
We are developing kinetic ion models for the simulation of extended MHD phenomena. The model they have developed uses full Lorentz force ions, and either drift-kinetic or gyro-kinetic electrons. Quasi-neutrality is assumed and the displacement current is neglected. They are also studying alpha particle driven Toroidal Alfven Eigenmodes (TAE) in the GEM gyrokinetic code [Chen 07]. The basic kinetic ion MHD model was recently reported in an invited talk given by Dan Barnes at the 2007 American Physical Society - Division of Plasma Physics (APS-DPP) and it has been published [Jones 04, Barnes 08]. The model uses an Ohm's law that includes the Hall term, pressure term and the electron inertia [Jones 04]. These results focused on the ion physics and assumed an isothermal electron closure. It is found in conventional gyrokinetic turbulence simulations that the timestep cannot be made much greater than the ion cyclotron period. However, the kinetic ion MHD model has the compressional mode, which further limits the timestep. They have developed an implicit scheme to avoid this timestep constraint. They have also added drift kinetic electrons. This model has been benchmarked linearly. Waves investigated where shear and compressional Alfven, whisterl, ion acoustic, and drift waves, including the kinetic damping rates. This work is ongoing and was first reported at the 2008 Sherwood Fusion Theory Conference [Chen 08] and they are working on a publication. They have also formulated an integrated gyrokinetic electron model, which is of interest for studying electron gradient instabilities and weak guide-field magnetic reconnection.
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Besse, N.; Bertrand, P.
2006-11-30
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
NASA Astrophysics Data System (ADS)
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Crouseilles, N.; Latu, G.; Sonnendrücker, E.; Besse, N.; Bertrand, P.
2006-11-01
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.
Gyrokinetic Calculations of Microinstabilities and Transport During RF H-Modes on Alcator C-Mod
M.H. Redi; C. Fiore; P. Bonoli; C. Bourdelle; R. Budny; W.D. Dorland; D. Ernst; G. Hammett; D. Mikkelsen; J. Rice; S. Wukitch
2002-06-18
Physics understanding for the experimental improvement of particle and energy confinement is being advanced through massively parallel calculations of microturbulence for simulated plasma conditions. The ultimate goal, an experimentally validated, global, non-local, fully nonlinear calculation of plasma microturbulence is still not within reach, but extraordinary progress has been achieved in understanding microturbulence, driving forces and the plasma response in recent years. In this paper we discuss gyrokinetic simulations of plasma turbulence being carried out to examine a reproducible, H-mode, RF heated experiment on the Alcator CMOD tokamak3, which exhibits an internal transport barrier (ITB). This off axis RF case represents the early phase of a very interesting dual frequency RF experiment, which shows density control with central RF heating later in the discharge. The ITB exhibits steep, spontaneous density peaking: a reduction in particle transport occurring without a central particle source. Since the central temperature is maintained while the central density is increasing, this also suggests a thermal transport barrier exists. TRANSP analysis shows that ceff drops inside the ITB. Sawtooth heat pulse analysis also shows a localized thermal transport barrier. For this ICRF EDA H-mode, the minority resonance is at r/a * 0.5 on the high field side. There is a normal shear profile, with q monotonic.
Hollywood log-homotopy: movies of particle flow for nonlinear filters
NASA Astrophysics Data System (ADS)
Daum, Fred; Huang, Jim
2011-06-01
In this paper we show five movies of particle flow to provide insight and intuition about this new algorithm. The particles flow solves the well known and important problem of particle degeneracy. Bayes' rule is implemented by particle flow rather than as a pointwise multiplication. This theory is roughly seven orders of magnitude faster than standard particle filters, and it often beats the extended Kalman filter by two orders of magnitude in accuracy for difficult nonlinear problems.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-15
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cell equations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheath boundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. This test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokinetic equations and some of the numerical challenges in developing an edge gyrokinetic code.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
NASA Astrophysics Data System (ADS)
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-01
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cell equations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheath boundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. This test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokinetic equations and some of the numerical challenges in developing an edge gyrokinetic code.
Map model for nonlinear alpha particle interaction with toroidal Alfven waves
Berk, H.L.; Breizman, B.N.; Ye, H.
1992-09-01
A map model has been developed for studying the nonlinear interaction of alpha particles with the toroidal Alfven eigenmodes. The map is constructed by assuming a linear interaction during a single poloidal transit, which allows the study of the nonlinear interaction over many transits. By using this map, analytic expressions are obtained for the particle nonlinear bounce frequency, and the wave amplitude threshold for the onset of particle orbit stochasticity. The map model can also facilitate self-consistent simulations which incorporate the time variation of the waves.
Differential formulation of the gyrokinetic Landau operator
NASA Astrophysics Data System (ADS)
Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David
2017-02-01
Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth-MacDonald-Judd potential functions must be kept gyroangle dependent.
Differential formulation of the gyrokinetic Landau operator
Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David
2017-01-05
Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.
Fedele, Renato; Jovanovic, Dusan
2004-12-01
Charged-particle beams are employed for a number of scientific and technological applications. The conventional description of their collective behavior is usually given in terms of the Vlasov equation. In the last 15 years some alternative descriptions have been developed in terms of a nonlinear Schroedinger equation governing the collective dynamics of the beam while interacting with the surrounding medium. This approach gives new insights, providing an alternative 'key of reading' of the charged-particle beam dynamics, and have been applied to a number of physical problems concerning conventional particle accelerating machines as well as plasma-based accelerator schemes. Remarkably, it is based on a mathematical formalism fully similar to those used for the propagation of e.m. radiation beams in nonlinear media a well as the nonlinear dynamics of the Bose-Einsten condensates.In this paper, a presentation of some significant nonlinear collective effects of a charged-particle beam in particle accelerators, that have been recently investigated in the framework of the above Schroedinger-like descriptions, is given.
Nonlinear alfvénic fast particle transport and losses
NASA Astrophysics Data System (ADS)
Schneller, M.; Lauber, Ph; García-Muñoz, M.; Brüdgam, M.; Günter, S.
2012-12-01
Magnetohydrodynamic instabilities like Toroidal Alfvén Eigenmodes or core-localized modes such as Beta Induced Alfvén Eigenmodes and Reversed Shear Alfvén Eigenmodes driven by fast particles can lead to significant redistribution and losses in fusion devices. This is observed in many ASDEX Upgrade discharges. The present work aims to understand the underlying resonance mechanisms, especially in the presence of multiple modes with different frequencies. Resonant mode coupling mechanisms are investigated using the drift kinetic HAGIS code [Pinches 1998]. Simulations were performed for different plasma equilibria, in particular for different q profiles, employing the availability of improved experimental data. A study was carried out, investigating double-resonant mode coupling with respect to various overlapping scenarios. It was found that, depending on the radial mode distance, double-resonance is able to enhance growth rates as well as mode amplitudes significantly. Small radial mode distances, however can also lead to strong nonlinear mode stabilization of a linear dominant mode. With the extended version of HAGIS, losses were simulated and directly compared with experimental loss measurements. The losses' phase space distribution as well as their ejection signal is consistent with experimental data. Furthermore, it allowed to characterize them as prompt, resonant or stochastic. It was found that especially in multiple mode scenarios (with different mode frequencies), abundant incoherent losses occur in the lower energy range, due to a broad phase-space stochastization. The incoherent higher energetic losses are "prompt", i.e. their initial energy is too large for confined orbits.
Electromagnetic Gyrokinetic Simulations
Wan, W
2003-11-19
A new electromagnetic kinetic electron {delta} particle simulation model has been demonstrated to work well at large values of plasma {beta} times the ion-to-electron mass ratio. The simulation is three-dimensional using toroidal flux-tube geometry and includes electron-ion collisions. The model shows accurate shear Alfven wave damping and microtearing physics. Zonal flows with kinetic electrons are found to be turbulent with the spectrum peaking at zero and having a width in the frequency range of the driving turbulence. This is in contrast with adiabatic electron cases where the zonal flows are near stationary, even though the linear behavior of the zonal flow is not significantly affected by kinetic electrons. zonal fields are found to be very weak, consistent with theoretical predictions for {beta} below the kinetic ballooning limit. Detailed spectral analysis of the turbulence data is presented in the various limits.
Gyrokinetic simulation of I-mode C-Mod pedestal using GENE
NASA Astrophysics Data System (ADS)
Liu, Xing; David, H.; Kotschenreuther, M.; Mahajan, S.; Huges, J.; Hubbard, A.; Valanju, P.
2016-10-01
Naturally stable to ELMs, and with widths larger than EPED predictions, the I-modes are an excellent laboratory for investigating the role of drift microinstabilities in pedestal formation since I-mode pedestal are not ``limited'' by MHD instabilities-Peeling Ballooning or the Kinetic Ballooning. Because the Weakly Coherent Mode (WCM) is shown to be correlated, primarily, to particle transport, the pedestal heat transport, in some sense, must be controlled by drift-type modes. We present here a study based on gyrokinetic simulations (using GENE) to model heat transport in the I-mode pedestals in C-Mod. Nonlinear ETG simulations, found to be streamer-dominated, can match experimental heat flux with profile adjustment well within experimental error bars. The ETG simulations reveal very notable fine-scale structure (in the parallel direction) of the eigenfunctions in both linear and nonlinear simulations. Simulations, varying impurity level (Zeff) and temperature and density profiles (within experimental error bars), are used to probe the sensitivity of ETG heat transport to the most important input parameters. Efforts to identify an instability corresponding to the WCM will also be discussed. Work supported by USDOE Grant DE-FG02-04ER54742.
Gyrokinetic Models for Edge Plasmas*
NASA Astrophysics Data System (ADS)
Dimits, Andris
2010-11-01
The use of gyrokinetic equations for the simulation of magnetic fusion edge and scrapeoff-layer plasmas requires that the equations be valid for large relative perturbation amplitudes and, possibly, large flows. The Hamiltonian gyrokinetic theory has therefore been extended to two new orderings [1,2] that are more general than the standard ones in that they allow for potential perturbations or ExB flows of order the thermal levels. These theories both generalize and show that additional terms should have been present some related prior work. Here, full (low-β) electromagnetic toroidal equation sets are presented, and he energy conservation relations are derived using Noether's theorem in a Lagrangian variational approach. Useful subsidiary and reduced orderings are also considered that result in considerable simplification, and methods for the numerical implementation of the new terms in the equations will also be discussed. *This work was performed for US DOE by LLNL under Contract DE-AC52-07NA27344 and is part of the ESL. [4pt] [1] A.M. Dimits et al., Phys. Fluids B4, 274 (1992). [0pt] [2] A.M. Dimits, Phys. Plasmas 17, 055901 (2010).
Gyrokinetic simulation and theory for kinetic ballooning mode
NASA Astrophysics Data System (ADS)
Li, Yue-Yan; Xiao, Yong
2016-10-01
The kinetic ballooning mode (KBM) plays an important role in H mode formation and edge-localized mode (ELM) physics and internal transport barrier. A thorough understanding of the linear KBM physics is crucial to understanding the nonlinear edge physics in tokamaks. The second stability regime in small shear and sufficiently large pressure gradient has been predicted by the ballooning MHD theory. In the present work, a kinetic ballooning mode is found for the second stability regime in s-alpha space. This KBM mode is characterized by a broad-spread eigenfunction in the ballooning space, and destabilized dramatically by the ion temperature gradient. Such KBM mode almost exists in the entire second stability regime. Also KBM has been found in the sufficiently small shear even with negative shear. The gyrokinetic code GTC is employed to study the KBM physics, and finds that the linear KBM growth rate and frequency are very sensitive to the equilibrium profile. The effect of parallel current and density has been investigated, and comparisons between gyrokinetic simulation and analytic theory are carried out. The results shows that parallel current response have a strong effect in stabilize KBM instability, which could have a large effect on nonlinear electromagnetic turbulent transport.
Nonlinear Gyroviscous Force in a Collisionless Plasma
Belova, E.V.
2001-05-23
Nonlinear gyroviscous forces in a collisionless plasma with temperature variations are calculated from the gyrofluid moments of the gyrokinetic Vlasov equation. The low-frequency gyrokinetic ordering and electrostatic perturbations are assumed, and an additional finite Larmor radius (FLR) expansion is performed. This approach leads naturally to an expression for the gyroviscous force in terms of the gyrocenter distribution function, thus including all resonant effects, and represents a systematic FLR expansion in a general form (no assumption of any closure is made). The expression for the gyroviscous force is also calculated in terms of the particle-fluid moments by making the transformation from the gyrocenter to particle coordinates. The calculated expression represents a modification of the Braginskii gyroviscosity for a collisionless plasma with nonuniform temperature. It is compared with previous calculations based on the traditional fluid approach. As a byproduct of the gyroviscosity calculations, we derive a set of nonlinear reduced gyrofluid (and a corresponding set of particle-fluid) moment equations with FLR corrections, which exhibit a generalized form of the ''gyroviscous cancellation.''
Transport equations for subdiffusion with nonlinear particle interaction.
Straka, P; Fedotov, S
2015-02-07
We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent.
Fast transport in phase space due to nonlinear wave-particle interaction in the radiation belts.
NASA Astrophysics Data System (ADS)
Artemyev, Anton; Vasiliev, Alexii; Mourenas, Didier; Agapitov, Oleksiy; Krasnoselskikh, Vladimir; Boscher, Daniel; Rolland, Guy
2014-05-01
We present an analytical, simplified formulation accounting for the fast transport of particles in phase space, in the presence of nonlinear wave-particle resonant interactions in an inhomogeneous magnetic field representative of the radiation belts. We show that the general approach for the description of the evolution of the particle velocity distribution based on the Fokker-Plank equation can be modified to consider the process of nonlinear wave-particle interaction, including particle trapping. Such a modification consists in one additional operator describing fast particle jumps in phase space. The proposed approach is illustrated by considering the acceleration of relativistic electrons by strongly oblique whistler waves. We determine the typical variation of electron phase-density due to nonlinear wave-particle interaction and compare this variation with pitch-angle/energy diffusion due to quasi-linear electron scattering. We show that relation between nonlinear and quasi-linear effects is controlled by the distribution of wave-amplitudes. When this distribution has a heavy tail, nonlinear effects can become dominant in the formation of the electron energy distribution.
Neoclassical equilibrium in gyrokinetic simulations
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.
2009-06-15
This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.
Neoclassical equilibrium in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.
2009-06-01
This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.
Laboratory Study of Triggered Emissions and Nonlinear Wave-Particle Interactions
NASA Astrophysics Data System (ADS)
Amatucci, B.; Tejero, E. M.; Crabtree, C. E.; Enloe, C. L.; Ganguli, G.
2016-12-01
Experiments conducted in the Space Physics Simulation Chamber at the Naval Research Laboratory using an electron beam propagating in a non-uniform magnetic field and an antenna launching counter-propagating Whistler waves have demonstrated nonlinear Whistler amplification and triggered emissions due to nonlinear wave-particle interactions. When the antenna was not used, chorus-like chirped Whistler waves were observed. These experiments provide a good testbed for studying nonlinear wave-particle interactions and the resulting wave phenomena. Recent results from these experiments will be presented. *Work supported by the Naval Research Laboratory Base Program
Graphics Processing Unit Acceleration of Gyrokinetic Turbulence Simulations
NASA Astrophysics Data System (ADS)
Hause, Benjamin; Parker, Scott; Chen, Yang
2013-10-01
We find a substantial increase in on-node performance using Graphics Processing Unit (GPU) acceleration in gyrokinetic delta-f particle-in-cell simulation. Optimization is performed on a two-dimensional slab gyrokinetic particle simulation using the Portland Group Fortran compiler with the OpenACC compiler directives and Fortran CUDA. Mixed implementation of both Open-ACC and CUDA is demonstrated. CUDA is required for optimizing the particle deposition algorithm. We have implemented the GPU acceleration on a third generation Core I7 gaming PC with two NVIDIA GTX 680 GPUs. We find comparable, or better, acceleration relative to the NERSC DIRAC cluster with the NVIDIA Tesla C2050 computing processor. The Tesla C 2050 is about 2.6 times more expensive than the GTX 580 gaming GPU. We also see enormous speedups (10 or more) on the Titan supercomputer at Oak Ridge with Kepler K20 GPUs. Results show speed-ups comparable or better than that of OpenMP models utilizing multiple cores. The use of hybrid OpenACC, CUDA Fortran, and MPI models across many nodes will also be discussed. Optimization strategies will be presented. We will discuss progress on optimizing the comprehensive three dimensional general geometry GEM code.
Nonlinear Frequency Chirping of beta-induced Aflven eigenmode
NASA Astrophysics Data System (ADS)
Zhang, Huasen
2011-10-01
The β-induced Alfvén eigenmode (BAE) is studied using global gyrokinetic toroidal code GTC. Linear simulations show that kinetic effects modify BAE mode structure and reduce the frequency relative to the MHD theory. Both passing and trapped energetic particles contribute to BAE excitation through transit and bounce- precessional resonance, respectively. Nonlinear simulations show that the unstable BAE saturates due to nonlinear wave-particle interaction with both thermal and energetic particles. The saturated amplitude exhibits a coherent oscillation with an asymmetric growing and damping phase. Wavelet analysis shows that the mode frequency has a strong chirping associated with the oscillation of the mode amplitude. Analysis of nonlinear wave-particle interaction shows that the frequency chirping is induced by the nonlinear evolution of coherent structures in the energetic particle phase space of toroidal angle and precessional frequency. Controlled simulations further find that thermal particle nonlinearity plays a key role in controlling the saturation amplitude. We will also report self-consistent energetic particle transport from turbulence simulation with wave-particle and wave-wave nonlinearity treated on the same footing for the first time. Work in collaboration with W. Deng, I. Holod, Z. Lin, Y. Xiao and supported by DOE SciDAC GSEP Center and INCITE Program.
Features and states of microscopic particles in nonlinear quantum-mechanics systems
NASA Astrophysics Data System (ADS)
Pang, Xiao-Feng
2008-06-01
In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles
Validation of the gyrokinetic model in ITG and TEM dominated L-mode plasmas
NASA Astrophysics Data System (ADS)
Howard, N. T.; White, A. E.; Reinke, M. L.; Greenwald, M.; Holland, C.; Candy, J.; Walk, J. R.
2013-12-01
A rigorous validation of the gyrokinetic model was performed in both ion temperature gradient (ITG) and trapped electron mode (TEM) dominated Alcator C-Mod plasmas at (normalized midplane minor radius) r/a = 0.5 and 0.8. Analysis focuses on two L-mode discharges operated with 1.2 and 3.5 MW of ion cyclotron resonance heating. In depth investigation into the experimental uncertainties and simulation sensitivities in these discharges allows for a stringent test of the gyrokinetic model implemented by the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) in both the centre of the stiff gradient region (r/a = 0.5) and the middle of the region often associated with the transport ‘shortfall’(r/a = 0.8). To identify the nature of the plasma turbulence and to ensure a robust evaluation of the model's ability to reproduce experiment, the sensitivity of the simulation results to experimental uncertainty in turbulence drive and suppression terms were determined at both radial locations. When significant TEM activity is present, nonlinear gyrokinetic simulations are found to reproduce both electron and ion experimental heat fluxes within their diagnosed uncertainties. In contrast, in the absence of TEM, electron heat fluxes are robustly under predicted by low-k, gyrokinetic simulation.
Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas
Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.
1996-12-17
A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, {delta}f = f {minus} f{sub 0}, from an initial analytic distribution f{sub 0}. High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question.
Zacharias, O.; Kleiber, R.; Borchardt, M.; Comisso, L.; Grasso, D.; Hatzky, R.
2014-06-15
The first detailed comparison between gyrokinetic and gyrofluid simulations of collisionless magnetic reconnection has been carried out. Both the linear and nonlinear evolution of the collisionless tearing mode have been analyzed. In the linear regime, we have found a good agreement between the two approaches over the whole spectrum of linearly unstable wave numbers, both in the drift kinetic limit and for finite ion temperature. Nonlinearly, focusing on the small-Δ′ regime, with Δ′ indicating the standard tearing stability parameter, we have compared relevant observables such as the evolution and saturation of the island width, as well as the island oscillation frequency in the saturated phase. The results are basically the same, with small discrepancies only in the value of the saturated island width for moderately high values of Δ′. Therefore, in the regimes investigated here, the gyrofluid approach can describe the collisionless reconnection process as well as the more complete gyrokinetic model.
Particle-Wave Micro-Dynamics in Nonlinear Self-Excited Dust Acoustic Waves
Tsai, C.-Y.; Teng, L.-W.; Liao, C.-T.; I Lin
2008-09-07
The large amplitude dust acoustic wave can be self-excited in a low-pressure dusty plasma. In the wave, the nonlinear wave-particle interaction determines particle motion, which in turn determines the waveform and wave propagation. In this work, the above behaviors are investigated by directly tracking particle motion through video-microscopy. A Lagrangian picture for the wave dynamics is constructed. The wave particle interaction associated with the transition from ordered to disordered particle oscillation, the wave crest trapping and wave heating are demonstrated and discussed.
Multi-code benchmark of global gyrokinetic electromagnetic instabilities
NASA Astrophysics Data System (ADS)
Goerler, Tobias; Bottino, Alberto; Hornsby, William A.; Kleiber, Ralf; Tronko, Natalia; Grandgirard, Virginie; Norscini, Claudia; Sonnendruecker, Eric
2015-11-01
Considering the recent major extensions of global gyrokinetic codes towards a comprehensive and self-consistent treatment of electromagnetic (EM) effects, corresponding verification tests are obvious and necessary steps to be taken. While a number of (semi-)analytic test cases and benchmarks exist in the axisymmetric limit, microinstabilities and particularly EM turbulence are rarely addressed. In order to remedy this problem, a hierarchical linear gyrokinetic benchmark study is presented starting with electrostatic ion temperature gradient microinstabilities with adiabatic electron response and progressing finally to the characterization of fully EM instabilities as a function of β. The inter-code comparison involves contributions from Eulerian Vlasov, Lagrangian PIC, and Semi-Lagrange codes at least in one level of this verification exercise, thus confirming a high degree of reliability for the implementations that has rarely been achieved before in this context. Additionally, possible extensions of this benchmark into the physically more relevant nonlinear turbulence regime will be discussed, e.g., relaxation problems or gradient-driven setups. This work has been carried out within the framework of the EUROfusion Consortium.
Direct identification of predator-prey dynamics in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Kobayashi, Sumire; Gürcan, Özgür D.; Diamond, Patrick H.
2015-09-01
The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.
Gyrokinetic simulations of microturbulence in DIII-D tokamak pedestal
NASA Astrophysics Data System (ADS)
Holod, Ihor; Fulton, Daniel; Taimourzadeh, Sam; Lin, Zhihong; Nazikian, Raffi; Spong, Donald
2015-11-01
The characteristics of H-mode pedestal are generally believed to be constrained by current-driven peeling-ballooning modes and pressure-driven instabilities, such as kinetic ballooning mode (KBM). In this work we use global gyrokinetic code (GTC) to identify and study the edge pressure-driven instabilities in the H-mode pedestal using realistic geometry and plasma profiles of DIII-D shot 131997. In our simulations we observe the KBM mode marginally dominant in the steep gradient region (ψN = 0 . 98), in the range of kθ ~ 1 cm-1 which corresponds to the most unstable mode number in the nonlinearly saturated state. For shorter wavelengths the trapped electron mode becomes dominant since its linear growth rate increases with the mode number, while the KBM gets saturated. In the pedestal top region (ψN = 0 . 95) the ITG dominates. Resonant magnetic perturbations (RMP) are widely applied for ELM mitigation. During RMP suppression, the increase of edge turbulence is often observed. To understand this phenomena we use gyrokinetic simulations to address the direct effect of magnetic perturbations on the microturbulence. Simulations with 3D equilibrium reconstructed by VMEC code have been compared with toroidally averaged equilibrium, using identical pressure profiles. Work supported by DOE grant DE-SC0010416 and by General Atomics subcontract.
Direct identification of predator-prey dynamics in gyrokinetic simulations
Kobayashi, Sumire Gürcan, Özgür D; Diamond, Patrick H.
2015-09-15
The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.
Self-consistent modeling of multiscale gyrokinetics and transport
NASA Astrophysics Data System (ADS)
Parker, Jeffrey; Lodestro, Lynda; Told, Daniel; Jenko, Frank
2016-10-01
In the core of tokamak plasmas, a separation of timescales between turbulence and transport makes direct simulation of both processes computationally expensive. A workable, practical method to exploit the separation of timescales will be a key component in enabling the self-consistent solution of macroscopic profiles of density and temperature. We report on progress to implement the LoDestro scheme coupled with the gyrokinetic code GENE to perform for the first time coupled turbulence and transport simulations using a global gyrokinetic code. One of the advantages of the LoDestro scheme, which is essentially a method of solving an implicitly advanced nonlinear transport problem, is that it does not use Newton iteration and hence avoids difficulties that arise from calculating Jacobians or Jacobian-vector products in the presence of noisy fluxes. Instead, the implicit timestep equation is solved with an iteration scheme by representing the turbulent flux as the sum of diffusive and convective pieces, after which Picard iteration is used to converge to the self-consistent solution. Preliminary results will be presented. Prepared by LLNL under Contract DE-AC52-07NA27344.
A 5D gyrokinetic full- f global semi-Lagrangian code for flux-driven ion turbulence simulations
NASA Astrophysics Data System (ADS)
Grandgirard, V.; Abiteboul, J.; Bigot, J.; Cartier-Michaud, T.; Crouseilles, N.; Dif-Pradalier, G.; Ehrlacher, Ch.; Esteve, D.; Garbet, X.; Ghendrih, Ph.; Latu, G.; Mehrenberger, M.; Norscini, C.; Passeron, Ch.; Rozar, F.; Sarazin, Y.; Sonnendrücker, E.; Strugarek, A.; Zarzoso, D.
2016-10-01
This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic GYSELA code is one of the few international 5D gyrokinetic codes able to perform global, full- f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the GYSELA code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.
Gyrokinetic simulations of collisionless reconnection in turbulent non-uniform plasmas
Kobayashi, Sumire; Rogers, Barrett N.; Numata, Ryusuke
2014-04-15
We present nonlinear gyrokinetic simulations of collisionless magnetic reconnection with non-uniformities in the plasma density, the electron temperature, and the ion temperature. The density gradient can stabilize reconnection due to diamagnetic effects but destabilize driftwave modes that produce turbulence. The electron temperature gradient triggers microtearing modes that drive rapid small-scale reconnection and strong electron heat transport. The ion temperature gradient destabilizes ion temperature gradient modes that, like the driftwaves, may enhance reconnection in some cases.
NASA Astrophysics Data System (ADS)
Bourouaine, Sofiane; Howes, Gregory G.
2017-06-01
The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time 2$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time 2$ for strong turbulence, and at 2$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval 22$ . Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form 2\\rangle =A(z/L\\Vert )p$ ( \\Vert $ is the correlation length parallel to the magnetic background field \\mathbf{0}$ , is the distance along \\mathbf{0}$ direction), providing functional forms of the amplitude coefficient and power-law exponent as a function of the nonlinearity parameter.
Bounce-Averaged Gyrokinetic Simulation of Current-Collection Feedback in a Laboratory Magnetosphere
NASA Astrophysics Data System (ADS)
Roberts, T. M.; Garnier, D.; Kesner, J.; Mauel, M. E.
2014-10-01
A self-consistent, nonlinear simulation of interchange dynamics including the bounce-averaged gyro-kinetics of trapped electrons was previously used to understand frequency sweeping and the turbulent cascades observed in dipole-confined plasmas. Through adjustment of the particle and heat sources this code reproduces dynamics that resemble the turbulence measured experimentally, both in spectral power-law trends and in the onset of a steepened density profile. Time stepping is performed in an explicit leap-frog manner and a flux-corrected transport algorithm is implemented. In this presentation, we discuss the physics and numerical methods of the simulations as well as plans for including the effects of a biasing electrode which can collect or inject electrons. By varying this source/sink of electrons at the electrode location based on the potential fluctuations occurring elsewhere, we study the effects of current-collection feedback to compare to recent experiments observed to regulate interchange turbulence. Supported by NSF-DOE Partnership for Plasma Science and DOE Grant DE-FG02-00ER54585 and NSF Award PHY-1201896.
Spectral attenuation of sound in dilute suspensions with nonlinear particle relaxation.
Kandula, Max
2008-11-01
Previous studies on the sound attenuation in particle-laden flows under Stokesian drag and conduction-controlled heat transfer have been extended to accommodate the nonlinear drag and heat transfer. It has been shown that for large particle-to-fluid density ratio, the particle Reynolds number bears a cubic relationship with omegatau(d) (where omega is the circular frequency and tau(d) is the Stokesian particle relaxation time). This dependence leads to the existence of a peak value in the linear absorption coefficient occurring at a finite value of omegatau(d). Comparison of the predictions with the test data for the spectral attenuation of sound with water injection in a perfectly expanded supersonic air jet shows a satisfactory trend of the theory accounting for nonlinear particle relaxation processes.
NASA Astrophysics Data System (ADS)
Hieber, Simone E.; Koumoutsakos, Petros
2008-11-01
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress-strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.
Spectral Attenuation of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
NASA Technical Reports Server (NTRS)
Kandula, Max
2008-01-01
Previous studies on the sound attenuation in particle-laden flows under Stokesian drag and conduction-controlled heat transfer have been extended to accommodate the nonlinear drag and heat transfer. It has been shown that for large particle-to-fluid density ratio, the particle Reynolds number bears a cubic relationship with (omega(tau))(sub d) (where omega is the circular frequency and (tau)(sub d) the Stokesian particle relaxation time). This dependence leads to the existence of a peak value in the linear absorption coefficient occurring at a finite value of(omega(tau))(sub d). Comparison of the predictions with the test data for the spectral attenuation of sound with water injection in a perfectly expanded supersonic air jet shows a satisfactory trend of the theory accounting for nonlinear particle relaxation processes.
Spectral Attenuation of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
NASA Technical Reports Server (NTRS)
Kandula, M.; Lonegran, M.
2008-01-01
Theoretical studies on the dissipation and dispersion of sound in two-phase suspensions have been briefly reviewed. Previous studies on the sound attenuation in particle-laden flows under Stokesian drag and conduction-controlled heat transfer have been extended to accommodate the nonlinear drag and heat transfer. It has been shown that for large particle-to-fluid density ratio, the particle Reynolds number bears a cubic relationship with Omega Tau(sub d) (where Omega is the circular frequency and Tau(sub d) the Stokesian particle relaxation time). This dependence leads to the existence of a peak value in the linear absorption coefficient occurring at a finite value Omega Tau (sub d). Comparison of the predictions with the test data for the spectral attenuation of sound with water injection in a perfectly expanded supersonic air jet shows a satisfactory trend of the theory accounting for nonlinear particle relaxation processes.
Hybrid Gyrofluid/Gyrokinetic Modeling of Tokamak Turbulence with GryfX
NASA Astrophysics Data System (ADS)
Mandell, Noah; Dorland, Bill; Highcock, Edmund; Hammett, Greg
2016-10-01
Gyrofluid models are more efficient than gyrokinetic models, but have a disadvantage in their potential lack of physics fidelity. Here we present three major improvements to the physics fidelity and speed of gyrofluid models, which we encapsulate in the GryfX gyrofluid turbulence code. First, we implement a new nonlinear closure to model the cascade of free energy simultaneously in k⊥ and v⊥ via nonlinear phase-mixing (NLPM). Second, we use a hybrid algorithm that improves zonal flow physics by simulating zonal flow modes with a fully gyrokinetic model. These two improvements bring heat flux predictions from nonlinear GryfX simulations into agreement with the gyrokinetic code GS2. Third, we implement the equations on modern heterogeneous computing platforms, both as a standalone simulation tool that exploits the power of GPUs and as a component of TRINITY (a transport modeling code for tokamaks). GryfX has a roughly 1,200 times performance advantage over GS2 due to the combination of GPU acceleration and the reduction of hundreds of velocity space grid points to six gyrofluid moments. This makes GryfX ideal for large parameter scans, and enables the use of the TRINITY-GryfX system for efficient multi-scale analysis of tokamak turbulence on transport time scales. Present address: Chalmers University, Gothenburg, Sweden.
Global gyrokinetic simulations with strong flows
NASA Astrophysics Data System (ADS)
Collier, J. D.; McMillan, B. F.; Robinson, J. R.
2016-11-01
We report on the investigation of strong toroidal rotation effects in a global tokamak code, ORB5. This includes the implementation of a strong flow gyrokinetic Lagrangian, allowing a complete treatment of centrifugal and Coriolis effects in the laboratory frame. In order to consistently perform the linear analysis in this system, an axisymmetric gyrokinetic equilibrium distribution function is defined using the constants of motion: we show it corresponds to the standard choice in the local limit and is close to the neoclassical solution in the banana regime. The energy and momentum transport equations are presented in an analogous form to those for the weak flow system. Linear studies of Ion Temperature Gradient (ITG) modes in rotating plasmas are performed to determine how the global effects interact with the effects of strong rotation. We also determine the geodesic acoustic mode dispersion with respect to plasma rotation rate in this gyrokinetic model and compare it to MHD theory.
Dynamic procedure for filtered gyrokinetic simulations
Morel, P.; Banon Navarro, A.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2012-01-15
Large eddy simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the gene code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved direct numerical simulations. Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in ion temperature gradient driven turbulence. Moreover, the degree of anisotropy of the problem, which can vary with parameters, can be adapted dynamically by the method that shows gyrokinetic large eddy simulation to be a serious candidate to reduce numerical cost of gyrokinetic solvers.
Edward A. Startsev; Ronald C. Davidson; Hong Qin
2002-05-07
In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T{sub {perpendicular}b} >> T{sub {parallel}b}). The most unstable modes are identified, and their eigen frequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with {partial_derivative}/{partial_derivative}{theta} = 0.
Nonlinear ion-mixing-mode particle transport in the dissipative trapped electron regime
Ware, A.S.; Terry, P.W.
1993-09-01
The nonlinear particle transport arising from the convection of nonadiabatic electron density by ion temperature gradient driven turbulence is examined for trapped electron collisionality regimes. The renormalized dissipative nonadiabatic trapped electron phase space density response is derived and used to calculate the nonlinear particle flux along with an ansatz for the turbulently broadened frequency spectrum. In the lower temperature end of this regime, trapped electrons are collisional and all components of the quasilinear particle flux are outward (i.e., in the direction of the gradients). Nonlinear effects can alter the phase between the nonadiabatic trapped electron phase space density and the electrostatic potential, producing inward components in the particle flux. Specifically, both turbulent shifting of the peak of the frequency spectrum and nonlinear source terms in the trapped electron response can give rise to inward components. However, in the dissipative regime these terms are small and the trapped electron response remains dominantly laminar. When the trapped electrons are collisionless, there is a temperature threshold above which the electron temperature gradient driven component of the quasilinear particle flux changes sign and becomes inward. For finite amplitude turbulence, however, turbulent broadening of both the electron collisional resonance and the frequency spectrum removes tills threshold., and the temperature gradient driven component remains outward.
Properties of Discontinuous Galerkin Algorithms and Implications for Edge Gyrokinetics
NASA Astrophysics Data System (ADS)
Hammett, G. W.; Hakim, A.; Shi, E. L.; Abel, I. G.; Stoltzfus-Dueck, T.
2015-11-01
The continuum gyrokinetic code Gkeyll uses Discontinuous Galerkin (DG) algorithms, which have a lot of flexibility in the choice of basis functions and inner product norm that can be useful in designing algorithms for particular problems. Rather than use regular polynomial basis functions, we consider here Maxwellian-weighted basis functions (which have similarities to Gaussian radial basis functions). The standard Galerkin approach loses particle and energy conservation, but this can be restored with a particular weight for the inner product (this is equivalent to a Petrov-Galerkin method). This allows a full- F code to have some benefits similar to the Gaussian quadrature used in gyrokinetic δf codes to integrate Gaussians times some polynomials exactly. In tests of Gkeyll for electromagnetic fluctuations, we found it is important to use consistent basis functions where the potential is in a higher-order continuity subspace of the space for the vector potential A| |. A regular projection method to this subspace is a non-local operation, while we show a self-adjoint averaging operator that can preserve locality and energy conservation. This does not introduce damping, but like gyro-averaging involves only the reactive part of the dynamics. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.
Implications of advanced collision operators for gyrokinetic simulation
NASA Astrophysics Data System (ADS)
Belli, E. A.; Candy, J.
2017-04-01
In this work, we explore both the potential improvements and pitfalls that arise when using advanced collision models in gyrokinetic simulations of plasma microinstabilities. Comparisons are made between the simple-but-standard electron Lorentz operator and specific variations of the advanced Sugama operator. The Sugama operator describes multi-species collisions including energy diffusion, momentum and energy conservation terms, and is valid for arbitrary wavelength. We report scans over collision frequency for both low and high {k}θ {ρ }s modes, with relevance for multiscale simulations that couple ion and electron scale physics. The influence of the ion–ion collision terms—not retained in the electron Lorentz model—on the damping of zonal flows is also explored. Collision frequency scans for linear and nonlinear simulations of ion-temperature-gradient instabilities including impurity ions are presented. Finally, implications for modeling turbulence in the highly collisional edge are discussed.
Gyrokinetic turbulence under near-separatrix or nonaxisymmetric conditionsa)
NASA Astrophysics Data System (ADS)
Jenko, F.; Told, D.; Xanthopoulos, P.; Merz, F.; Horton, L. D.
2009-05-01
Linear and nonlinear gyrokinetic simulations with the GENE code [F. Jenko et al., Phys. Plasmas 7, 1904 (2000)] for tokamak edge plasmas as well as for stellarator core plasmas are presented, shedding light on the behavior of plasma microturbulence under near-separatrix or nonaxisymmetric conditions. To this aim, the required geometric coefficients are inferred directly from the magnetohydrodynamic equilibria of three different devices via the newly developed GIST code. It is found that the residual electron heat transport level in the H-mode edge can be explained in terms of high-wave-number fluctuations driven by electron temperature gradient modes. Moreover, the study of adiabatic ion temperature gradient turbulence in optimized stellarators points to the possibility of a systematic geometric optimization with respect to anomalous transport in nonaxisymmetric devices.
Complex statistics and diffusion in nonlinear disordered particle chains
Antonopoulos, Ch. G.; Bountis, T.; Skokos, Ch.; Drossos, L.
2014-06-15
We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10{sup 9}, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.
Complex statistics and diffusion in nonlinear disordered particle chains
Antonopoulos, Ch. G.; Bountis, T.; Skokos, Ch.; Drossos, L.
2014-06-15
We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10{sup 9}, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.
Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulationsa)
NASA Astrophysics Data System (ADS)
White, A. E.; Howard, N. T.; Greenwald, M.; Reinke, M. L.; Sung, C.; Baek, S.; Barnes, M.; Candy, J.; Dominguez, A.; Ernst, D.; Gao, C.; Hubbard, A. E.; Hughes, J. W.; Lin, Y.; Mikkelsen, D.; Parra, F.; Porkolab, M.; Rice, J. E.; Walk, J.; Wukitch, S. J.; Team, Alcator C-Mod
2013-05-01
Multi-channel transport experiments have been conducted in auxiliary heated (Ion Cyclotron Range of Frequencies) L-mode plasmas at Alcator C-Mod [Marmar and Alcator C-Mod Group, Fusion Sci. Technol. 51(3), 3261 (2007)]. These plasmas provide good diagnostic coverage for measurements of kinetic profiles, impurity transport, and turbulence (electron temperature and density fluctuations). In the experiments, a steady sawtoothing L-mode plasma with 1.2 MW of on-axis RF heating is established and density is scanned by 20%. Measured rotation profiles change from peaked to hollow in shape as density is increased, but electron density and impurity profiles remain peaked. Ion or electron heat fluxes from the two plasmas are the same. The experimental results are compared directly to nonlinear gyrokinetic theory using synthetic diagnostics and the code GYRO [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. We find good agreement with experimental ion heat flux, impurity particle transport, and trends in the fluctuation level ratio (T˜e/Te)/(n ˜e/ne), but underprediction of electron heat flux. We find that changes in momentum transport (rotation profiles changing from peaked to hollow) do not correlate with changes in particle transport, and also do not correlate with changes in linear mode dominance, e.g., Ion Temperature Gradient versus Trapped Electron Mode. The new C-Mod results suggest that the drives for momentum transport differ from drives for heat and particle transport. The experimental results are inconsistent with present quasilinear models, and the strong sensitivity of core rotation to density remains unexplained.
Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulations
White, A. E.; Howard, N. T.; Greenwald, M.; Reinke, M. L.; Sung, C.; Baek, S.; Barnes, M.; Dominguez, A.; Ernst, D.; Gao, C.; Hubbard, A. E.; Hughes, J. W.; Lin, Y.; Parra, F.; Porkolab, M.; Rice, J. E.; Walk, J.; Wukitch, S. J.; Team, Alcator C-Mod; Candy, J.; and others
2013-05-15
Multi-channel transport experiments have been conducted in auxiliary heated (Ion Cyclotron Range of Frequencies) L-mode plasmas at Alcator C-Mod [Marmar and Alcator C-Mod Group, Fusion Sci. Technol. 51(3), 3261 (2007)]. These plasmas provide good diagnostic coverage for measurements of kinetic profiles, impurity transport, and turbulence (electron temperature and density fluctuations). In the experiments, a steady sawtoothing L-mode plasma with 1.2 MW of on-axis RF heating is established and density is scanned by 20%. Measured rotation profiles change from peaked to hollow in shape as density is increased, but electron density and impurity profiles remain peaked. Ion or electron heat fluxes from the two plasmas are the same. The experimental results are compared directly to nonlinear gyrokinetic theory using synthetic diagnostics and the code GYRO [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. We find good agreement with experimental ion heat flux, impurity particle transport, and trends in the fluctuation level ratio (T(tilde sign){sub e}/T{sub e})/(ñ{sub e}/n{sub e}), but underprediction of electron heat flux. We find that changes in momentum transport (rotation profiles changing from peaked to hollow) do not correlate with changes in particle transport, and also do not correlate with changes in linear mode dominance, e.g., Ion Temperature Gradient versus Trapped Electron Mode. The new C-Mod results suggest that the drives for momentum transport differ from drives for heat and particle transport. The experimental results are inconsistent with present quasilinear models, and the strong sensitivity of core rotation to density remains unexplained.
Nonlinear dispersive evolution of coherent trapped particle structures in collisionless plasmas
NASA Astrophysics Data System (ADS)
Mandal, Debraj; Sharma, Devendra
2016-10-01
The nonlinear limit of the collective perturbations in plasma is characterized by the onset of amplitude dependence in the wave dispersion. In a special class of nonlinear effects having origin in plasma kinetic theory, this amplitude dependence is removed only by collisions such that perturbations have no linear counterpart in collisionless limit and must follow a nonlinear dispersion relation (NDR). Exploring whether these fundamentally nonlinear perturbations can be driven unstable without entropy production might transform the character of the linear threshold based operating mechanism of the plasma turbulence that relies on well defined discrete spectrum prescribed by the linear plasma dispersion. In our multiscale, exact mass ratio, kinetic simulations the evolution of fundamentally nonlinear trapped particle structures is explored on both fast and slow ion and electron acoustic branches of the associated Nonlinear dispersion relation, respectively. The propagating structures that mutually interact exhibit a near continuum of the phase velocities and show microscopic evolution of the separatrix between streaming and trapped particle regions in the phase space, describing the subtle continuity between discrete and continuum bases of the plasma turbulence.
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Waelbroeck, F. L.
2012-03-01
Static external resonant magnetic field perturbations (RMPs) have been added to the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comp. Phys. 186, 545 (2003)]. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr, and the corresponding j→×B→ plasma torque (density) R[jrBp/c], induced by magnetic islands that break the toroidal symmetry of a tokamak. This extends the previous GYRO formulation for the transport of toroidal angular momentum (TAM) [R. E. Waltz, G. M. Staebler, J. Candy, and F. L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)]. The focus is on electrostatic full torus radial slice simulations of externally induced q =m/n=6/3 islands with widths 5% of the minor radius or about 20 ion gyroradii. Up to moderately strong E ×B rotation, the island torque scales with the radial electric field at the resonant surface Er, the island width w, and the intensity I of the high-n micro-turbulence, as Erw√I . The radial current inside the island is carried (entirely in the n =3 component) and almost entirely by the ion E ×B flux, since the electron E ×B and magnetic flutter particle fluxes are cancelled. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that while the expected magnetic braking of the toroidal plasma rotation occurs at strong co- and counter-current rotation, at null toroidal rotation, there is a small co-directed magnetic acceleration up to the small diamagnetic (ion pressure gradient driven) co-rotation corresponding to the zero Er and null torque. This could be called the residual stress from an externally induced island. At zero Er, the only effect is the expected partial flattening of the electron temperature gradient within the island. Finite-beta GYRO simulations demonstrate almost complete RMP field screening and n =3 mode unlocking at strong Er.
NASA Astrophysics Data System (ADS)
Sajeeb, R.; Manohar, C. S.; Roy, D.
2007-09-01
The problem of active control of nonlinear structural dynamical systems, in the presence of both process and measurement noises, is considered. The focus of the study is on the use of particle filters for state estimation in feedback control algorithms for nonlinear structures, when a limited number of noisy output measurements are available. The control design is done using the state-dependent Riccati equation (SDRE) method. The stochastic differential equations (SDEs) governing the dynamical systems are discretized using explicit forms of Ito-Taylor expansions. The Bayesian bootstrap filter and that based on sequential important sampling (SIS) are employed for state estimation. The simulation results show the feasibility of using particle filters and SDRE techniques in control of nonlinear structural dynamical systems.
Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams
Nikolas C. Logan and Ronald C. Davidson
2012-07-18
This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllT⊥ < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.
Particle-like representation for the field of a moving point charge in nonlinear electrodynamics
NASA Astrophysics Data System (ADS)
Gitman, D. M.; E Shabad, A.; Shishmarev, A. A.
2017-05-01
In a simple nonlinear model stemming from quantum electrodynamics wherein the pointlike charge has finite field-self-energy, we demonstrate that the latter can be presented as a soliton with its energy-momentum vector satisfying the standard mechanical relation characteristic of a free moving massive relativistic particle.
A baker's dozen of new particle flows for nonlinear filters, Bayesian decisions and transport
NASA Astrophysics Data System (ADS)
Daum, Fred; Huang, Jim
2015-05-01
We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.
Beyond scale separation in gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Garbet, X.; Sarazin, Y.; Grandgirard, V.; Dif-Pradalier, G.; Darmet, G.; Ghendrih, Ph.; Angelino, P.; Bertrand, P.; Besse, N.; Gravier, E.; Morel, P.; Sonnendrücker, E.; Crouseilles, N.; Dischler, J.-M.; Latu, G.; Violard, E.; Brunetti, M.; Brunner, S.; Lapillonne, X.; Tran, T.-M.; Villard, L.; Boulet, M.
2007-09-01
This paper presents the results obtained with a set of gyrokinetic codes based on a semi-Lagrangian scheme. Several physics issues are addressed, namely, the comparison between fluid and kinetic descriptions, the intermittent behaviour of flux driven turbulence and the role of large scale flows in toroidal ITG turbulence. The question of the initialization of full-F simulations is also discussed.
NASA Technical Reports Server (NTRS)
Tkalcevic, S.
1982-01-01
The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.
NASA Astrophysics Data System (ADS)
Liu, Tianyu; Jiao, Licheng; Ma, Wenping; Shang, Ronghua
2017-03-01
In this paper, an improved quantum-behaved particle swarm optimization (CL-QPSO), which adopts a new collaborative learning strategy to generate local attractors for particles, is proposed to solve nonlinear numerical problems. Local attractors, which directly determine the convergence behavior of particles, play an important role in quantum-behaved particle swarm optimization (QPSO). In order to get a promising and efficient local attractor for each particle, a collaborative learning strategy is introduced to generate local attractors in the proposed algorithm. Collaborative learning strategy consists of two operators, namely orthogonal operator and comparison operator. For each particle, orthogonal operator is used to discover the useful information that lies in its personal and global best positions, while comparison operator is used to enhance the particle's ability of jumping out of local optima. By using a probability parameter, the two operators cooperate with each other to generate local attractors for particles. A comprehensive comparison of CL-QPSO with some state-of-the-art evolutionary algorithms on nonlinear numeric optimization functions demonstrates the effectiveness of the proposed algorithm.
The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence
Staebler, Gary M.; Candy, John; Howard, Nathan T.; ...
2016-06-29
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the thresholdmore » for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. Finally, the zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ionscale gyrokinetic simulations.« less
The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence
Staebler, Gary M.; Candy, John; Howard, Nathan T.; Holland, Christopher
2016-06-29
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. Finally, the zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ionscale gyrokinetic simulations.
The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence
Staebler, G. M.; Candy, J.; Howard, N. T.; Holland, C.
2016-06-15
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.
Gyrokinetic simulation of edge blobs and divertor heat-load footprint
NASA Astrophysics Data System (ADS)
Chang, C. S.; Ku, S.; Hager, R.; Churchill, M.; D'Azevedo, E.; Worley, P.
2015-11-01
Gyrokinetic study of divertor heat-load width Lq has been performed using the edge gyrokinetic code XGC1. Both neoclassical and electrostatic turbulence physics are self-consistently included in the simulation with fully nonlinear Fokker-Planck collision operation and neutral recycling. Gyrokinetic ions and drift kinetic electrons constitute the plasma in realistic magnetic separatrix geometry. The electron density fluctuations from nonlinear turbulence form blobs, as similarly seen in the experiments. DIII-D and NSTX geometries have been used to represent today's conventional and tight aspect ratio tokamaks. XGC1 shows that the ion neoclassical orbit dynamics dominates over the blob physics in setting Lq in the sample DIII-D and NSTX plasmas, re-discovering the experimentally observed 1/Ip type scaling. Magnitude of Lq is in the right ballpark, too, in comparison with experimental data. However, in an ITER standard plasma, XGC1 shows that the negligible neoclassical orbit excursion effect makes the blob dynamics to dominate Lq. Differently from Lq 1mm (when mapped back to outboard midplane) as was predicted by simple-minded extrapolation from the present-day data, XGC1 shows that Lq in ITER is about 1 cm that is somewhat smaller than the average blob size. Supported by US DOE and the INCITE program.
Simulating the effects of stellarator geometry on gyrokinetic drift-wave turbulence
NASA Astrophysics Data System (ADS)
Baumgaertel, Jessica Ann
Nuclear fusion is a clean, safe form of energy with abundant fuel. In magnetic fusion energy (MFE) experiments, the plasma fuel is confined by magnetic fields at very high temperatures and densities. One fusion reactor design is the non-axisymmetric, torus-shaped stellarator. Its fully-3D fields have advantages over the simpler, better-understood axisymmetric tokamak, including the ability to optimize magnetic configurations for desired properties, such as lower transport (longer confinement time). Turbulence in the plasma can break MFE confinement. While turbulent transport is known to cause a significant amount of heat loss in tokamaks, it is a new area of research in stellarators. Gyrokinetics is a good mathematical model of the drift-wave instabilities that cause turbulence. Multiple gyrokinetic turbulence codes that had great success comparing to tokamak experiments are being converted for use with stellarator geometry. This thesis describes such adaptations of the gyrokinetic turbulence code, GS2. Herein a new computational grid generator and upgrades to GS2 itself are described, tested, and benchmarked against three other gyrokinetic codes. Using GS2, detailed linear studies using the National Compact Stellarator Experiment (NCSX) geometry were conducted. The first compares stability in two equilibria with different β=(plasma pressure)/(magnetic pressure). Overall, the higher β case was more stable than the lower β case. As high β is important for MFE experiments, this is encouraging. The second compares NCSX linear stability to a tokamak case. NCSX was more stable with a 20% higher critical temperature gradient normalized by the minor radius, suggesting that the fusion power might be enhanced by ˜ 50%. In addition, the first nonlinear, non-axisymmetric GS2 simulations are presented. Finally, linear stability of two locations in a W7-AS plasma were compared. The experimentally-measured parameters used were from a W7-AS shot in which measured heat fluxes
Gyrokinetic studies of core turbulence features in ASDEX Upgrade H-mode plasmas
Navarro, A. Bañón Told, D.; Happel, T.; Görler, T.; Abiteboul, J.; Bustos, A.; Doerk, H.; Jenko, F.
2015-04-15
Gyrokinetic validation studies are crucial for developing confidence in the model incorporated in numerical simulations and thus improving their predictive capabilities. As one step in this direction, we simulate an ASDEX Upgrade discharge with the GENE code, and analyze various fluctuating quantities and compare them to experimental measurements. The approach taken is the following. First, linear simulations are performed in order to determine the turbulence regime. Second, the heat fluxes in nonlinear simulations are matched to experimental fluxes by varying the logarithmic ion temperature gradient within the expected experimental error bars. Finally, the dependence of various quantities with respect to the ion temperature gradient is analyzed in detail. It is found that density and temperature fluctuations can vary significantly with small changes in this parameter, thus making comparisons with experiments very sensitive to uncertainties in the experimental profiles. However, cross-phases are more robust, indicating that they are better observables for comparisons between gyrokinetic simulations and experimental measurements.
Barnes, M.; Dorland, W.; Tatsuno, T.; Abel, I. G.; Hammett, G. W.; Ricci, P.; Rogers, B. N.; Schekochihin, A. A.
2009-07-15
A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Comm. 88, 128 (1995)] is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-03
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. We focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cellequations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheathboundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. Finally, this test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
Shi, E. L.; Hakim, A. H.; Hammett, G. W.
2015-02-03
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. We focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cellequations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheathboundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. Finally, this test problem also helps illustratemore » some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.« less
A nonlinear auxetic structural vibration damper with metal rubber particles
NASA Astrophysics Data System (ADS)
Ma, Yanhong; Scarpa, Fabrizio; Zhang, Dayi; Zhu, Bin; Chen, Lulu; Hong, Jie
2013-08-01
The work describes the mechanical performance of a metal rubber particles (MRP) damper design based on an auxetic (negative Poisson’s ratio) cellular configuration. The auxetic damper configuration is constituted by an anti-tetrachiral honeycomb, where the cylinders are filled with the MRP material. The MRP samples have been subjected to quasi-static loading to measure the stiffness and loss factor from the static hysteresis curve. A parametric experimental analysis has been carried out to investigate the effect of relative density and filling percentage on the static performance of the MRP, and to identify design guidelines for best use of MRP devices. An experimental assessment of the integrated auxetic-MRP damper concept has been provided through static and dynamic force response techniques.
Huang, Xiaobiao; Safranek, James
2014-09-01
Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles
G.Y. Fu
2010-10-01
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles
G. Y. Fu
2010-06-04
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Nonlinear simulations of particle source effects on edge localized mode
Huang, J.; Tang, C. J.; Chen, S. Y.; Wang, Z. H.
2015-12-15
The effects of particle source (PS) with different intensities and located positions on Edge Localized Mode (ELM) are systematically studied with BOUT++ code. The results show the ELM size strongly decreases with increasing the PS intensity once the PS is located in the middle or bottom of the pedestal. The effects of PS on ELM depend on the located position of PS. When it is located at the top of the pedestal, peeling-ballooning (P-B) modes can extract more free energy from the pressure gradient and grow up to be a large filament at the initial crash phase and the broadening of mode spectrum can be suppressed by PS, which leads to more energy loss. When it is located in the middle or bottom of the pedestal, the extraction of free energy by P-B modes can be suppressed, and a small filament is generated. During the turbulence transport phase, the broader mode spectrum suppresses the turbulence transport when PS is located in the middle, while the zonal flow plays an important role in damping the turbulence transport when PS is located at the bottom.
Non-perturbative aspects of particle acceleration in non-linear electrodynamics
Burton, David A.; Flood, Stephen P.; Wen, Haibao
2015-04-15
We undertake an investigation of particle acceleration in the context of non-linear electrodynamics. We deduce the maximum energy that an electron can gain in a non-linear density wave in a magnetised plasma, and we show that an electron can “surf” a sufficiently intense Born-Infeld electromagnetic plane wave and be strongly accelerated by the wave. The first result is valid for a large class of physically reasonable modifications of the linear Maxwell equations, whilst the second result exploits the special mathematical structure of Born-Infeld theory.
Verification of nonlinear particle simulation of radio frequency waves in tokamak
Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.; Zhang, W.; Sun, G. Y.; Fisch, N. J.
2015-10-15
Nonlinear simulation model for radio frequency waves in fusion plasmas has been developed and verified using fully kinetic ion and drift kinetic electron. Ion cyclotron motion in the toroidal geometry is implemented using Boris push in the Boozer coordinates. Linear dispersion relation and nonlinear particle trapping are verified for the lower hybrid wave and ion Bernstein wave (IBW). Parametric decay instability is observed where a large amplitude pump wave decays into an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating, with a heating rate proportional to the pump wave intensity.
Overview of gyrokinetic studies of finite-β microturbulence
NASA Astrophysics Data System (ADS)
Terry, P. W.; Carmody, D.; Doerk, H.; Guttenfelder, W.; Hatch, D. R.; Hegna, C. C.; Ishizawa, A.; Jenko, F.; Nevins, W. M.; Predebon, I.; Pueschel, M. J.; Sarff, J. S.; Whelan, G. G.
2015-10-01
Recent results on electromagnetic turbulence from gyrokinetic studies in different magnetic configurations are overviewed, detailing the physics of electromagnetic turbulence and transport, and the effect of equilibrium magnetic field scale lengths. Ion temperature gradient (ITG) turbulence is shown to produce magnetic stochasticity through nonlinear excitation of linearly stable tearing-parity modes. The excitation, which is catalyzed by the zonal flow, produces an electron heat flux proportional to β2 that deviates markedly from quasilinear theory. Above a critical beta known as the non-zonal transition (NZT), the magnetic fluctuations disable zonal flows by allowing electron streaming that shorts zonal potential between flux surfaces. This leads to a regime of very high transport levels. Kinetic ballooning mode (KBM) saturation is described. For tokamaks saturation involves twisted structures arising from magnetic shear; for helical plasmas oppositely inclined convection cells interact by mutual shearing. Microtearing modes are unstable in the magnetic geometry of tokamaks and the reversed field pinch (RFP). In NSTX instability requires finite collisionality, large beta, and is favored by increasing magnetic shear and decreasing safety factor. In the RFP, a new branch of microtearing with finite growth rate at vanishing collisionality is shown from analytic theory to require the electron grad-B/curvature drift resonance. However, gyrokinetic modeling of experimental MST RFP discharges at finite beta reveals turbulence that is electrostatic, has large zonal flows, and a large Dimits shift. Analysis shows that the shorter equilibrium magnetic field scale lengths increase the critical gradients associated with the instability of trapped electron modes, ITG and microtearing, while increasing beta thresholds for KBM instability and the NZT.
Nonlinear Wave-particle Interaction and Particle Trapping in Large Amplitude Dust Acoustic Waves
Chang, Mei-Chu; Teng, Lee-Wen; Lin, I.
2011-11-29
Large amplitude dust acoustic wave can be self-excited by the strong downward ion flow in a dusty plasma liquid formed by negatively charged dusts suspended in a weakly ionized low pressure discharge. In this work, we investigate experimentally the wave-particle phase space dynamics of the large amplitude dust acoustic wave by connecting the Lagrangian and Eulerian views, through directly tracking particle motion and measuring local dust density fluctuations. The microscopic pictures of wave steepening and breaking, resonant particle-wave crest trapping, and the absence of trough trapping observed in our experiment are constructed.
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.
2015-11-01
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.
Menzel, Andreas M
2015-11-01
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.
NASA Astrophysics Data System (ADS)
Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.
2016-06-01
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker-Planck-Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker-Planck-Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.
Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.
2016-04-04
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.
Hager, Robert; Yoon, E. S.; Ku, S.; ...
2016-04-04
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less
Hager, Robert; Yoon, E.S.; Ku, S.; D'Azevedo, E.F.; Worley, P.H.; Chang, C.S.
2016-06-15
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J. W.
2015-09-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a stochastic Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Non-linear interactions of plasma waves in the context of solar particle acceleration
NASA Astrophysics Data System (ADS)
Gallegos-Cruz, A.; Perez-Peraza, J.
2001-08-01
Stochastic particle acceleration in plasmas by means of MHD turbulence in-volves a wide range of alternatives according to, the specific wave mode, the frequency regime of the turbulence, the kind of particles to be accelerated, the assumed plasma model and so on. At present most of the alternatives have been studied with relatively deepness, though some features are not yet com-pletely understood. One of them is the delimitation of the real importance of non-lineal effects of turbulence waves in the process of particle acceleration. In this work we analyse such effects taking into account the temporal evolution of the turbulence. For illustration we exemplify our analysis with the fast MHD mode. Our results show that in some specific stages of the turbulence evolu-tion, non-linear interactions have important effects in the process of particle acceleration.
Nonlinear wave-particle interactions in the outer radiation belts: Van Allen Probes results
NASA Astrophysics Data System (ADS)
Agapitov, Oleksiy; Mozer, Forrest; Artemyev, Anton; Drake, James; Vasko, Ivan
2016-10-01
Huge numbers of different nonlinear structures (double layers, electron holes, non-linear whistlers, etc. referred to as Time Domain Structures - TDS) have been observed by the electric field experiment on board the Van Allen Probes. A large part of the observed non-linear structures are associated with whistler waves and some of them can be directly driven by whistlers. Observations of electron velocity distributions and chorus waves by the Van Allen Probe B provided long-lasting signatures of electron Landau resonant interactions with oblique chorus waves in the outer radiation belt. In the inhomogeneous geomagnetic field, such resonant interactions then lead to the formation of a plateau in the parallel (with respect to the geomagnetic field) velocity distribution due to trapping of electrons into the wave effective potential. The feedback from trapped particles provides steepening of parallel electric field and development of TDS seeded from initial whistler structure (well explained in terms of Particle-In-Cell model). The decoupling of the whistler wave and the nonlinear electrostatic component is shown in PIC simulation in the inhomogeneous magnetic field system and are observed by the Van Allen Probes in the radiation belts.
Gyrokinetic Simulations of Microinstabilities in Stellarator Geometry
J.L.V. Lewandowski
2003-08-29
A computational study of microinstabilities in general geometry is presented. The ion gyrokinetic is solved as an initial value problem. The advantage of this approach is the accurate treatment of some important kinetic effects. The magnetohydrodynamic equilibrium is obtained from a three-dimensional local equilibrium model. The use of a local magnetohydrodynamic equilibrium model allows for a computationally-efficient systematic study of the impact of the magnetic structure on microinstabilities.
1983-09-01
Waves During Resonant Plasma Heating , Fiz. Pld my 6 (1980), 1105 (Sov. J. Plasma Phys., 6 (1980). 6081. 14 -%. .-:.-..v...of Clectromagnetic aves Wuring Resonant Plasma Heating , Fiz. Plazmy 6 (1980), 1105 (Soy. J. Plasma Phys., 6 (1980), 608). 16 %. ..... 4. THE NONLINEAR...DYNAMIC POLARIZATION FORCE + The dynamic polarization force Fdp on a test particle is given by the Lorentz force acting on the polarization charge
Nonlinear delta(f) Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qin
2003-01-21
A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, et al., in Proc. of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688.] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.
Candy, J.; Waltz, R.E.
2006-03-15
Equations which describe the evolution of volume-averaged gyrokinetic entropy are derived and added to GYRO [J. Candy and R.E. Waltz, J. Comput. Phys. 186, 545 (2003)], a Eulerian gyrokinetic turbulence simulation code. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor energy flux is significantly changed by a 16-fold increase (from 32 to 512 grid points per cell) in the number of grid points in the two-dimensional velocity space. Third, the measured flux is invariant to an eightfold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that Eulerian gyrokinetic codes miss important velocity-space structure. The issues of density and energy conservation and their relation to negligible second-order effects such as the parallel nonlinearity are also discussed.
A flux-matched gyrokinetic analysis of DIII-D L-mode turbulence
NASA Astrophysics Data System (ADS)
Görler, T.; White, A. E.; Told, D.; Jenko, F.; Holland, C.; Rhodes, T. L.
2014-12-01
Previous nonlinear gyrokinetic simulations of specific DIII-D L-mode cases have been found to significantly underpredict the ion heat transport and associated density and temperature fluctuation levels by up to almost one of order of magnitude in the outer-core domain, i.e., roughly in the last third of the minor radius. Since then, this so-called shortfall issue has been subject to various speculations on possible reasons and furthermore motivation for a number of dedicated comparisons for L-mode plasmas in comparable machines. However, only a rather limited number of simulations and gyrokinetic codes has been applied to the original scenario, thus calling for further dedicated investigations in order to broaden the scientific basis. The present work contributes along these lines by employing another well-established gyrokinetic code in a numerically and physically comprehensive manner. Contrary to the previous studies, only a mild underprediction is observed at the outer radial positions which can furthermore be overcome by varying the ion temperature gradient within the error bars associated with the experimental measurement. The significance and reliability of these simulations are demonstrated by benchmarks, numerical convergence tests, and furthermore by extensive validation studies. The latter involve cross-phase and cross-power spectra analyses of various fluctuating quantities and confirm a high degree of realism. The code discrepancies come as a surprise since the involved software packages had been benchmarked repeatedly and very successfully in the past. Further collaborative effort in identifying the underlying difference is hence required.
A flux-matched gyrokinetic analysis of DIII-D L-mode turbulence
Görler, T. Told, D.; White, A. E.; Jenko, F.; Holland, C.; Rhodes, T. L.
2014-12-15
Previous nonlinear gyrokinetic simulations of specific DIII-D L-mode cases have been found to significantly underpredict the ion heat transport and associated density and temperature fluctuation levels by up to almost one of order of magnitude in the outer-core domain, i.e., roughly in the last third of the minor radius. Since then, this so-called shortfall issue has been subject to various speculations on possible reasons and furthermore motivation for a number of dedicated comparisons for L-mode plasmas in comparable machines. However, only a rather limited number of simulations and gyrokinetic codes has been applied to the original scenario, thus calling for further dedicated investigations in order to broaden the scientific basis. The present work contributes along these lines by employing another well-established gyrokinetic code in a numerically and physically comprehensive manner. Contrary to the previous studies, only a mild underprediction is observed at the outer radial positions which can furthermore be overcome by varying the ion temperature gradient within the error bars associated with the experimental measurement. The significance and reliability of these simulations are demonstrated by benchmarks, numerical convergence tests, and furthermore by extensive validation studies. The latter involve cross-phase and cross-power spectra analyses of various fluctuating quantities and confirm a high degree of realism. The code discrepancies come as a surprise since the involved software packages had been benchmarked repeatedly and very successfully in the past. Further collaborative effort in identifying the underlying difference is hence required.
Gyrokinetic modeling of impurity peaking in JET H-mode plasmas
NASA Astrophysics Data System (ADS)
Manas, P.; Camenen, Y.; Benkadda, S.; Weisen, H.; Angioni, C.; Casson, F. J.; Giroud, C.; Gelfusa, M.; Maslov, M.
2017-06-01
Quantitative comparisons are presented between gyrokinetic simulations and experimental values of the carbon impurity peaking factor in a database of JET H-modes during the carbon wall era. These plasmas feature strong NBI heating and hence high values of toroidal rotation and corresponding gradient. Furthermore, the carbon profiles present particularly interesting shapes for fusion devices, i.e., hollow in the core and peaked near the edge. Dependencies of the experimental carbon peaking factor ( R / L nC ) on plasma parameters are investigated via multilinear regressions. A marked correlation between R / L nC and the normalised toroidal rotation gradient is observed in the core, which suggests an important role of the rotation in establishing hollow carbon profiles. The carbon peaking factor is then computed with the gyrokinetic code GKW, using a quasi-linear approach, supported by a few non-linear simulations. The comparison of the quasi-linear predictions to the experimental values at mid-radius reveals two main regimes. At low normalised collisionality, ν * , and T e / T i < 1 , the gyrokinetic simulations quantitatively recover experimental carbon density profiles, provided that rotodiffusion is taken into account. In contrast, at higher ν * and T e / T i > 1 , the very hollow experimental carbon density profiles are never predicted by the simulations and the carbon density peaking is systematically over estimated. This points to a possible missing ingredient in this regime.
Gyrokinetic statistical absolute equilibrium and turbulence
NASA Astrophysics Data System (ADS)
Zhu, Jian-Zhou; Hammett, Gregory W.
2010-12-01
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.
Gyrokinetic Statistical Absolute Equilibrium and Turbulence
Jian-Zhou Zhu and Gregory W. Hammett
2011-01-10
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.
NASA Astrophysics Data System (ADS)
Zhu, Zhiliang; Meng, Zhiqiang; Cao, Tingting; Zhang, Zhengjiang; Dai, Yuxing
2017-06-01
State and parameter estimation (SPE) plays an important role in process monitoring, online optimization, and process control. The estimation of states and parameters is generally solved simultaneously in the SPE problem, where the parameters to be estimated are specified as augmented states. When state and/or measurement equations are highly nonlinear and the posterior probability of the state is non-Gaussian, particle filter (PF) is commonly used for SPE. However, when the parameters switch with the operating conditions, the change of parameters cannot be detected and tracked by the conventional SPE method. This paper proposes a PF-based robust SPE method for a nonlinear process system with variable parameters. The measurement test criterion based on observation error is introduced to indirectly identify whether the parameters are changed. Based on the result of identification, the variances of the particles are modified adaptively for the tracking of the changed parameters. Finally, reliable SPE can be derived through iterative particles. The proposed PF-based robust SPE method is applied to two nonlinear process systems. The results demonstrate the effectiveness and robustness of the proposed method.
Nonlinear kinetic effects in inductively coupled plasmas via particle-in-cell simulations
NASA Astrophysics Data System (ADS)
Froese, Aaron; Smolyakov, Andrei; Sydorenko, Dmytro
2007-11-01
Kinetic effects in inductively coupled plasmas due to thermal motion of particles modified by self-consistent magnetic fields are studied using a particle-in-cell code. In the low pressure, low frequency regime, electron mean free paths are large relative to device size and the trajectories are strongly curved by the induced rf magnetic field. Analytic linear theories are unable to recover effects accumulated along each nonlinear path. Therefore, the simulated ICP is made progressively more complex to find the source of observed plasma behaviours. With only thermal motion modifying the wave-particle interaction, nonlocal behaviour becomes dominant at low frequencies, causing an anomalous skin effect with increased skin depth and power absorption and decreased ponderomotive force. However, when influenced by magnetic fields, the nonlocal effects are suppressed at large wave amplitudes due to nonlinear trapping. A mechanism is proposed for this low frequency restoration of local behaviour. Finally, a low rate of electron-neutral collisions is found to counteract the nonlinear behaviour, and hence reinforces nonlocal behaviour.
Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation
Zonca, Fulvio; Chen, Liu
2014-07-15
A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, “Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation,” Phys. Plasmas 21, 072121 (2014)].
Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation
NASA Astrophysics Data System (ADS)
Zonca, Fulvio; Chen, Liu
2014-07-01
A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, "Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation," Phys. Plasmas 21, 072121 (2014)].
Electromagnetic gyrokinetic turbulence in finite-beta helical plasmas
Ishizawa, A.; Watanabe, T.-H.; Sugama, H.; Nakajima, N.; Maeyama, S.
2014-05-15
A saturation mechanism for microturbulence in a regime of weak zonal flow generation is investigated by means of electromagnetic gyrokinetic simulations. The study identifies a new saturation process of the kinetic ballooning mode (KBM) turbulence originating from the spatial structure of the KBM instabilities in a finite-beta Large Helical Device (LHD) plasma. Specifically, the most unstable KBM in LHD has an inclined mode structure with respect to the mid-plane of a torus, i.e., it has a finite radial wave-number in flux tube coordinates, in contrast to KBMs in tokamaks as well as ion-temperature gradient modes in tokamaks and helical systems. The simulations reveal that the growth of KBMs in LHD is saturated by nonlinear interactions of oppositely inclined convection cells through mutual shearing as well as by the zonal flow. The saturation mechanism is quantitatively investigated by analysis of the nonlinear entropy transfer that shows not only the mutual shearing but also a self-interaction with an elongated mode structure along the magnetic field line.
Non-physical momentum sources in slab geometry gyrokinetics
NASA Astrophysics Data System (ADS)
Parra, Felix I.; Catto, Peter J.
2010-08-01
We investigate momentum transport in the Hamiltonian electrostatic gyrokinetic formulation of Dubin et al (1983 Phys. Fluids 26 3524). We prove that the long wavelength electric field obtained from the gyrokinetic quasineutrality introduces a non-physical momentum source in the low flow ordering.
Mikkelsen, D. R. Bitter, M.; Delgado-Aparicio, L.; Hill, K. W.; Greenwald, M.; Howard, N. T.; Hughes, J. W.; Rice, J. E.; Reinke, M. L.; Podpaly, Y.; Ma, Y.; Candy, J.; Waltz, R. E.
2015-06-15
Peaked density profiles in low-collisionality AUG and JET H-mode plasmas are probably caused by a turbulently driven particle pinch, and Alcator C-Mod experiments confirmed that collisionality is a critical parameter. Density peaking in reactors could produce a number of important effects, some beneficial, such as enhanced fusion power and transport of fuel ions from the edge to the core, while others are undesirable, such as lower beta limits, reduced radiation from the plasma edge, and consequently higher divertor heat loads. Fundamental understanding of the pinch will enable planning to optimize these impacts. We show that density peaking is predicted by nonlinear gyrokinetic turbulence simulations based on measured profile data from low collisionality H-mode plasma in Alcator C-Mod. Multiple ion species are included to determine whether hydrogenic density peaking has an isotope dependence or is influenced by typical levels of low-Z impurities, and whether impurity density peaking depends on the species. We find that the deuterium density profile is slightly more peaked than that of hydrogen, and that experimentally relevant levels of boron have no appreciable effect on hydrogenic density peaking. The ratio of density at r/a = 0.44 to that at r/a = 0.74 is 1.2 for the majority D and minority H ions (and for electrons), and increases with impurity Z: 1.1 for helium, 1.15 for boron, 1.3 for neon, 1.4 for argon, and 1.5 for molybdenum. The ion temperature profile is varied to match better the predicted heat flux with the experimental transport analysis, but the resulting factor of two change in heat transport has only a weak effect on the predicted density peaking.
Quasi-linear gyrokinetic predictions of the Coriolis momentum pinch in NSTX
Guttenfelder, W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Kaye, S. M. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Ren, Y. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Solomon, W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Bell, R. E. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Candy, J. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Gerhardt, S. P. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); LeBlanc, B. P. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Yuh, H. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2016-04-01
This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio NSTX H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostatic ballooning modes are also unstable, which are effective at transporting energy, particles and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. As the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.
Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.
2016-05-11
This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostaticballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. Lastly, as the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.
Guttenfelder, W.; Kaye, S. M.; Ren, Y.; ...
2016-05-11
This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostaticballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes inmore » a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. Lastly, as the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.« less
Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.
2016-05-11
This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostaticballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. Lastly, as the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.
NASA Astrophysics Data System (ADS)
Ellison, Donald C.; Warren, Donald C.; Bykov, Andrei M.
2016-03-01
We include a general form for the scattering mean free path, λmfp(p), in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path with a stronger momentum dependence than the λmfp ∝ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to γ-ray bursts, pulsar winds, type Ibc supernovae, and extragalactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of λmfp(p) has an important influence on the efficiency of cosmic ray production as well as the accelerated particle spectral shape. These effects are absent in non-relativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of γ-ray emission from proton-proton interactions and pion-decay radiation.
Nonlinear dynamics of spherical particles in Poiseuille flow under creeping-flow condition.
Reddig, S; Stark, H
2013-06-21
We study the nonlinear dynamics of spherical colloids under the influence of a pressure driven flow at vanishing Reynolds number. The colloids are confined between two parallel planar walls with a distance comparable to the particle diameter and they interact hydrodynamically via the solvent. We show that the bounded Poiseuille flow gives rise to new classes of trajectories resulting in cross-streamline migration. Two particles moving on these new trajectories exhibit either bound or unbound states. In the first case they oscillate on closed trajectories in the center-of-mass frame. In the second case, they exhibit cross-swapping trajectories in addition to swapping trajectories which were already observed in unbounded or bounded linear shear flow. The different classes of trajectories occur depending on the initial positions of the two particles and their size. We present state diagrams in the lateral positions, where we categorize the trajectories and color code the oscillation frequencies of the bound states. Finally we discuss how the results on the two-particle system help to understand the stability of particle trains composed of several particles.
Dif-Pradalier, G; Grandgirard, V; Sarazin, Y; Garbet, X; Ghendrih, Ph
2009-08-07
The impact of ion-ion collisions on confinement is investigated with the full-f and global gyrokinetic Gysela code through a series of nonlinear turbulence simulations for tokamak parameters. A twofold scan in the turbulence drive and in collisionality is performed, highlighting (i) a heat transport expressed in terms of critical quantities-threshold and exponent, (ii) a first evidence of turbulent generation of poloidal momentum, and (iii) the dominance of mean flow shear, mediated through the turbulent corrugation of the mean profiles, with regard to the oft-invoked zonal flow shear.
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.
2009-08-01
The impact of ion-ion collisions on confinement is investigated with the full-f and global gyrokinetic Gysela code through a series of nonlinear turbulence simulations for tokamak parameters. A twofold scan in the turbulence drive and in collisionality is performed, highlighting (i) a heat transport expressed in terms of critical quantities—threshold and exponent, (ii) a first evidence of turbulent generation of poloidal momentum, and (iii) the dominance of mean flow shear, mediated through the turbulent corrugation of the mean profiles, with regard to the oft-invoked zonal flow shear.
Non-Maxwellian background effects in gyrokinetic simulations with GENE
NASA Astrophysics Data System (ADS)
Di Siena, A.; Görier, T.; Doerk, H.; Citrin, J.; Johnson, T.; Schneider, M.; Poli, E.; Contributors, JET
2016-11-01
The interaction between fast particles and core turbulence has been established as a central issue for a tokamak reactor. Recent results predict significant enhancement of electromagnetic stabilisation of ITG turbulence in the presence of fast ions. However, most of these simulations were performed with the assumption of equivalent Maxwellian distributed particles, whereas to rigorously model fast ions, a non-Maxwellian background distribution function is needed. To this aim, the underlying equations in the gyrokinetic code GENE have been re-derived and implemented for a completely general background distribution function. After verification studies, a previous investigation on a particular JET plasma has been revised with linear simulations. The plasma is composed by Deuterium, electron, Carbon impurities, NBI fast Deuterium and ICRH 3He. Fast particle distributions have been modelled with a number of different analytic choices in order to study the impact of non-Maxwellian distributions on the plasma turbulence: slowing down and anisotropic Maxwellian. Linear growth rates are studied as a function of the wave number and compared with those obtained using an equivalent Maxwellian. Generally, the choice of the 3He distribution seems to have a stronger impact on the microinstabilities than that of the fast Deuterium.
NASA Astrophysics Data System (ADS)
Lee, W. W.; Kolesnikov, R. A.
2009-12-01
We show in this response that the nonlinear Poisson's equation in our original paper derived from the drift kinetic approach can be verified by using the nonlinear gyrokinetic Poisson's equation of Dubin et al. [Phys. Fluids 26, 3524 (1983)]. This nonlinear contribution in ϕ2 is indeed of the order of k⊥4 in the long wavelength limit and remains finite for zero ion temperature, in contrast with the nonlinear term by Parra and Catto [Plasma Phys. Controlled Fusion 50, 065014 (2008)], which is of the order of k⊥2 and diverges for Ti→0. For comparison, the leading term for the gyrokinetic Poisson's equation in this limit is of the order of k⊥2ϕ.
Kim, Seongho; Li, Lang
2013-01-01
The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiablity of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. PMID:24216078
Kim, Seongho; Li, Lang
2014-02-01
The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiability of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Nonlinear dynamics of beta-induced Alfvén eigenmode in tokamak
NASA Astrophysics Data System (ADS)
Zhang, H. S.; Lin, Z.; Deng, W.; Holod, I.; Wang, Z. X.; Xiao, Y.; Zhang, W. L.
2013-01-01
The beta-induced Alfvén eigenmode (BAE) excited by energetic particles in toroidal plasmas is studied in the global gyrokinetic simulations. It is found that the nonlinear BAE dynamics depends on the deviation from the marginality. In the strongly driven case, the mode exhibits a bursting state with fast and repetitive chirping. The nonlinear saturation is determined by the thermal ion nonlinearity and has no clear dependence on the linear growth rate. In the weakly driven case, the mode reaches a nearly steady state with small frequency chirping. The nonlinear dynamics is dominated by the energetic particle nonlinearity. In both cases, the nonlinear intensity oscillation and frequency chirping are correlated with the evolution of the coherent structures in the energetic particle phase space. Due to the radial variation of the mode amplitude and the radially asymmetric guiding center dynamics, the wave-particle interaction in the toroidal geometry is much more complex than the conventional one-dimensional wave-particle interaction paradigm.
THE LOCAL LIMIT OF GLOBAL GYROKINETIC SIMULATIONS
CANDY J; WALTZ RE; DORLAND W
2003-10-01
OAK-B135 Global gyrokinetic simulations of turbulence include physical effects that are not retained in local flux-tube simulations. nevertheless, in the limit of sufficiently small {rho}* (gyroradius compared to system size) it is expected that a local simulation should agree with a global one (at the local simulation radius) since all effects that are dropped in the local simulations are expected to vanish as {rho}* {yields} 0. In this note, global simulations of a well-established test case are indeed shown to recover the flux-tube limit at each radius.
NASA Astrophysics Data System (ADS)
Kikuchi, Takashi; Horioka, Kazuhiko
2016-06-01
A procedure to obtain a ratio of beam radii at final and initial states in arbitrary particle distributions is proposed, and is applied to the estimation of possible emittance growth for Gaussian and thermal equilibrium distributions. The ratios are estimated for Gaussian and thermal equilibrium distributions as a function of tune depression. The possible emittance growth as a function of tune depression and nonlinear field energy factor is also estimated with and without a constant radius ratio approximation. It is confirmed that the possible emittance growths are almost the same in comparison to the cases with and without the constant radius ratio approximation at each distribution.
NASA Technical Reports Server (NTRS)
Kandula, Max
2012-01-01
The Sound attenuation and dispersion in saturated gas-vapor-droplet mixture in the presence of evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson to accommodate the effects of nonlinear particle relaxation processes of mass, momentum and energy transfer on sound attenuation and dispersion. The results indicate the existence of a spectral broadening effect in the attenuation coefficient (scaled with respect to the peak value) with a decrease in droplet mass concentration. It is further shown that for large values of the droplet concentration the scaled attenuation coefficient is characterized by a universal spectrum independent of droplet mass concentration.
Numerical solution of the nonlinear Schrödinger equation using smoothed-particle hydrodynamics
NASA Astrophysics Data System (ADS)
Mocz, Philip; Succi, Sauro
2015-05-01
We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrödinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.
Numerical solution of the nonlinear Schrödinger equation using smoothed-particle hydrodynamics.
Mocz, Philip; Succi, Sauro
2015-05-01
We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrödinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.
NASA Astrophysics Data System (ADS)
Krasnoselskikh, V.; Artemyev, A.; Agapitov, O. V.; Mourenas, D.
2013-12-01
We present selected THEMIS observations of highly-oblique and large amplitude chorus waves at medium latitudes. The major part of observed waves propagates at nearly-electrostatic mode with normal angles close to resonance cone. We use test particle simulations and analytical theory to estimate efficiency of nonlinear particle acceleration by these waves via Landau and fundamental cyclotron resonances. We show that trapping into the Landau resonance corresponds to a decrease of electron equatorial pitch-angles, while trapping into the first cyclotron resonance increases electron equatorial pitch-angles. For 100 keV electrons, the energy gain is larger for the trapping due to Landau resonance. Moreover, trapping into the Landau resonance is accessible for a wider range of initial pitch-angles in comparison with the fundamental resonance.
Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Hatch, D. R.; Jenko, F.; Bratanov, V.; Navarro, A. Bañón; Navarro
2014-08-01
A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phase-space scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code - the DNA code - that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is a critical balance - an equilibration of the parallel streaming time and the nonlinear correlation time - that extends to high Hermite number n. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using the Gene code are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.
Gyrokinetic Simulation of Microturbulent Saturation at Finite β
NASA Astrophysics Data System (ADS)
Terry, P. W.; Pueschel, M. J.; Carmody, D.; Whelan, G. G.
2014-10-01
Saturation and zonal flow physics for microturbulence is investigated for tokamaks and the RFP using gyrokinetic computation to understand scalings with respect magnetic shear and β. Modeling an MST discharge shows that the critical instability gradient for TEM is higher than the tokamak threshold by the aspect ratio (R / a) . This factor is rooted in the shorter magnetic field scale length of the RFP. Nonlinear simulations show strong zonal flows and a large Dimits shift exceeding the tokamak shift by a factor of order (R / a) . The non zonal transition (NZT), a critical β for which zonal flows are disabled by flutter-induced charge loss is also considered. The critical β occurs when the radial displacement of a magnetic field line over a half connection length is equal to the radial correlation length. These quantities scale with the connection length and magnetic drift scale lengths entering the instability threshold and quasilinear diffusivities, making the RFP critical β for NZT higher than the tokamak value by (R / a) 1 . 5 times tokamak q. These results are consistent with magnetic shear and q dependence in the kinetic ballooning threshold, indicating that β effects will only arise at high β relative to typical RFP operation.
Gyrokinetic Study of L-H Transition with Profile Evolution
NASA Astrophysics Data System (ADS)
Xie, Hua-Sheng; GTC Team
2015-11-01
Recent simulations based on gyrokinetic toroidal code (GTC) and theory based on model eigen equation (H. S. Xie and Y. Xiao, arXiv:1503.04440) have found that the eigenstates of mirco-instabilities (trapped electron mode TEM or ion temperature gradient mode ITG) under strong and weak gradients are not the same. Under weak gradient, the most unstable mode is on the ground state, with conventional ballooning mode structure. When the gradient exceed a critical value, the most unstable mode jump to non-ground state. The mode structures of non-ground state are rich and unconventional, and thus can reduced the transport level, which can provide a explanation to the H-mode in the mirco-scale aspect. Nonlinear simulations (H. S. Xie, Y. Xiao and Z. Lin, 9th West Lake International Symposium on Plasma Simulation, May. 18-21, 2015, Hangzhou, China) verified this and have also found a turning point of the gradient. The turbulent transport coefficient would decrease with the gradient increasing when the gradient exceed a critical value. This provide a new route for the L to H transition without invoking shear flow or zonal flow. In the above works, the profiles are fixed. In this work, we will give some preliminary results on self-consistent simulations of L-H transition including the evolution of the radial plasma profiles. Collaboration with GTC team.
Toroidal universal drift instability: A global gyrokinetic study
Chowdhury, J.; Ganesh, R.; Brunner, S.; Vaclavik, J.; Villard, L.
2010-10-15
An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau resonance and transit resonance, which are considered to be important for the toroidal universal mode, are kept for both species. A systematic parametric study is carried out for the mode. The toroidal universal drift mode is observed to sustain finite temperature gradient and can thus coexist with the temperature gradient driven modes and may contribute to the observed particle transport along with other drift modes. Especially at intermediate scales between the ion temperature gradient driven mode and electron temperature gradient driven mode, this branch of the drift instability can also be a plausible candidate for the observed particle loss. The effect of magnetic fluctuations on the mode is also investigated. In contrast to the slab mode, the toroidal branch of the universal drift mode is found to be strongly stabilized by electromagnetic effects at finite plasma {beta}. Finally, the effect of trapped electrons on the universal mode is studied and compared with the other possible modes in the same parameter regime, namely, ion temperature gradient mode in the presence of trapped electrons and pure trapped electron modes.
Toroidal universal drift instability: A global gyrokinetic study
NASA Astrophysics Data System (ADS)
Chowdhury, J.; Ganesh, R.; Brunner, S.; Vaclavik, J.; Villard, L.
2010-10-01
An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau resonance and transit resonance, which are considered to be important for the toroidal universal mode, are kept for both species. A systematic parametric study is carried out for the mode. The toroidal universal drift mode is observed to sustain finite temperature gradient and can thus coexist with the temperature gradient driven modes and may contribute to the observed particle transport along with other drift modes. Especially at intermediate scales between the ion temperature gradient driven mode and electron temperature gradient driven mode, this branch of the drift instability can also be a plausible candidate for the observed particle loss. The effect of magnetic fluctuations on the mode is also investigated. In contrast to the slab mode, the toroidal branch of the universal drift mode is found to be strongly stabilized by electromagnetic effects at finite plasma β. Finally, the effect of trapped electrons on the universal mode is studied and compared with the other possible modes in the same parameter regime, namely, ion temperature gradient mode in the presence of trapped electrons and pure trapped electron modes.
Global particle-in-cell simulations of microturbulence with kinetic electrons
Lewandowski, J. L. V.; Rewoldt, G.; Ethier, S.; Lee, W. W.; Lin, Z.
2006-07-15
The effects of nonadiabatic electrons on ion temperature gradient drift instabilities have been studied in global toroidal geometry using the gyrokinetic particle simulation approach. Compared to the nonlinear global simulations based on only the adiabatic response of the electrons, we have found that the cross-field ion heat transport is two to three times larger in the presence of trapped electrons as compared to the purely adiabatic electron case, and that the zonal component of the electrostatic potential has a shorter wavelength. The numerical methods for calculating both the adiabatic and the nonadiabatic responses for the electrons are presented.
Rapid decay of nonlinear whistler waves in two dimensions: Full particle simulation
NASA Astrophysics Data System (ADS)
Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro
2017-05-01
The decay of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave is investigated by utilizing a two-dimensional (2D) fully relativistic electromagnetic particle-in-cell code. The simulation is performed under a low-beta condition in which the plasma pressure is much lower than the magnetic pressure. It has been shown that the nonlinear (large-amplitude) parent whistler wave decays through the parametric instability in a one-dimensional (1D) system. The present study shows that there is another channel for the decay of the parent whistler wave in 2D, which is much faster than in the timescale of the parametric decay in 1D. The parent whistler wave decays into two sideband daughter whistlers propagating obliquely with respect to the ambient magnetic field with a frequency close to the parent wave and two quasi-perpendicular electromagnetic modes with a frequency close to zero via a 2D decay instability. The two sideband daughter oblique whistlers also enhance a nonlinear longitudinal electrostatic wave via a three-wave interaction as a secondary process.
Gyrofluid-Gyrokinetic Hybrid Turbulence Model
NASA Astrophysics Data System (ADS)
Dorland, William; Mandell, Noah
2015-11-01
Gyrofluid models of tokamak turbulence are efficient compared to gyrokinetic models, in three senses. First, it is typically easier to develop one's intuition from fluid equations than kinetic equations. Second, because gyrofluid equations are only three-dimensional (instead of 5D or 6D), simulations with gyrofluid models require less memory than kinetic simulations and can therefore more easily fit on highly-optimized computing hardware, such as graphics processors. The third advantage is a result of the first two: one can develop and test ideas quickly with gyrofluid models. The disadvantage of gyrofluid models is their potential lack of physics fidelity. In this poster, we present our attempt to take full advantage of gyrofluid models, without sacrificing physics fidelity. Our approach is encapsulated in the Gryf-X code, which is an implementation of hybrid gyrofluid/gyrokinetic equations. The key improvements that we have brought to bear are: an improved understanding of the cascade of free energy simultaneously in k⊥ and v⊥ an improved model of zonal flow physics; and an implementation of the equations on modern heterogeneous computing platforms, both as a standalone simulation tool and as a component of TRINITY (a transport modeling code for tokamaks).
NASA Astrophysics Data System (ADS)
Wen, Shulai; Liu, Ying; Zhao, Xiuchen; Cheng, Jingwei; Li, Hong
2014-03-01
Hcp-cobalt particles were successfully prepared by a liquid phase reduction method, and the microstructure, static magnetic properties, electromagnetic and microwave absorption properties of the cobalt particles with irregular shape were investigated in detail. The measured results indicate that the saturation magnetization was less than that of hcp-Co single crystals, and the coercivity was larger than that of bulk cobalt crystal. The permittivity presents multi-nonlinear dielectric resonance, which may result from the irregular shape containing parts of cutting angle of dodecahedron of cobalt particles. The real part of permeability decreases with the frequency, and the imaginary part has a wide resonant peak. The paraffin-based composite containing 70 wt% cobalt particles possessed strong absorption characteristics with a minimum RL of -38.97 dB at 10.81 GHz and an absorption band with RL under -10 dB from 8.72 to 13.26 GHz when the thickness is 1.8 mm, which exhibits excellent microwave absorption in middle and high frequency. The architectural design of material morphologies is important for improving microwave absorption properties toward future application.
Angioni, C.
2015-10-15
A gyrokinetic study based on numerical and analytical calculations is presented, which computes the dependence of the turbulent diffusion of highly charged impurities on the ratio of the electron to the ion heat flux of the plasma. Nonlinear simulations show that the size of the turbulent diffusion of heavy impurities can vary by one order of magnitude with fixed total heat flux and is an extremely sensitive function of the electron to ion heat flux ratio. Numerical linear calculations are found to reproduce the nonlinear results. Thereby, a quasi-linear analytical approach is used to explain the origin of this dependence.
Gyrokinetic GDC turbulence simulations: confirming a new instability regime in LAPD plasmas
NASA Astrophysics Data System (ADS)
Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.
2016-10-01
Recent high-beta experiments at the LArge Plasma Device have found significant parallel magnetic fluctuations in the region of large pressure gradients. Linear gyrokinetic simulations show the dominant instability at these radii to be the gradient-driven drift coupling (GDC) mode, a non-textbook mode driven by pressure gradients and destabilized by the coupling of ExB and grad-B∥ drifts. Unlike in previous studies, the large parallel extent of the device allows for finite-kz versions of this instability in addition to kz = 0 . The locations of maximum linear growth match very well with experimentally observed peaks of B∥ fluctuations. Local nonlinear simulations reproduce many features of the observations fairly well, with the exception of Bperp fluctuations, for which experimental profiles suggest a source unrelated to pressure gradients. In toto, the results presented here show that turbulence and transport in these experiments are driven by the GDC instability, that important characteristics of the linear instability carry over to nonlinear simulations, and - in the context of validation - that the gyrokinetic framework performs surprisingly well far outside its typical area of application, increasing confidence in its predictive abilities. Supported by U.S. DOE.
Proposal of a brand-new gyrokinetic algorithm for global MHD simulation
NASA Astrophysics Data System (ADS)
Naitou, Hiroshi; Kobayashi, Kenichi; Hashimoto, Hiroki; Andachi, Takehisa; Lee, Wei-Li; Tokuda, Shinji; Yagi, Masatoshi
2009-11-01
A new algorithm for the gyrokinetic PIC code is proposed. The basic equations are energy conserving and composed of (1) the gyrokinetic Vlasov (GKV) equation, (2) the Vortex equation, and (3) the generalized Ohm's law along the magnetic field. Equation (2) is used to advance electrostatic potential in time. Equation (3) is used to advance longitudinal component of vector potential in time as well as estimating longitudinal induced electric field to accelerate charged particles. The particle information is used to estimate pressure terms in equation (3). The idea was obtained in the process of reviewing the split-weight-scheme formalism. This algorithm was incorporated in the Gpic-MHD code. Preliminary results for the m=1/n=1 internal kink mode simulation in the cylindrical geometry indicate good energy conservation, quite low noise due to particle discreteness, and applicability to larger spatial scale and higher beta regimes. The advantage of new Gpic-MHD is that the lower order moments of the GKV equation are estimated by the moment equation while the particle information is used to evaluate the second order moment.
Gyrokinetic characterization of the isotope effect in turbulent transport at the FT-2 tokamak
NASA Astrophysics Data System (ADS)
Niskala, P.; Gurchenko, A. D.; Gusakov, E. Z.; Altukhov, A. B.; Esipov, L. A.; Kantor, M. Yu; Kiviniemi, T. P.; Kouprienko, D.; Korpilo, T.; Lashkul, S. I.; Leerink, S.; Perevalov, A. A.; Rochford, R.
2017-04-01
Isotope effect allows fusion devices to perform better when heavier hydrogen isotopes are used as fuel, but the reason for this improvement is not yet understood. We present the first direct evidence of the isotope effect on particle confinement in the FT-2 tokamak and investigate it via gyrokinetic simulations. Experimental measurements for comparable hydrogen and deuterium discharges show that the particle confinement time increases by 40% for the heavier isotope species. The isotope effect on particle flux is reproduced in global and local gyrokinetic simulations. Global ELMFIRE simulations demonstrate a systemic reduction in particle fluxes across the radial range, showing a ratio of fluxes {{{Γ }}}{{H}}/{{{Γ }}}{{D}}=1.3 at the edge and {{{Γ }}}{{H}}/{{{Γ }}}{{D}}=1.4 at r/a=0.6. Local GENE simulations agree qualitatively with the result. Besides the fluctuation level, smaller scales and a favorable shift in the cross-phase between the turbulent fluctuations are found to contribute to the isotope effect in the simulations.
J. Squire, H. Qin and W.M. Tang
2012-09-25
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with the Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. __________________________________________________
Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows
Lin, Z.; Hahm, T.S.; Lee, W.W.; Tang, W.M.; White, R.B.
2000-02-15
A fully three-dimensional gyrokinetic particle code using magnetic coordinates for general geometry has been developed and applied to the investigation of zonal flows dynamics in toroidal ion-temperature-gradient turbulence. Full torus simulation results support the important conclusion that turbulence-driven zonal flows significantly reduce the turbulent transport. Linear collisionless simulations for damping of an initial poloidal flow perturbation exhibit an asymptotic residual flow. The collisional damping of this residual causes the dependence of ion thermal transport on the ion-ion collision frequency even in regimes where the instabilities are collisionless.
Gyrokinetic Calculations of the Neoclassical Radial Electric Field in Stellarator Plasmas
Lewandowski, J.L.V.; Williams, J.; Boozer, A.H.; Lin, Z.
2001-04-09
A novel method to calculate the neoclassical radial electric field in stellarator plasmas is described. The method, which does not have the inconvenience of large statistical fluctuations (noise) of standard Monte Carlo technique, is based on the variation of the combined parallel and perpendicular pressures on a magnetic surface. Using a three-dimensional gyrokinetic delta f code, the calculation of the radial electric field in the National Compact Stellarator Experiment has been carried out. It is shown that a direct evaluation of radial electric field based on a direct calculation of the radial particle flux is not tractable due to the considerable noise.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-09-15
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and current drive experiments.
NASA Astrophysics Data System (ADS)
Akramov, Tohir; Baty, Hubert
2017-08-01
The nonlinear evolution of double tearing modes (DTMs) is investigated within the framework of resistive magnetohydrodynamic (MHD) simulations in a two-dimensional Cartesian geometry. We have explored the explosive reconnection phase associated with the growth of the secondary structure-driven instability for a range of resistivity values. The time scale of the explosive phase (that is of order of a few Alfvénic time scales) is shown to be quasi-independent of the resistivity, even when fast growing plasmoids develop for the highest enough Lundquist number cases. Test particle accelerations are performed using the MHD explosive simulations as input parameters. Our results show that reconnection DTM dynamics is able to provide an efficient process for accelerating charged particles far beyond characteristic thermal velocities within the reconnection layers. The main acceleration mechanism is attributed to the strong inductive electric field generated by the island structure-driven instability, with an additional smaller contribution due to the presence of plasmoids. Finally, our results are used to discuss some features of the accelerated particle spectra during flaring activity in the solar corona.
Kim, Seongho; Li, Lang
2011-08-01
NONMEM is one of the most popular approaches to a population pharmacokinetics/pharmacodynamics (PK/PD) analysis in fitting nonlinear mixed-effects models. As a local optimization algorithm, NONMEM usually requires an initial value close enough to the global optimum. This paper proposes a novel global search algorithm called P-NONMEM. It combines the global search strategy by particle swarm optimization (PSO) and the local estimation strategy of NONMEM. In the proposed algorithm, initial values (particles) are generated randomly by PSO, and NONMEM is implemented for each particle to find a local optimum for fixed effects and variance parameters. P-NONMEM guarantees the global optimization for fixed effects and variance parameters. Under certain regularity conditions, it also leads to global optimization for random effects. Because P-NONMEM doesn't run PSO search for random effect estimation, it avoids tremendous computational burden. In the simulation studies, we have shown that P-NONMEM has much improved convergence performance than NONMEM. Even when the initial values were far away from the global optima, P-NONMEM converged nicely for all fixed effects, random effects, and variance components.
NASA Astrophysics Data System (ADS)
Gao, Xiaotian; Liu, Kaijun; Wang, Xueyi; Min, Kyungguk; Lin, Yu; Wang, Xiaogang
2017-06-01
Two-dimensional simulations using a gyrokinetic electron and fully kinetic ion (GeFi) scheme are preformed to study the excitation of fast magnetosonic waves in the terrestrial magnetosphere, which arise from the ion Bernstein instability driven by proton velocity distributions with a positive slope with respect to the perpendicular velocity. Since both ion and electron kinetics are relevant, particle-in-cell (PIC) simulations have often been employed to study the wave excitation. However, the full particle-in-cell scheme is computationally expensive for simulating waves in the ion scale because the electron scale must be fully resolved. Therefore, such simulations are limited to reduced proton-to-electron mass ratio ( m p / m e) and light-to-Alfvén speed ratio ( c / v A). The present study exploits the GeFi scheme that can break through these limitations to some extent, so larger m p / m e and c / v A can be used. In the simulations presented, the ion Bernstein instability is driven by a proton velocity distribution composed of 10% energetic protons with a shell distribution and 90% relatively cool, background protons with a Maxwellian distribution. The capability of the GeFi code in simulating the ion Bernstein instability is first demonstrated by comparing a GeFi simulation using reduced mass ratio ( m p / m e = 100) and speed ratio ( c / v A = 15) to a corresponding PIC simulation as well as linear dispersion analysis. A realistic speed ratio ( c / v A = 400) and a larger mass ratio ( m p / m e = 400) are then adopted in the GeFi code to explore how the results vary. It is shown that, as the increased m p / m e and c / v A lead to a larger lower hybrid frequency, ion Bernstein waves are excited at more ion cyclotron harmonics, consistent with the general prediction of linear dispersion theory. On the other hand, the GeFi simulations also revealed some interesting features after the instability saturation, which are likely related to nonlinear wave
Propagation of global shear Alfven waves in gyrokinetic tokamak plasmas
NASA Astrophysics Data System (ADS)
Nishimura, Y.; Lin, Z.; Holod, I.; Chen, L.; Decyk, V.; Klasky, S.; Ma, K.; Adams, M.; Ethier, S.; Hahm, T.; Lee, W.; Lewandowski, J.; Rewoldt, G.; Wang, W.
2006-04-01
Employing the electromagnetic gyrokinetic simulation models, Alfven wave dynamics in global tokamak geometry is studied. Based on a small parameter expansion by the square-root of the electron-ion mass ratio, the fluid-kinetic hybrid electron model solves the adiabatic response in the lowest order and solves the kinetic response in the higher orders. We verify the propagation of shear Alfven waves in the absence of drives or damping mechanisms by perturbing the magnetic field lines at t=0 in a global eigenmode structure. The Alfven wave experiences continuum damping. In the presence of energetic particles, excitations of toroidal Alfven eigenmode (TAE) is expected within the frequency gap. With the ηi gradient drive, at a critical β value, the kinetic ballooning mode (KBM) is excited below the ideal MHD limit. W.W.Lee et al., Phys. Plasmas 8, 4435 (2001). Z.Lin and L.Chen, Phys. Plasmas 8, 1447 (2001). J.A.Tataronis and W. Grossman, Z. Phys. 14, 203 (1973). C.Z.Cheng, L.Chen, and M.S.Chance, Ann.Phys. 161, 21 (1984). C.Z.Cheng, Nucl. Fusion 22, 773 (1982).
Benchmarking gyrokinetic simulations in a toroidal flux-tube
NASA Astrophysics Data System (ADS)
Chen, Y.; Parker, S. E.; Wan, W.; Bravenec, R.
2013-09-01
A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementation shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v||-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.
Benchmarking gyrokinetic simulations in a toroidal flux-tube
Chen, Y.; Parker, S. E.; Wan, W.; Bravenec, R.
2013-09-15
A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementation shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v{sub ||}-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.
Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence
NASA Astrophysics Data System (ADS)
Wang, Eric
2010-11-01
One of the fundamental components of a steady state tokamak or stellerator fusion reactor is the structural integrity of nested magnetic surfaces. The consequences of losing this integrity can have very serious implications, ranging from sawtooth crashes to disruptions. In the present work, we use GYRO to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as β is varied from .1% to .7%, as first investigated in [J. Candy, Phys. Plasmas 12, 072307 (2005)]. By integrating the self-consistent magnetic field lines to produce Poincare surface of section plots, we demonstrate destruction of magnetic surfaces for all nonzero values of β. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. We can quantify the stochastic electron heat transport by using test particles to estimate the magnetic diffusion coefficient Dst [A.B. Rechester and M.N. Rosenbluth, PRL 40, 38 (1978)] for hundreds of time slices in each simulation and find the time-history of Dst to be highly correlated with the electron heat transport due to ``magnetic-flutter'' computed in the simulations. The mechanism that couples electromagnetic turbulence to the linearly damped high-n tearing modes that are responsible for reconnection will be discussed.
Gyrokinetic simulations predict anomalous poloidal rotation in tokamak plasmas
NASA Astrophysics Data System (ADS)
Dif-Pradalier, Guilhem; Grandgirard, Virginie; Sarazin, Yanick; Garbet, Xavier; Ghendrih, Phillippe; Angelino, Paolo
2008-11-01
First-principle based collisionless gyrokinetic theory consensually provides today's deepest insight on turbulence-related problems in plasma physics. Conversely, neoclassical theory describes the effects of binary Coulomb collisions in a toroidal and inhomogeneous magnetic geometry and its consequences on particle trapping. The interplay between turbulence and collisions is a subject of great current focus for first-principle modeling since recent evidences have started to emphasise its relevance for the onset and the control of enhanced confinement regimes in the next-generation devices like Iter. A finite differences Fokker-Planck ion-ion collision operator is implemented in the full-f and global GYSELA code and has been thoroughly benchmarked in neoclassical regimes. Two types of simulations are compared, either purely neoclassical or turbulent including neoclassical effects. In each case, three different values of collisionality in the banana regime are investigated. Preliminary results show an enhancement of about 30% of the poloidal rotation of the main ions (Z=1) in the turbulent regime as compared to its neoclassical value. In all cases the radial force balance equation is satisfied within a few percent. Most of this increase comes from the radial electric field.
Numerical Instability in a 2D Gyrokinetic Code Caused by Divergent E × B Flow
NASA Astrophysics Data System (ADS)
Byers, J. A.; Dimits, A. M.; Matsuda, Y.; Langdon, A. B.
1994-12-01
In this paper, a numerical instability first observed in a 2D electrostatic gyrokinetic code is described. The instability should also be present in some form in many versons of particle-in-cell simulation codes that employ guiding center drifts. A perturbation analysis of the instability is given and its results agree quantitatively with the observations from the gyrokinetic code in all respects. The basic mechanism is a false divergence of the E × B flow caused by the interpolation between the grid and the particles as coupled with the specific numerical method for calculating E - ∇φ. Stability or instability depends in detail on the specific choice of particle interpolation method and field method. One common interpolation method, subtracted dipole, is stable. Other commonly used interpolation methods, linear and quadratic, are unstable when combined with a finite difference for the electric field. Linear and quadratic interpolation can be rendered stable if combined with another method for the electric field, the analytic differential of the interpolated potential.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
NASA Astrophysics Data System (ADS)
Carlevaro, Nakia; Falessi, Matteo V.; Montani, Giovanni; Zonca, Fulvio
2015-10-01
> In this paper we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analysed.
The possible evidence of the non-linear particle acceleration in Cas A from Planck data
NASA Astrophysics Data System (ADS)
Urošević, Dejan
2015-08-01
Arnaud et al. (2014, arXiv:1409.5746) have recently published their microwave survey Of Galactic supernova remnants by using results of observations made by Planck telescope. The high frequency radio data obtained by Planck reveal obvious concave up form of spectrum of Galactic supernova remnant (SNR) Cas A. It is expected form of spectrum if non-linear diffuse shock acceleration (DSA) process is active. The radio spectral index (the flux density Sν ˜ ν -α ) of Cas A at low and middle frequencies (< 30 GHz) has value α = 0.77. At higher frequencies (between 30 GHz and 353 GHz) this spectral index becomes flatter, α ˜ 0.6. Under assumption of the test particle DSA, as the first approximation, the corresponding compression ratio should increase from 3 (α = 0.77) to 3.5 (α = 0.6). This represents a possible observational evidence for the existence of a modified shock wave.
Fuzzy controller training using particle swarm optimization for nonlinear system control.
Karakuzu, Cihan
2008-04-01
This paper proposes and describes an effective utilization of particle swarm optimization (PSO) to train a Takagi-Sugeno (TS)-type fuzzy controller. Performance evaluation of the proposed fuzzy training method using the obtained simulation results is provided with two samples of highly nonlinear systems: a continuous stirred tank reactor (CSTR) and a Van der Pol (VDP) oscillator. The superiority of the proposed learning technique is that there is no need for a partial derivative with respect to the parameter for learning. This fuzzy learning technique is suitable for real-time implementation, especially if the system model is unknown and a supervised training cannot be run. In this study, all parameters of the controller are optimized with PSO in order to prove that a fuzzy controller trained by PSO exhibits a good control performance.
Gyrokinetic simulations of solar wind turbulence from ion to electron scales.
Howes, G G; TenBarge, J M; Dorland, W; Quataert, E; Schekochihin, A A; Numata, R; Tatsuno, T
2011-07-15
A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.
Gyrokinetic simulation of turbulence driven geodesic acoustic modes in edge plasmas of HL-2A tokamak
Liu Feng; Zhao, K. J.; Lin, Z.; Dong, J. Q.
2010-11-15
Strong correlation between high frequency microturbulence and low frequency geodesic acoustic mode (GAM) has been observed in the edge plasmas of the HL-2A tokamak, suggesting possible GAM generation via three wave coupling with turbulence, which is in turn modulated by the GAM. In this work, we use the gyrokinetic toroidal code to study the linear and nonlinear development of the drift instabilities, as well as the generation of the GAM (and low frequency zonal flows) and its interaction with the turbulence for realistic parameters in the edge plasmas of the HL-2A tokamak for the first time. The simulation results indicate that the unstable drift wave drives strong turbulence in the edge plasma of HL-2A. In addition, the generation of the GAM and its interaction with the turbulence are all observed in the nonlinear simulation. The simulation results are in reasonable agreement with the experimental observations.
NASA Astrophysics Data System (ADS)
Fedotov, Sergei; Korabel, Nickolay
2015-12-01
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.
Fedotov, Sergei; Korabel, Nickolay
2015-12-01
We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.
NASA Astrophysics Data System (ADS)
Denisov, V. I.; Ilyina, V. A.; Sokolov, V. A.
2016-02-01
In this paper, we studied how nonlinear vacuum electrodynamics can affect charged collapsar spacetime structure and properties of particles movement in this spacetime. Analysis of uncharged particle orbits stability shows that the main features of this orbit in Reissner-Nordström spacetime remains actual for Einstein-Born-Infeld theory. At the same time, there is a significant quantitative difference between stable orbits parameters in these theories and this fact may influence on accretion rate predictions for charged collapsar.
Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong
2016-01-01
In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405
Particle-in-Cell simulation of energetic particles driven instabilities
NASA Astrophysics Data System (ADS)
Chen, Yang; Parker, Scott E.; Lang, Jianying; Fu, Guoyong
2009-11-01
We present simulations of the evolution of energetic particles driven modes with the gyrokinetic turbulence code GEMfootnotetextY. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007), except that kinetic electrons are replaced by a mass-less fluid model. PIC simulations of energetic particles use either the conventional full-f method or the δ method. The latter is adequate for low-amplitude fluctuation amplitudes. The collisional δ -methodfootnotetextY. Chen and R. White, Phys. Plasmas 4, 3591 (1997) is used to systematically account for collisions and particle source and sink. Steady state saturation amplitudes are benchmarked with predictions of analytic theory. We also employ full-f simulationsfootnotetextY. Todo et. al, Phys. Plasmas 10, 2888 (2003) to study bursty events in which the instabilities reach large amplitudes and cause macroscopic redistribution or loss of the particles. With full-f it is easy to retain all the nonlinear effects and treat accurately discontinuities in the distribution function at phase-space boundaries. Whereas the energetic particle current is neglegible in the Ampere's law in δ simulations, it is important in full-f simulations. Thermal ion kinetic effects are observed to be important.
NASA Astrophysics Data System (ADS)
Camporeale, Enrico; Zimbardo, Gaetano
2015-09-01
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles and comparing with test-particle simulations, we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.
Camporeale, Enrico; Zimbardo, Gaetano
2015-09-15
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles and comparing with test-particle simulations, we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.
Fahey, Mark R.; Candy, Jeff
2013-11-07
This project initiated the development of TGYRO ? a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale GYRO turbulence simulations into a framework for practical multi-scale simulation of conventional tokamaks as well as future reactors. Using a lightweight master transport code, multiple independent (each massively parallel) gyrokinetic simulations are coordinated. The capability to evolve profiles using the TGLF model was also added to TGYRO and represents a more typical use-case for TGYRO. The goal of the project was to develop a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale gyrokinetic turbulence simulations into a framework for practical multi-scale simulation of a burning plasma core ? the International Thermonuclear Experimental Reactor (ITER) in particular. This multi-scale simulation capability will be used to predict the performance (the fusion energy gain, Q) given the H-mode pedestal temperature and density. At present, projections of this type rely on transport models like GLF23, which are based on rather approximate fits to the results of linear and nonlinear simulations. Our goal is to make these performance projections with precise nonlinear gyrokinetic simulations. The method of approach is to use a lightweight master transport code to coordinate multiple independent (each massively parallel) gyrokinetic simulations using the GYRO code. This project targets the practical multi-scale simulation of a reactor core plasma in order to predict the core temperature and density profiles given the H-mode pedestal temperature and density. A master transport code will provide feedback to O(16) independent gyrokinetic simulations (each massively parallel). A successful feedback scheme offers a novel approach to predictive modeling of an important national and international problem. Success in this area of fusion simulations will allow US scientists to direct the research path of ITER over the next two
A model of the saturation of coupled electron and ion scale gyrokinetic turbulence
NASA Astrophysics Data System (ADS)
Staebler, G. M.; Howard, N. T.; Candy, J.; Holland, C.
2017-06-01
A new paradigm of zonal flow mixing as the mechanism by which zonal E × B fluctuations impact the saturation of gyrokinetic turbulence has recently been deduced from the nonlinear 2D spectrum of electric potential fluctuations in gyrokinetic simulations. These state of the art simulations span the physical scales of both ion and electron turbulence. It was found that the zonal flow mixing rate, rather than zonal flow shearing rate, competes with linear growth at both electron and ion scales. A model for saturation of the turbulence by the zonal flow mixing was developed and applied to the quasilinear trapped gyro-Landau fluid transport model (TGLF). The first validation tests of the new saturation model are reported in this paper with data from L-mode and high-β p regime discharges from the DIII-D tokamak. The shortfall in the predicted L-mode edge electron energy transport is improved with the new saturation model for these discharges but additional multiscale simulations are required in order to verify the safety factor and collisionality dependencies found in the modeling.
Poloidal tilting symmetry of high order tokamak flux surface shaping in gyrokinetics
NASA Astrophysics Data System (ADS)
Ball, Justin; Parra, Felix I.; Barnes, Michael
2016-04-01
A poloidal tilting symmetry of the local nonlinear δ f gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using up-down asymmetry.
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Waelbroeck, F. L.
2012-03-01
Static external resonant magnetic perturbations (RMPs) have been added to the δf gyrokinetic code GYRO. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr and the corresponding plasma torque (density) R[jrBθ/c], induced by islands that break the toroidal symmetry of a tokamak. This extends previous GYRO simulations for the transport of toroidal angular momentum (TAM) [1,2]. The focus is on full torus radial slice electrostatic simulations of induced q=m/n=6/3 islands with widths 5% of the minor radius. The island torque scales with the radial electric field Er the island width w, and the intensity I of the high-n micro-turbulence, as wErI^1/2. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that there is a small co-directed magnetic acceleration to the small diamagnetic co-rotation corresponding to the zero Er which can be called the residual stress [2] from an externally induced island. Finite-beta GYRO simulations of a core radial slice demonstrate island unlocking and the RMP screening. 6pt[1] R.E. Waltz, et al., Phys. Plasmas 14, 122507 (2007). [2] R.E. Waltz, et al., Phys. Plasmas 18, 042504 (2011).
A model of the saturation of coupled electron and ion scale gyrokinetic turbulence
Staebler, Gary M.; Howard, Nathan T.; Candy, Jeffrey M.; ...
2017-05-09
A new paradigm of zonal flow mixing as the mechanism by which zonal E × B fluctuations impact the saturation of gyrokinetic turbulence has recently been deduced from the nonlinear 2D spectrum of electric potential fluctuations in gyrokinetic simulations. These state of the art simulations span the physical scales of both ion and electron turbulence. It was found that the zonal flow mixing rate, rather than zonal flow shearing rate, competes with linear growth at both electron and ion scales. A model for saturation of the turbulence by the zonal flow mixing was developed and applied to the quasilinear trappedmore » gyro-Landau fluid transport model (TGLF). The first validation tests of the new saturation model are reported in this paper with data from L-mode and high-βp regime discharges from the DIII-D tokamak. Lastly, the shortfall in the predicted L-mode edge electron energy transport is improved with the new saturation model for these discharges but additional multiscale simulations are required in order to verify the safety factor and collisionality dependencies found in the modeling.« less
NASA Astrophysics Data System (ADS)
Field, A. R.; Dunai, D.; Ghim, Y.-c.; Hill, P.; McMillan, B.; Roach, C. M.; Saarelma, S.; Schekochihin, A. A.; Zoletnik, S.; the MAST Team
2014-02-01
Observations of ion-scale (kyρi ⩽ 1) density turbulence of relative amplitude ≳0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial × 4 poloidal channel) imaging beam emission spectroscopy diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport barrier in the ion channel, the observed turbulence characteristics are compared with synthetic density turbulence data generated from global, non-linear, gyro-kinetic simulations using the particle-in-cell code NEMORB. This validation exercise highlights the need to include increasingly sophisticated physics, e.g., kinetic treatment of trapped electrons, equilibrium flow shear and collisions, to reproduce most of the characteristics of the observed turbulence. Even so, significant discrepancies remain: an underprediction by the simulations of the turbulence amplitude and heat flux at plasma periphery and the finding that the correlation times of the numerically simulated turbulence are typically two orders of magnitude longer than those measured in MAST. Comparison of these correlation times with various linear timescales suggests that, while the measured turbulence is strong and may be ‘critically balanced’, the simulated turbulence is weak.
NASA Astrophysics Data System (ADS)
Gusakov, E. Z.; Altukhov, A. B.; Bulanin, V. V.; Gurchenko, A. D.; Heikkinen, J. A.; Janhunen, S. J.; Leerink, S.; Esipov, L. A.; Kantor, M. Yu; Kiviniemi, T. P.; Korpilo, T.; Kouprienko, D. V.; Lashkul, S. I.; Petrov, A. V.; Teplova, N. V.
2013-12-01
Quantitative reproduction of selected micro-, meso- and macro-scale transport phenomena as measured in the FT-2 tokamak is reached by Elmfire global full-f nonlinear gyrokinetic particle-in-cell simulation predictions. A detailed agreement with mean equilibrium flows, oscillating fine-scale zonal flows and turbulence radial correlation length observed by a set of sophisticated microwave backscattering techniques, as well as a good fit of the thermal diffusivity data in the central and gradient region of discharge are demonstrated. Both the shift and the broadening of the power spectrum of synthetic and experimental Doppler reflectometry diagnostics have been found to overlap perfectly at various radial positions, indicating similar rotation and spreading of the selected density fluctuations. At the same time similar radial electric field dynamics, spatial structure and outward geodesic acoustic mode (GAM) propagation have been observed by comparisons of the probability distribution function, the dominant frequency, the coherence and the cross-phase of the simulated and experimentally measured radial electric field fluctuations, identifying the turbulent driven GAM as a key contributor to the observed strong temporal variation of the radial electric field affected by impurity ions.
Matsumoto, Taro; Naitou, Hiroshi; Tokuda, Shinji; Kishimoto, Yasuaki
2005-09-15
The behavior of the collisionless magnetohydrodynamics modes is investigated by the gyrokinetic particle simulation in a cylindrical tokamak plasma in the parameter region where the effects of electron inertia and electron parallel compressibility are competitive for magnetic reconnection. Although the linear growth of the m=1 internal kink-tearing mode is dominated by the electron inertia, it is found that the growth rate can be nonlinearly accelerated due to the electron parallel compressibility proportional to the ion sound Larmor radius {rho}{sub s}. It is also found that, as decreasing the electron skin depth {delta}{sub e}, the maximum growth rate before the internal collapse saturates independently of the microscopic scales such as {delta}{sub e} and {rho}{sub s}. The acceleration of growth rate is also observed in the nonlinear phase of the m=2 double tearing mode.
Benchmarking Nonlinear Turbulence Simulations on Alcator C-Mod
M.H. Redi; C.L. Fiore; W. Dorland; M.J. Greenwald; G.W. Hammett; K. Hill; D. McCune; D.R. Mikkelsen; G. Rewoldt; J.E. Rice
2004-06-22
Linear simulations of plasma microturbulence are used with recent radial profiles of toroidal velocity from similar plasmas to consider nonlinear microturbulence simulations and observed transport analysis on Alcator C-Mod. We focus on internal transport barrier (ITB) formation in fully equilibrated H-mode plasmas with nearly flat velocity profiles. Velocity profile data, transport analysis and linear growth rates are combined to integrate data and simulation, and explore the effects of toroidal velocity on benchmarking simulations. Areas of interest for future nonlinear simulations are identified. A good gyrokinetic benchmark is found in the plasma core, without extensive nonlinear simulations. RF-heated C-Mod H-mode experiments, which exhibit an ITB, have been studied with the massively parallel code GS2 towards validation of gyrokinetic microturbulence models. New, linear, gyrokinetic calculations are reported and discussed in connection with transport analysis near the ITB trigger time of shot No.1001220016.
In-situ imaging of reacting single-particle zeolites by non-linear optical microscopy
NASA Astrophysics Data System (ADS)
Wrzesinski, Paul J.; Slipchenko, Mikhail N.; Zaman, Taslima A.; Rioux, Robert M.; Gord, James R.; Roy, Sukesh
2015-03-01
Zeolite catalysis has been exploited by the petrochemical industry since the 1940's for catalytic cracking reactions of long chain hydrocarbons. The selectivity of zeolites strongly depends on a pore size, which is controlled by the chosen structure-directing agent (SDA) and by the SDA decomposition/removal process. Although zeolites are composed of micron-sized crystals, studies of zeolite materials typically focus on bulk (i.e., ensemble) measurements to elucidate structure-function information or to optimize catalysts and/or process parameters. To examine these phenomena on the microscale, non-linear optical microscopy is used to provide real-time imaging of chemical reactions in zeolites at temperatures exceeding 400°C. The template decomposition mechanism is studied, as elucidation of the mechanism is critical to understanding the relationship between the decomposition chemistry and the nanoscale features of the zeolite (topology, Si/Al ratio, added dopants). Forward stimulated Raman scattering (SRS), forward coherent anti-Stokes Raman scattering (CARS) and epi two-photon fluorescence (TPF) modalities are acquired simultaneously providing video-rate structural and chemical information. A high-temperature cell with gas inlet system is used for the study of reactions under various temperatures and gas environments. Examining the decomposition process with single-particle resolution enables access to ensemble-level and spatially-resolved behavior. Parallel experiments on bulk zeolite powders are conducted to enable comparison of ensemble and single-particle behavior during template decomposition. Our multi-technique approach has high potential for gaining insight into the link between nanoscale structure and catalytic activity and selectivity of zeolitic materials.
Gyrokinetic theory and simulation of turbulent energy exchange
Waltz, R. E.; Staebler, G. M.
2008-01-15
A previous gyrokinetic theory of turbulent heating [F. L. Hinton and R. E. Waltz, Phys. Plasma 13, 102301 (2006)] is simplified and extended to show that the local radial average of terms in the gyrokinetic turbulent heating (which survive in the drift kinetic limit) are actually closer to a turbulent energy exchange between electrons and ions. The integrated flow for the local exchange is simulated with the GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] delta-f gyrokinetic code and found to be small in a well studied DIII-D [M. A. Mahdavi and J. L. Luxon, ''DIII-D Tokamak Special Issue'' Fusion Sci. Technol. 48, 2 (2005)] L-mode discharge.
Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective
Lee, W. W.
2016-07-15
The effort to obtain a set of MagnetoHydroDynamic (MHD) equations for a magnetized collisionless plasma was started nearly 60 years ago by Chew et al. [Proc. R. Soc. London, Ser. A 236(1204), 112–118 (1956)]. Many attempts have been made ever since. Here, we will show the derivation of a set of these equations from the gyrokinetic perspective, which we call it gyrokinetic MHD, and it is different from the conventional ideal MHD. However, this new set of equations still has conservation properties and, in the absence of fluctuations, recovers the usual MHD equilibrium. Furthermore, the resulting equations allow for the plasma pressure balance to be further modified by finite-Larmor-radius effects in regions with steep pressure gradients. The present work is an outgrowth of the paper on “Alfven Waves in Gyrokinetic Plasmas” by Lee and Qin [Phys. Plasmas 10, 3196 (2003)].
Krommes, J. A.
2013-12-15
Some physical interpretations are given of the well-known second-order gyrokinetic Hamiltonian in the magnetohydrodynamic limit. Its relations to the conservation of the true (Galilean-invariant) magnetic moment and fluid nonlinearities are described. Subtleties about its derivation as a cold-ion limit are explained; it is important to take that limit in the frame moving with the E×B velocity. The discussion also provides some geometric understanding of certain well-known Lie generating functions, and it makes contact with general discussions of ponderomotive potentials and the thermodynamics of dielectric media.
Leerink, S; Bulanin, V V; Gurchenko, A D; Gusakov, E Z; Heikkinen, J A; Janhunen, S J; Lashkul, S I; Altukhov, A B; Esipov, L A; Kantor, M Yu; Kiviniemi, T P; Korpilo, T; Kuprienko, D V; Petrov, A V
2012-10-19
Direct measurements of micro-, meso-, and macroscale transport phenomena in the FT-2 tokamak are shown to be quantitatively reproduced by global full f nonlinear gyrokinetic simulation predictions. A detailed agreement with mean equilibrium E×B flows, oscillating fine-scale zonal flows, and turbulence spectra observed by a set of sophisticated microwave backscattering techniques as well as a good fit of the thermal diffusivity data are demonstrated. A clear influence of the impurity ions on the fluctuating radial electric field is observed.
A nonlinear particle dynamics map of wakefield acceleration in a linear collider
Tajima, T.; Cheshkov, S.; Horton, W.; Yokoya, K.
1998-08-01
The performance of a wakefield accelerator in a high energy collider application is analyzed. In order to carry out this task, it is necessary to construct a strawman design system (no matter how preliminary) and build a code of the systems approach. A nonlinear dynamics map built on a simple theoretical model of the wakefield generated by the laser pulse (or whatever other method) is obtained and they employ this as a base for building a system with multi-stages (and components) as a high energy collider. The crucial figures of merit for such a system other than the final energy include the emittance (that determines the luminosity). The more complex the system is, the more opportunities the system has to degrade the emittance (or entropy of the beam). Thus the map gu ides one to identify where the crucial elements lie that affect the emittance. They find that a strong focusing force of the wakefield coupled with a possible jitter of the axis (or laser aiming) of each stage and a spread in the betatron frequencies arising from different phase space positions for individual particles leads to a phase space mixing. This sensitively controls the emittance degradation. They show that in the case of a uniform plasma the effect of emittance growth is large and may cause serious problems. They discuss possibilities to avoid it and control the situation.
Peralta-Ramos, J; Calzetta, E
2009-05-27
Using closed-time-path two-particle irreducible coarse-grained effective action (CTP 2PI CGEA) techniques, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the CTP 2PI CGEA is invariant under a simultaneous gauge transformation of the external field and the full Schwinger-Keldysh propagator, and that this property holds even when the loop expansion of the CTP 2PI CGEA is truncated at arbitrary order. The effective action approach provides a systematic way of calculating the propagator and response functions of the system, via the Schwinger-Dyson equation and the Bethe-Salpeter equations, respectively. We show that, due to the invariance of the CTP 2PI CGEA under external gauge transformations, the response functions calculated from it satisfy the Ward-Takahashi hierarchy, thus warranting the conservation of the electronic current beyond the expectation value level. We also clarify the connection between nonlinear response theory and the WT hierarchy, and discuss an example of an ad hoc approximation that violates it. These findings may be useful in the study of current fluctuations in correlated electronic pumping devices.
Li, Tao; Yuan, Gannan; Li, Wang
2016-01-01
The derivation of a conventional error model for the miniature gyroscope-based measurement while drilling (MGWD) system is based on the assumption that the errors of attitude are small enough so that the direction cosine matrix (DCM) can be approximated or simplified by the errors of small-angle attitude. However, the simplification of the DCM would introduce errors to the navigation solutions of the MGWD system if the initial alignment cannot provide precise attitude, especially for the low-cost microelectromechanical system (MEMS) sensors operated in harsh multilateral horizontal downhole drilling environments. This paper proposes a novel nonlinear error model (NNEM) by the introduction of the error of DCM, and the NNEM can reduce the propagated errors under large-angle attitude error conditions. The zero velocity and zero position are the reference points and the innovations in the states estimation of particle filter (PF) and Kalman filter (KF). The experimental results illustrate that the performance of PF is better than KF and the PF with NNEM can effectively restrain the errors of system states, especially for the azimuth, velocity, and height in the quasi-stationary condition. PMID:26999130
Construction of symplectic maps for nonlinear motion of particles in accelerators
NASA Astrophysics Data System (ADS)
Berg, J. S.; Warnock, R. L.; Ruth, R. D.; Forest, É.
1994-01-01
We explore an algorithm for the construction of symplectic maps to describe nonlinear particle motion in circular accelerators. We emphasize maps for motion over one or a few full turns, which may provide an economical way of studying long-term stability in large machines such as the Superconducting Super Collider (SSC). The map is defined implicitly by a mixed-variable generating function, represented as a Fourier series in betatron angle variables, with coefficients given as B-spline functions of action variables and the total energy. Despite the implicit definition, iteration of the map proves to be a fast process. The method is illustrated with a realistic model of the SSC. We report extensive tests of accuracy and iteration time in various regions of phase space, and demonstrate the results by using single-turn maps to follow trajectories symplectically for 107 turns on a workstation computer. The same method may be used to construct the Poincaré map of Hamiltonian systems in other fields of physics.
Li, Tao; Yuan, Gannan; Li, Wang
2016-03-15
The derivation of a conventional error model for the miniature gyroscope-based measurement while drilling (MGWD) system is based on the assumption that the errors of attitude are small enough so that the direction cosine matrix (DCM) can be approximated or simplified by the errors of small-angle attitude. However, the simplification of the DCM would introduce errors to the navigation solutions of the MGWD system if the initial alignment cannot provide precise attitude, especially for the low-cost microelectromechanical system (MEMS) sensors operated in harsh multilateral horizontal downhole drilling environments. This paper proposes a novel nonlinear error model (NNEM) by the introduction of the error of DCM, and the NNEM can reduce the propagated errors under large-angle attitude error conditions. The zero velocity and zero position are the reference points and the innovations in the states estimation of particle filter (PF) and Kalman filter (KF). The experimental results illustrate that the performance of PF is better than KF and the PF with NNEM can effectively restrain the errors of system states, especially for the azimuth, velocity, and height in the quasi-stationary condition.
NASA Astrophysics Data System (ADS)
Angioni, C.; Bilato, R.; Casson, F. J.; Fable, E.; Mantica, P.; Odstrcil, T.; Valisa, M.; ASDEX Upgrade Team; Contributors, JET
2017-02-01
In tokamaks, the role of turbulent transport of heavy impurities, relative to that of neoclassical transport, increases with increasing size of the plasma, as clarified by means of general scalings, which use the ITER standard scenario parameters as reference, and by actual results from a selection of discharges from ASDEX Upgrade and JET. This motivates the theoretical investigation of the properties of the turbulent convection of heavy impurities by nonlinear gyrokinetic simulations in the experimentally relevant conditions of comparable ion and electron heat fluxes. These conditions also correspond to an intermediate regime between dominant ion temperature gradient turbulence and trapped electron mode turbulence. At moderate plasma toroidal rotation, the turbulent convection of heavy impurities, computed with nonlinear gyrokinetic simulations, is found to be directed outward, in contrast to that obtained by quasi-linear calculations based on the most unstable linear mode, which is directed inward. In this mixed turbulence regime, with comparable electron and ion heat fluxes, the nonlinear results of the impurity transport can be explained by the coexistence of both ion temperature gradient and trapped electron modes in the turbulent state, both contributing to the turbulent convection and diffusion of the impurity. The impact of toroidal rotation on the turbulent convection is also clarified.
Incorrectness of the usual gyrokinetic treatment in cylindrically symmetric systems
Linsker, R.
1980-07-01
It is shown that the usual gyrokinetic theory does not consistently retain all terms of leading order in the expansion parameter epsilon = gyroradius/equilibrium scale length. This is illustrated for cylindrically symmetric systems by comparing the perturbed distribution function calculated by the gyrokinetic method with that obtained by explicitly integrating the Vlasov equation over the unperturbed orbit. The integral equation used in some recent treatments of drift waves in sheared-slab geometry is shown to be incorrect. The correct calculation of the ion density perturbation for a collisionless ..beta.. = 0 plasma with cylindrical symmetry is presented.
Ion transport barriers triggered by plasma polarization in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Strugarek, A.; Sarazin, Y.; Zarzoso, D.; Abiteboul, J.; Brun, A. S.; Cartier-Michaud, T.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, Ph; Grandgirard, V.; Latu, G.; Passeron, C.; Thomine, O.
2013-07-01
The creation of ion transport barriers by externally induced sheared E × B flows is investigated with the global, full-f and flux-driven gyrokinetic code GYSELA. A gyrokinetic source of vorticity is designed and proves to be efficient in polarizing the plasma. Induced sheared electric fields develop in the turbulent core and are accompanied by the creation of a transport barrier. The barrier and the sheared flow relax quasi-periodically because of zonal flow activity and a destabilizing temperature anisotropy induced by the vorticity source. A new cyclic mechanism leading to the relaxation of transport barriers in tokamaks is discovered.
W.M. Tang
2005-01-03
The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics--the research arena from which this formalism was originally developed. It was presented as a component of the ''Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations'' held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources.
NASA Astrophysics Data System (ADS)
Xie, H. S.; Li, Y. Y.; Lu, Z. X.; Ou, W. K.; Li, B.
2017-07-01
To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on the integral equation, Euler initial value simulation, Euler matrix eigenvalue solution, and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift mode equation in Z-pinch with slab simplification and in tokamak with a ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at a strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas.
Collision-dependent power law scalings in two dimensional gyrokinetic turbulence
Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.
2014-08-15
Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.
Gyrokinetic turbulence cascade via predator-prey interactions between different scales
Kobayashi, Sumire Gurcan, Ozgur D.
2015-05-15
Gyrokinetic simulations in a closed fieldline geometry are presented to explore the physics of nonlinear transfer in plasma turbulence. As spontaneously formed zonal flows and small-scale turbulence demonstrate “predator-prey” dynamics, a particular cascade spectrum emerges. The electrostatic potential and the density spectra appear to be in good agreement with the simple theoretical prediction based on Charney-Hasegawa-Mima equation | ϕ{sup ~}{sub k} |{sup 2}∼| n{sup ~}{sub k} |{sup 2}∝k{sup −3}/(1+k{sup 2}){sup 2}, with the spectra becoming anisotropic at small scales. The results indicate that the disparate scale interactions, in particular, the refraction and shearing of larger scale eddies by the self-consistent zonal flows, dominate over local interactions, and contrary to the common wisdom, the comprehensive scaling relation is created even within the energy injection region.
Search for gyrokinetic dependencies in helium transport at Alcator C-Mod
NASA Astrophysics Data System (ADS)
Liao, Kenneth; Rowan, William; Hatch, David; Bespamyatnov, Igor; Horton, Wendell
2013-10-01
Helium-3 and helium-4 impurity transport measurements and density profile measurements have been obtained on Alcator C-Mod in a variety of discharge conditions, using the core Charge Exchange Recombination Spectroscopy (CXRS) diagnostic. The helium concentrations range from trace (< 2 %) to large minority (~ 20 %). L-mode, H-mode, and I-mode results are included, with Ohmic heated, ICRF heated, and LH heated plasmas. Helium profiles are observed to vary with plasma current, and also change in time during ICRF shots. Linear and nonlinear gyrokinetic simulations are performed for some shots using the GENE code. Sensitivity scans are done for magnetic shear, impurity density, and other plasma parameters and transport scalings are compared with experimental results. Simulated transport flux is compared with experimentally derived D and v parameters. Supported by USDoE awards DE-FG03-96ER-54373 and DE-FC02-99ER54512.
Faber, B. J.; Pueschel, M. J.; Terry, P. W.; Proll, J. H. E.; Hegna, C. C.; Weir, G. M.; Likin, K. M.; Talmadge, J. N.
2015-07-15
Gyrokinetic simulations of plasma microturbulence in the Helically Symmetric eXperiment are presented. Using plasma profiles relevant to experimental operation, four dominant drift wave regimes are observed in the ion wavenumber range, which are identified as different flavors of density-gradient-driven trapped electron modes. For the most part, the heat transport exhibits properties associated with turbulence driven by these types of modes. Additionally, long-wavelength, radially localized, nonlinearly excited coherent structures near the resonant central flux surface, not predicted by linear simulations, can further enhance flux levels. Integrated heat fluxes are compatible with experimental observations in the corresponding density gradient range. Despite low shearing rates, zonal flows are observed to regulate turbulence but can be overwhelmed at higher density gradients by the long-wavelength coherent structures.
NASA Astrophysics Data System (ADS)
Khaki, Mehdi; Forootan, Ehsan; Kuhn, Michael; Awange, Joseph; Pattiaratchi, Charitha
2016-04-01
Quantifying large-scale (basin/global) water storage changes is essential to understand the Earth's hydrological water cycle. Hydrological models have usually been used to simulate variations in storage compartments resulting from changes in water fluxes (i.e., precipitation, evapotranspiration and runoff) considering physical or conceptual frameworks. Models however represent limited skills in accurately simulating the storage compartments that could be the result of e.g., the uncertainty of forcing parameters, model structure, etc. In this regards, data assimilation provides a great chance to combine observational data with a prior forecast state to improve both the accuracy of model parameters and to improve the estimation of model states at the same time. Various methods exist that can be used to perform data assimilation into hydrological models. The one more frequently used particle-based algorithms suitable for non-linear systems high-dimensional systems is the Ensemble Kalman Filtering (EnKF). Despite efficiency and simplicity (especially in EnKF), this method indicate some drawbacks. To implement EnKF, one should use the sample covariance of observations and model state variables to update a priori estimates of the state variables. The sample covariance can be suboptimal as a result of small ensemble size, model errors, model nonlinearity, and other factors. Small ensemble can also lead to the development of correlations between state components that are at a significant distance from one another where there is no physical relation. To investigate the under-sampling issue raise by EnKF, covariance inflation technique in conjunction with localization was implemented. In this study, a comparison between latest methods used in the data assimilation framework, to overcome the mentioned problem, is performed. For this, in addition to implementing EnKF, we introduce and apply the Local Ensemble Kalman Filter (LEnKF) utilizing covariance localization to remove
NASA Astrophysics Data System (ADS)
Devi, Anita; De, Arijit K.
2017-08-01
Experimental evidence indicates that high-repetition-rate ultrafast pulsed excitation is more efficient in optical trapping of dielectric nanoparticles as compared with continuous-wave excitation at the same average power. The physics behind the different nature of force under these two excitation conditions remained deceptive until quite recently when it was theoretically explained, in the dipole limit, as a combined effect of (1) repetitive instantaneous momentum transfer and (2) optical Kerr nonlinearity. The role of optical Kerr effect was theoretically studied for larger dielectric spherical particles, in the ray optics limit, also. However, a theoretical underpinning is yet to be established as to whether the effect of optical nonlinearity is omnipresent across different particle sizes, which we investigate here. Using localized approximation of generalized Lorenz-Mie theory, we theoretically analyze the nature of force (and potential) and provide a detailed comparative discussion between this generalized scattering formulation with dipole scattering formulation for dielectric nanoparticles.
Gyrokinetic predictions of multiscale transport in a DIII-D ITER baseline discharge
NASA Astrophysics Data System (ADS)
Holland, C.; Howard, N. T.; Grierson, B. A.
2017-06-01
New multiscale gyrokinetic simulations predict that electron energy transport in a DIII-D ITER baseline discharge with dominant electron heating and low input torque is multiscale in nature, with roughly equal amounts of the electron energy flux Q e coming from long wavelength ion-scale (k y ρ s < 1) and short wavelength electron-scale (k y ρ s > 1) fluctuations when the gyrokinetic results match independent power balance calculations. Corresponding conventional ion-scale simulations are able to match the power balance ion energy flux Q i, but systematically underpredict Q e when doing so. Significant nonlinear cross-scale couplings are observed in the multiscale simulations, but the exact simulation predictions are found to be extremely sensitive to variations of model input parameters within experimental uncertainties. Most notably, depending upon the exact value of the equilibrium E × B shearing rate γ E×B used, either enhancement or suppression of the long-wavelength turbulence and transport levels in the multiscale simulations is observed relative to what is predicted by ion-scale simulations. While the enhancement of the long wavelength fluctuations by inclusion of the short wavelength turbulence was previously observed in similar multiscale simulations of an Alcator C-Mod L-mode discharge, these new results show for the first time a complete suppression of long-wavelength turbulence in a multiscale simulation, for parameters at which conventional ion-scale simulation predicts small but finite levels of low-k turbulence and transport consistent with the power balance Q i. Although computational resource limitations prevent a fully rigorous validation assessment of these new results, they provide significant new evidence that electron energy transport in burning plasmas is likely to have a strong multiscale character, with significant nonlinear cross-scale couplings that must be fully understood to predict the performance of
Gyrokinetic predictions of multiscale transport in a DIII-D ITER baseline discharge
Holland, C.; Howard, N. T.; Grierson, B. A.
2017-05-08
New multiscale gyrokinetic simulations predict that electron energy transport in a DIII-D ITER baseline discharge with dominant electron heating and low input torque is multiscale in nature, with roughly equal amounts of the electron energy flux Qe coming from long wavelength ion-scale (kyρs < 1) and short wavelength electron-scale (kyρs > 1) fluctuations when the gyrokinetic results match independent power balance calculations. Corresponding conventional ion-scale simulations are able to match the power balance ion energy flux Qi, but systematically underpredict Qe when doing so. We observe significant nonlinear cross-scale couplings in the multiscale simulations, but the exact simulation predictions aremore » found to be extremely sensitive to variations of model input parameters within experimental uncertainties. Most notably, depending upon the exact value of the equilibrium E x B shearing rate γ E x B used, either enhancement or suppression of the long-wavelength turbulence and transport levels in the multiscale simulations is observed relative to what is predicted by ion-scale simulations. And while the enhancement of the long wavelength fluctuations by inclusion of the short wavelength turbulence was previously observed in similar multiscale simulations of an Alcator C-Mod L-mode discharge, these new results show for the first time a complete suppression of long-wavelength turbulence in a multiscale simulation, for parameters at which conventional ion-scale simulation predicts small but finite levels of low-k turbulence and transport consistent with the power balance Qi. Though computational resource limitations prevent a fully rigorous validation assessment of these new results, they provide significant new evidence that electron energy transport in burning plasmas is likely to have a strong multiscale character, with significant nonlinear cross-scale couplings that must be fully understood to predict the performance of those plasmas with confidence.« less
NASA Astrophysics Data System (ADS)
Lin, Cheng-Jian; Lee, Chi-Yung
2010-04-01
This article introduces a recurrent fuzzy neural network based on improved particle swarm optimisation (IPSO) for non-linear system control. An IPSO method which consists of the modified evolutionary direction operator (MEDO) and the Particle Swarm Optimisation (PSO) is proposed in this article. A MEDO combining the evolutionary direction operator and the migration operation is also proposed. The MEDO will improve the global search solution. Experimental results have shown that the proposed IPSO method controls the magnetic levitation system and the planetary train type inverted pendulum system better than the traditional PSO and the genetic algorithm methods.
Kovachev, L. M.
2009-10-29
We present an analytical approach to the theory of optical pulses with superbroad spectrum propagated in air. The corresponding modified amplitude envelope equation admits oscillated with terahertz frequency nonlinear term The fluctuation is due to the group and phase velocity difference. In the partial case of femtosecond pulses with power, little above the critical for self-focusing, exact (3+1)D particle-like solution is found.
Phase space structures in gyrokinetic simulations of fusion plasma turbulence
NASA Astrophysics Data System (ADS)
Ghendrih, Philippe; Norscini, Claudia; Cartier-Michaud, Thomas; Dif-Pradalier, Guilhem; Abiteboul, Jérémie; Dong, Yue; Garbet, Xavier; Gürcan, Ozgür; Hennequin, Pascale; Grandgirard, Virginie; Latu, Guillaume; Morel, Pierre; Sarazin, Yanick; Storelli, Alexandre; Vermare, Laure
2014-10-01
Gyrokinetic simulations of fusion plasmas give extensive information in 5D on turbulence and transport. This paper highlights a few of these challenging physics in global, flux driven simulations using experimental inputs from Tore Supra shot TS45511. The electrostatic gyrokinetic code GYSELA is used for these simulations. The 3D structure of avalanches indicates that these structures propagate radially at localised toroidal angles and then expand along the field line at sound speed to form the filaments. Analysing the poloidal mode structure of the potential fluctuations (at a given toroidal location), one finds that the low modes m = 0 and m = 1 exhibit a global structure; the magnitude of the m = 0 mode is much larger than that of the m = 1 mode. The shear layers of the corrugation structures are thus found to be dominated by the m = 0 contribution, that are comparable to that of the zonal flows. This global mode seems to localise the m = 2 mode but has little effect on the localisation of the higher mode numbers. However when analysing the pulsation of the latter modes one finds that all modes exhibit a similar phase velocity, comparable to the local zonal flow velocity. The consequent dispersion like relation between the modes pulsation and the mode numbers provides a means to measure the zonal flow. Temperature fluctuations and the turbulent heat flux are localised between the corrugation structures. Temperature fluctuations are found to exhibit two scales, small fluctuations that are localised by the corrugation shear layers, and appear to bounce back and forth radially, and large fluctuations, also readily observed on the flux, which are associated to the disruption of the corrugations. The radial ballistic velocity of both avalanche events if of the order of 0.5ρ∗c0 where ρ∗ = ρ0/a, a being the tokamak minor radius and ρ0 being the characteristic Larmor radius, ρ0 = c0/Ω0. c0 is the reference ion thermal velocity and Ω0 = qiB0/mi the reference
Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses
NASA Astrophysics Data System (ADS)
Fan, Meng; Zhang, Kai; Schroers, Jan; Shattuck, Mark D.; O'Hern, Corey S.
2017-09-01
Amorphous materials such as metallic, polymeric, and colloidal glasses exhibit complex preparation-dependent mechanical response to applied shear. In particular, glassy solids yield, with a mechanical response that transitions from elastic to plastic, with increasing shear strain. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate R used to prepare them. The ensemble-averaged stress versus strain curve 〈σ (γ )〉 resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak in stress at intermediate strain, and a plastic flow regime at large strains. In contrast, for each glass configuration in the ensemble, the stress-strain curve σ (γ ) consists of many short nearly linear segments that are punctuated by particle-rearrangement-induced rapid stress drops. To explain the nonlinearity of 〈σ (γ )〉 , we quantify the shape of the small stress-strain segments and the frequency and size of the stress drops in each glass configuration. We decompose the stress loss [i.e., the deviation in the slope of 〈σ (γ )〉 from that at 〈σ (0 )〉 ] into the loss from particle rearrangements and the loss from softening [i.e., the reduction of the slopes of the linear segments in σ (γ ) ], and then compare the two contributions as a function of R and γ . For the current studies, the rearrangement-induced stress loss is larger than the softening-induced stress loss, however, softening stress losses increase with decreasing cooling rate. We also characterize the structure of the potential energy landscape along the strain direction for glasses prepared with different R , and observe a dramatic change of the properties of the landscape near the yielding transition. We then show that the rearrangement-induced energy loss per strain can serve as
NASA Astrophysics Data System (ADS)
Siade, A. J.; Prommer, H.; Welter, D.
2014-12-01
Groundwater management and remediation requires the implementation of numerical models in order to evaluate the potential anthropogenic impacts on aquifer systems. In many situations, the numerical model must, not only be able to simulate groundwater flow and transport, but also geochemical and biological processes. Each process being simulated carries with it a set of parameters that must be identified, along with differing potential sources of model-structure error. Various data types are often collected in the field and then used to calibrate the numerical model; however, these data types can represent very different processes and can subsequently be sensitive to the model parameters in extremely complex ways. Therefore, developing an appropriate weighting strategy to address the contributions of each data type to the overall least-squares objective function is not straightforward. This is further compounded by the presence of potential sources of model-structure errors that manifest themselves differently for each observation data type. Finally, reactive transport models are highly nonlinear, which can lead to convergence failure for algorithms operating on the assumption of local linearity. In this study, we propose a variation of the popular, particle swarm optimization algorithm to address trade-offs associated with the calibration of one data type over another. This method removes the need to specify weights between observation groups and instead, produces a multi-dimensional Pareto front that illustrates the trade-offs between data types. We use the PEST++ run manager, along with the standard PEST input/output structure, to implement parallel programming across multiple desktop computers using TCP/IP communications. This allows for very large swarms of particles without the need of a supercomputing facility. The method was applied to a case study in which modeling was used to gain insight into the mobilization of arsenic at a deepwell injection site
Gyrokinetic simulations of turbulent transport: size scaling and chaotic behaviour
NASA Astrophysics Data System (ADS)
Villard, L.; Bottino, A.; Brunner, S.; Casati, A.; Chowdhury, J.; Dannert, T.; Ganesh, R.; Garbet, X.; Görler, T.; Grandgirard, V.; Hatzky, R.; Idomura, Y.; Jenko, F.; Jolliet, S.; Khosh Aghdam, S.; Lapillonne, X.; Latu, G.; McMillan, B. F.; Merz, F.; Sarazin, Y.; Tran, T. M.; Vernay, T.
2010-12-01
Important steps towards the understanding of turbulent transport have been made with the development of the gyrokinetic framework for describing turbulence and with the emergence of numerical codes able to solve the set of gyrokinetic equations. This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. Solving 5D gyrokinetic equations for each species requires state-of-the-art high performance computing techniques involving massively parallel computers and parallel scalable algorithms. The various numerical schemes that have been explored until now, Lagrangian, Eulerian and semi-Lagrangian, each have their advantages and drawbacks. A past controversy regarding the finite size effect (finite ρ*) in ITG turbulence has now been resolved. It has triggered an intensive benchmarking effort and careful examination of the convergence properties of the different numerical approaches. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the ρ* → 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary: inconsistent approximations that are sometimes used can lead to important discrepancies. Turbulent processes are characterized by a chaotic behaviour, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation. Further developments concerning non-adiabatic electron dynamics around mode-rational surfaces and electromagnetic effects are discussed.
A basic plasma test for gyrokinetics: GDC turbulence in LAPD
NASA Astrophysics Data System (ADS)
Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.
2017-02-01
Providing an important step towards validating gyrokinetics under comparatively little-explored conditions, simulations of pressure-gradient-driven plasma turbulence in the Large Plasma Device (LAPD) are compared with experimental observations. The corresponding signatures confirm the existence of a novel regime of turbulence, based on the recently-discovered gradient-driven drift coupling (GDC) instability, which is thus confirmed as a candidate mechanism for turbulence in basic, space and astrophysical plasmas. Despite the limitations of flux-tube gyrokinetics for this scenario, when accounting for box size scaling by applying a scalar factor η =6, agreement between simulations and experiment improves to within a factor of two for key observables: compressional magnetic, density, and temperature fluctuations, both in amplitude and structure. Thus, a first, strong indication is presented that the GDC instability seen in gyrokinetics appears to operate in the experiment and that the essential instability physics is present in the numerical model. Overall, the gyrokinetic framework and its numerical implementation in the Gene code therefore perform well for LAPD plasmas very different from their brethren in fusion experiments.
GYROKINETIC PARTICLE SIMULATION OF TURBULENT TRANSPORT IN BURNING PLASMAS
Horton, Claude Wendell
2014-06-10
The SciDAC project at the IFS advanced the state of high performance computing for turbulent structures and turbulent transport. The team project with Prof Zhihong Lin [PI] at Univ California Irvine produced new understanding of the turbulent electron transport. The simulations were performed at the Texas Advanced Computer Center TACC and the NERSC facility by Wendell Horton, Lee Leonard and the IFS Graduate Students working in that group. The research included a Validation of the electron turbulent transport code using the data from a steady state university experiment at the University of Columbia in which detailed probe measurements of the turbulence in steady state were used for wide range of temperature gradients to compare with the simulation data. These results were published in a joint paper with Texas graduate student Dr. Xiangrong Fu using the work in his PhD dissertation. X.R. Fu, W. Horton, Y. Xiao, Z. Lin, A.K. Sen and V. Sokolov, “Validation of electron Temperature gradient turbulence in the Columbia Linear Machine, Phys. Plasmas 19, 032303 (2012).
Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas
Diamond, P.H.; Lin, Z.; Wang, W.; Horton, W.; Klasky, S.; Decyk, V.; Ma, K.-L.; Chames, J.; Adams, M.
2011-09-21
The three-year project GPS-TTBP resulted in over 152 publications and 135 presentations. This summary focuses on the scientific progress made by the project team. A major focus of the project was on the physics intrinsic rotation in tokamaks. Progress included the first ever flux driven study of net intrinsic spin-up, mediated by boundary effects (in collaboration with CPES), detailed studies of the microphysics origins of the Rice scaling, comparative studies of symmetry breaking mechanisms, a pioneering study of intrinsic torque driven by trapped electron modes, and studies of intrinsic rotation generation as a thermodynamic engine. Validation studies were performed with C-Mod, DIII-D and CSDX. This work resulted in very successful completion of the FY2010 Theory Milestone Activity for OFES, and several prominent papers of the 2008 and 2010 IAEA Conferences. A second major focus was on the relation between zonal flow formation and transport non-locality. This culminated in the discovery of the ExB staircase - a conceptually new phenomenon. This also makes useful interdisciplinary contact with the physics of the PV staircase, well-known in oceans and atmospheres. A third topic where progress was made was in the simulation and theory of turbulence spreading. This work, now well cited, is important for understanding the dynamics of non-locality in turbulent transport. Progress was made in studies of conjectured non-diffusive transport in trapped electron turbulence. Pioneering studies of ITB formation, coupling to intrinsic rotation and hysteresis were completed. These results may be especially significant for future ITER operation. All told, the physics per dollar performance of this project was quite good. The intense focus was beneficial and SciDAC resources were essential to its success.
NASA Astrophysics Data System (ADS)
Todo, Y.; Berk, H. L.; Breizman, B. N.
2012-03-01
A hybrid simulation code for nonlinear magnetohydrodynamics (MHD) and energetic-particle dynamics has been extended to simulate recurrent bursts of Alfvén eigenmodes by implementing the energetic-particle source, collisions and losses. The Alfvén eigenmode bursts with synchronization of multiple modes and beam ion losses at each burst are successfully simulated with nonlinear MHD effects for the physics condition similar to a reduced simulation for a TFTR experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874, Todo et al 2003 Phys. Plasmas 10 2888). It is demonstrated with a comparison between nonlinear MHD and linear MHD simulation results that the nonlinear MHD effects significantly reduce both the saturation amplitude of the Alfvén eigenmodes and the beam ion losses. Two types of time evolution are found depending on the MHD dissipation coefficients, namely viscosity, resistivity and diffusivity. The Alfvén eigenmode bursts take place for higher dissipation coefficients with roughly 10% drop in stored beam energy and the maximum amplitude of the dominant magnetic fluctuation harmonic δBm/n/B ~ 5 × 10-3 at the mode peak location inside the plasma. Quadratic dependence of beam ion loss rate on magnetic fluctuation amplitude is found for the bursting evolution in the nonlinear MHD simulation. For lower dissipation coefficients, the amplitude of the Alfvén eigenmodes is at steady levels δBm/n/B ~ 2 × 10-3 and the beam ion losses take place continuously. The beam ion pressure profiles are similar among the different dissipation coefficients, and the stored beam energy is higher for higher dissipation coefficients.
NASA Astrophysics Data System (ADS)
Sekhar, H.; Narayana Rao, D.
2012-07-01
Cuprous oxide nanoclusters, micro-cubes and micro-particles were successfully synthesized by reducing copper(II) salt with ascorbic acid in the presence of sodium hydroxide via a co-precipitation method. The X-ray diffraction and FTIR studies revealed that the formation of pure single-phase cubic. Raman and EPR spectral studies show the presence of CuO in as-synthesized powders of Cu2O. Transmission electron microscopy and field emission scanning electron microscopy data revealed that the morphology evolves from nanoclusters to micro-cubes and micro-particles by increasing the concentration of NaOH. Linear optical measurements show absorption peak maximum shifts towards red with changing morphology from nanoclusters to micro-cubes and micro-particles. The nonlinear optical properties were studied using open aperture Z-scan technique with 532 nm 6 ns laser pulses. Samples-exhibited both saturable as well as reverse saturable absorption. Due to confinement effects (enhanced band gap), we observed enhanced nonlinear absorption coefficient (β) in the case of nanoclusters compared to their micro-cubes and micro-particles.
NASA Astrophysics Data System (ADS)
Leboeuf, Jean-Noel; Dimits, Andris; Shumaker, Dan
2005-10-01
Development of the PG3EQ/NC module within the SUMMIT gyrokinetic PIC FORTRAN 90 framework is largely completed. It provides SUMMIT with the capability of performing 3D nonlinear toroidal gyrokinetic computations of ion turbulence in real DIII-D geometry. PG3EQ/NC uses local, field line following, quasi-ballooning coordinates and direct interface with DIII-D equilibrium data via the EFIT and ONETWO codes. In addition, Holger Saint John's PLOTEQ code is used to determine the (r,z) position of each flux surface. The thus initialized SUMMIT computations have been carried out for shot /118561 at times 01450 and 02050 at many of the 51 flux surfaces from the core to the edge. Linear SUMMIT results will be compared to available data from calculations with the GKS code for the same discharges. Nonlinear SUMMIT results will also be compared with scattering measurements of turbulence, as well as with accessible measurements of fluctuation amplitudes and spectra from other diagnostics.
NASA Astrophysics Data System (ADS)
Bhatti, M. M.; Zeeshan, A.; Ellahi, R.
2016-09-01
In this article, heat transfer with nonlinear thermal radiation on sinusoidal motion of magnetic solid particles in a dust Jeffrey fluid has been studied. The effects of Magnetohydrodynamic (MHD) and hall current are also taken under consideration. The governing equation of motion and energy equation are modelled with help of Ohms law for fluid and dust phases. The solutions of the resulting ordinary coupled partial differential equations are solved analytically. The impact of all the physical parameters of interest such as Hartmann number, slip parameter, Hall parameter, radiation parameter, Prandtl number, Eckert number and particle volume fraction are demonstrated mathematically and graphically. Trapping mechanism is also discussed in detail by drawing contour lines. The present analysis affirms many interesting behaviours, which permit further study on solid particles motion with heat and mass transfer.
Quasilinear model for energetic particle diffusion in radial and velocity space
Waltz, R. E.; Staebler, G. M.; Bass, E. M.
2013-04-15
A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2 Multiplication-Sign 2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.
Quasilinear model for energetic particle diffusion in radial and velocity space
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Bass, E. M.; Staebler, G. M.
2013-04-01
A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2×2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.
Gyrokinetic theory of the screw pinch
NASA Astrophysics Data System (ADS)
Stéfant, Robert J.
1989-06-01
The gyrokinetic differential equation for waves propagating in a hot collisionless current-carrying plasma is derived in cylindrical geometry. It is shown that the averaging of the wave electric field over the ion Larmor circle leads to a transcendental differential equation (d.e.) of infinite order in the radial derivative. This reduces to a d.e. of sixth order when the scale length of the plasma inhomogeneity Ln is greater than the ion gyroradius ρi by a factor (M/m)1/2, where M and m are, respectively, the ion and electron mass. This sixth-order d.e. describes the properties of the two (compressional and torsional) Alfvén modes and the ion acoustic mode. When Ln <(M/m)1/2ρi, the plasma can only support modes of the magnetokinetic (short wavelength) type. In the absence of a finite Larmor radius (FLR) effect, shear, and equilibrium current, we find that the correct equation to start with is the Hain and Lust [Z. Naturforsch. A 13, 936 (1958)] d.e. of second order that is singular at the Alfvén resonance layer (ARL). The ARL behaves in that case like a Budden absorption layer that traps the global Alfvén eigenmodes (GAEM) inside the plasma cavity where they are damped by transit time magnetic pumping (TTMP). The logarithmic singularity does not disappear with the introduction of the FLR effect in the Hain and Lust d.e., but only with the TTMP damping term. There is no mode conversion between the fast magnetosonic mode and the shear or magnetokinetic mode at the ARL or anywhere in the plasma. In the presence of shear and equilibrium current, the correct equation to use is a d.e. of fourth (or greater) order whose solutions descibe the shear Alfvén mode in the long wavelength limit or the magnetokinetic mode at shorter wavelengths. In the true magnetohydrodynamic (MHD) limit, both modes become degenerate. It is shown that the slow Alfvén eigenmodes are (almost) completely decoupled from the fast magnetosonic wave and therefore the growth rates show no
NASA Astrophysics Data System (ADS)
Zank, G. P.
2015-09-01
The 14th Annual International Astrophysics Conference was held at the Sheraton Tampa Riverwalk Hotel, Tampa, Florida, USA, during the week of 19-24 April 2015. The meeting drew some 75 participants from all over the world, representing a wide range of interests and expertise in the energization of particles from the perspectives of theory, modelling and simulations, and observations. The theme of the meeting was "Linear and Nonlinear Particle Energization throughout the Heliosphere and Beyond." Energetic particles are ubiquitous to plasma environments, whether collisionless such as the supersonic solar wind, the magnetospheres of planets, the exospheres of nonmagnetized planets and comets, the heliospheric-local interstellar boundary regions, interstellar space and supernova remnant shocks, and stellar wind boundaries. Energetic particles are found too in more collisional regions such as in the solar corona, dense regions of the interstellar medium, accretion flows around stellar objects, to name a few. Particle acceleration occurs wherever plasma boundaries, magnetic and electric fields, and turbulence are present. The meeting addressed the linear and nonlinear physical processes underlying the variety of particle acceleration mechanisms, the role of particle acceleration in shaping different environments, and acceleration processes common to different regions. Both theory and observations were addressed with a view to encouraging crossdisciplinary fertilization of ideas, concepts, and techniques. The meeting addressed all aspects of particle acceleration in regions ranging from the Sun to the interplanetary medium to magnetospheres, exospheres, and comets, the boundaries of the heliosphere, and beyond to supernova remnant shocks, galactic jets, stellar winds, accretion flows, and more. The format of the meeting included 25-minute presentations punctuated by two 40-minute talks, one by Len Fisk that provided an historical overview of particle acceleration in the
From charge motion in general magnetic fields to the non perturbative gyrokinetic equation
Di Troia, C.
2015-04-15
The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem, even if it has not been solved until now, apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field; the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.
Grid-based Parallel Data Streaming Implemented for the Gyrokinetic Toroidal Code
S. Klasky; S. Ethier; Z. Lin; K. Martins; D. McCune; R. Samtaney
2003-09-15
We have developed a threaded parallel data streaming approach using Globus to transfer multi-terabyte simulation data from a remote supercomputer to the scientist's home analysis/visualization cluster, as the simulation executes, with negligible overhead. Data transfer experiments show that this concurrent data transfer approach is more favorable compared with writing to local disk and then transferring this data to be post-processed. The present approach is conducive to using the grid to pipeline the simulation with post-processing and visualization. We have applied this method to the Gyrokinetic Toroidal Code (GTC), a 3-dimensional particle-in-cell code used to study microturbulence in magnetic confinement fusion from first principles plasma theory.
Extended gyrokinetic field theory for time-dependent magnetic confinement fields
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2014-01-15
A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.
Squire, J.; Tang, W. M.; Qin, H.; Chandre, C.
2013-02-15
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.
Extended gyrokinetic field theory for time-dependent magnetic confinement fields
NASA Astrophysics Data System (ADS)
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2014-01-01
A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.
Czerwonko, J.
1988-04-01
Since nonlinear effects are of the same importance as the particle-hole asymmetry (PHA) effects for normal Fermi liquids, at least for some physical situations, a formalism is presented taking both into account. Moreover, because the nonlinearity or PHA is easiest to induce by strong magnetic fields, weak polarization effects are also included. The kinetic equations for the weakly coupled density and magnetization modes are obtained under these circumstances. They lead to an additional effective mass equation in comparison to the Landau formula, joining the suitable angular average of the effective interaction of triples of quasiparticles with gradient of the two-quasiparticle interaction with PHA effects included. The equations are investigated in detail for ac magnetic field much smaller than the dc field in two cases: (1) at almost equilibrium magnetization of the sample and (2) at almost equilibrium (in the length) magnetization precessing around a dc field tipped to it by an angle Theta not equal to O.
Multi-scale gyrokinetic simulation of Alcator C-Mod tokamak discharges
NASA Astrophysics Data System (ADS)
Howard, N. T.; White, A. E.; Greenwald, M.; Holland, C.; Candy, J.
2014-03-01
Alcator C-Mod tokamak discharges have been studied with nonlinear gyrokinetic simulation simultaneously spanning both ion and electron spatiotemporal scales. These multi-scale simulations utilized the gyrokinetic model implemented by GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and the approximation of reduced electron mass (μ = (mD/me).5 = 20.0) to qualitatively study a pair of Alcator C-Mod discharges: a low-power discharge, previously demonstrated (using realistic mass, ion-scale simulation) to display an under-prediction of the electron heat flux and a high-power discharge displaying agreement with both ion and electron heat flux channels [N. T. Howard et al., Nucl. Fusion 53, 123011 (2013)]. These multi-scale simulations demonstrate the importance of electron-scale turbulence in the core of conventional tokamak discharges and suggest it is a viable candidate for explaining the observed under-prediction of electron heat flux. In this paper, we investigate the coupling of turbulence at the ion (kθρs˜O(1.0)) and electron (kθρe˜O(1.0)) scales for experimental plasma conditions both exhibiting strong (high-power) and marginally stable (low-power) low-k (kθρs < 1.0) turbulence. It is found that reduced mass simulation of the plasma exhibiting marginally stable low-k turbulence fails to provide even qualitative insight into the turbulence present in the realistic plasma conditions. In contrast, multi-scale simulation of the plasma condition exhibiting strong turbulence provides valuable insight into the coupling of the ion and electron scales.
Multi-scale gyrokinetic simulation of Alcator C-Mod tokamak discharges
Howard, N. T. White, A. E.; Greenwald, M.; Holland, C.; Candy, J.
2014-03-15
Alcator C-Mod tokamak discharges have been studied with nonlinear gyrokinetic simulation simultaneously spanning both ion and electron spatiotemporal scales. These multi-scale simulations utilized the gyrokinetic model implemented by GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and the approximation of reduced electron mass (μ = (m{sub D}/m{sub e}){sup .5} = 20.0) to qualitatively study a pair of Alcator C-Mod discharges: a low-power discharge, previously demonstrated (using realistic mass, ion-scale simulation) to display an under-prediction of the electron heat flux and a high-power discharge displaying agreement with both ion and electron heat flux channels [N. T. Howard et al., Nucl. Fusion 53, 123011 (2013)]. These multi-scale simulations demonstrate the importance of electron-scale turbulence in the core of conventional tokamak discharges and suggest it is a viable candidate for explaining the observed under-prediction of electron heat flux. In this paper, we investigate the coupling of turbulence at the ion (k{sub θ}ρ{sub s}∼O(1.0)) and electron (k{sub θ}ρ{sub e}∼O(1.0)) scales for experimental plasma conditions both exhibiting strong (high-power) and marginally stable (low-power) low-k (k{sub θ}ρ{sub s} < 1.0) turbulence. It is found that reduced mass simulation of the plasma exhibiting marginally stable low-k turbulence fails to provide even qualitative insight into the turbulence present in the realistic plasma conditions. In contrast, multi-scale simulation of the plasma condition exhibiting strong turbulence provides valuable insight into the coupling of the ion and electron scales.
NASA Astrophysics Data System (ADS)
Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander
2015-04-01
The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.
Verification of particle simulation of radio frequency waves in fusion plasmas
Kuley, Animesh; Lin, Z.; Wang, Z. X.; Wessel, F.
2013-10-15
Radio frequency (RF) waves can provide heating, current and flow drive, as well as instability control for steady state operations of fusion experiments. A particle simulation model has been developed in this work to provide a first-principles tool for studying the RF nonlinear interactions with plasmas. 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. This model has been implemented in a global gyrokinetic toroidal code using real electron-to-ion mass ratio. To verify the model, linear simulations of ion plasma oscillation, ion Bernstein wave, and lower hybrid wave are carried out in cylindrical geometry and found to agree well with analytic predictions.
NASA Technical Reports Server (NTRS)
Goldstein, M. L.
1976-01-01
The propagation of charged particles through interstellar and interplanetary space has often been described as a random process in which the particles are scattered by ambient electromagnetic turbulence. In general, this changes both the magnitude and direction of the particles' momentum. Some situations for which scattering in direction (pitch angle) is of primary interest were studied. A perturbed orbit, resonant scattering theory for pitch-angle diffusion in magnetostatic turbulence was slightly generalized and then utilized to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field, Kappa. All divergences inherent in the quasilinear formalism when the power spectrum of the fluctuation field falls off as K to the minus Q power (Q less than 2) were removed. Various methods of computing Kappa were compared and limits on the validity of the theory discussed. For Q less than 1 or 2, the various methods give roughly comparable values of Kappa, but use of perturbed orbits systematically results in a somewhat smaller Kappa than can be obtained from quasilinear theory.
Russell, Steven J.; Carlsten, Bruce E.
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
NASA Astrophysics Data System (ADS)
Pétri, J.
2009-08-01
Context: The physics of the pulsar magnetosphere near the neutron star surface remains poorly constrained by observations. Indeed, little is known about its emission mechanism, from radio to high-energy X-ray and gamma-rays. Nevertheless, it is believed that large vacuum gaps exist in this magnetosphere, and a non-neutral plasma partially fills the neutron star surroundings to form an electrosphere in differential rotation. Aims: According to several of our previous works, the equatorial disk in this electrosphere is diocotron and magnetron unstable, at least in the linear regime. To better assess the long term evolution of these instabilities, we study the behavior of the non-neutral plasma using particle simulations. Methods: We designed a two-dimensional electrostatic particle-in-cell (PIC) code in cylindrical coordinates, solving Poisson equation for the electric potential. In the diocotron regime, the equation of motion for particles obeys the electric drift approximation. As in the linear study, the plasma is confined between two conducting walls. Moreover, in order to simulate a pair cascade in the gaps, we add a source term feeding the plasma with charged particles having the same sign as those already present in the electrosphere. Results: First we checked our code by looking for the linear development of the diocotron instability in the same regime as the one used in our previous work, for a plasma annulus and for a typical electrosphere with differential rotation. To very good accuracy, we retrieve the same growth rates, supporting the correctness of our PIC code. Next, we consider the long term non-linear evolution of the diocotron instability. We found that particles tend to cluster together to form a small vortex of high charge density rotating around the axis of the cylinder with only little radial excursion of the particles. This grouping of particles generates new low density or even vacuum gaps in the plasma column. Finally, in more general
Gyrokinetic treatment of a grazing angle magnetic presheath
NASA Astrophysics Data System (ADS)
Geraldini, A.; Parra, F. I.; Militello, F.
2017-02-01
We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, α \\ll 1 (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, {ρ }{{i}}. The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered l={ρ }{{i}}/δ , where δ \\ll 1 is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field {E} in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with α =δ =0. By using these new coordinates as variables in the limit α ∼ δ \\ll 1, we obtain a generalised ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.
A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations
NASA Astrophysics Data System (ADS)
Xanthopoulos, P.; Cooper, W. A.; Jenko, F.; Turkin, Yu.; Runov, A.; Geiger, J.
2009-08-01
The GENE/GIST code package is developed for the investigation of plasma microturbulence, suitable for both stellarator and tokamak configurations. The geometry module is able to process typical equilibrium files and create the interface for the gyrokinetic solver. The analytical description of the method for constructing the geometric elements is documented, together with several numerical evaluation tests. As a concrete application of this product, a cross-machine comparison of the anomalous ion heat diffusivity is presented.
Gyrokinetic simulations of neoclassical transport using a minimal collision operator
NASA Astrophysics Data System (ADS)
Dif-Pradalier, G.; Grandgirard, V.; Sarazin, Y.; Garbet, X.; Ghendrih, Ph.; Angelino, P.
2008-11-01
Conventional neoclassical predictions are successfully recovered within a gyrokinetic framework using a minimal Fokker-Planck collision operator. This operator is shown to accurately describe some essential features of neoclassical theory, namely the neoclassical transport, the poloidal rotation and the linear damping of axisymmetric flows while interestingly preserving a high numerical efficiency. Its form makes it especially adapted to Eulerian or Semi-Lagrangian schemes.
NASA Astrophysics Data System (ADS)
Ding, Bo; Fang, Huajing
2016-12-01
This paper is concerned with the fault detection and estimation for nonlinear stochastic system with additive multi-faults. The states of system are estimated by the improved particle filter which composed of basic particle filter and preliminary fault estimation. Since the preliminary fault estimation contains noise, the faults are detected by the method of hypothesis testing, while the amplitude of each fault is estimated by the average of the sample of preliminary fault estimation. Meanwhile, the relationship of the sample size, the significance level of two types of error, the amplitude of fault and the variance of the error of preliminary fault estimation are also given. The effectiveness of the proposed method is verified by the simulation of three-vessel water tank system.
Verification of gyrokinetic microstability codes with an LHD configuration
Mikkelsen, D. R.; Nunami, M.; Watanabe, T. -H.; Sugama, H.; Tanaka, K.
2014-11-01
We extend previous benchmarks of the GS2 and GKV-X codes to verify their algorithms for solving the gyrokinetic Vlasov-Poisson equations for plasma microturbulence. Code benchmarks are the most complete way of verifying the correctness of implementations for the solution of mathematical models for complex physical processes such as those studied here. The linear stability calculations reported here are based on the plasma conditions of an ion-ITB plasma in the LHD configuration. The plasma parameters and the magnetic geometry differ from previous benchmarks involving these codes. We find excellent agreement between the independently written pre-processors that calculate the geometrical coefficients used in the gyrokinetic equations. Grid convergence tests are used to establish the resolution and domain size needed to obtain converged linear stability results. The agreement of the frequencies, growth rates and eigenfunctions in the benchmarks reported here provides additional verification that the algorithms used by the GS2 and GKV-X codes are correctly finding the linear eigenvalues and eigenfunctions of the gyrokinetic Vlasov-Poisson equations.