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.
Global gyrokinetic simulation of tokamak transport
Furnish, G.; Horton, W.; Kishimoto, Y.; LeBrun, M.J.; Tajima, T. |
1998-10-01
A kinetic simulation code based on the gyrokinetic ion dynamics in global general metric (including a tokamak with circular or noncircular cross-section) has been developed. This gyrokinetic simulation is capable of examining the global and semi-global driftwave structures and their associated transport in a tokamak plasma. The authors investigate the property of the ion temperature gradient (ITG) or {eta}{sub i}({eta}{sub i} {equivalent_to} {partial_derivative}{ell}nT{sub i}/{partial_derivative}{ell}n n{sub i}) driven drift waves in a tokamak plasma. The emergent semi-global drift wave modes give rise to thermal transport characterized by the Bohm scaling.
Global spectral investigation of plasma turbulence in gyrokinetic simulations
Henriksson, S. V.; Janhunen, S. J.; Kiviniemi, T. P.; Heikkinen, J. A.
2006-07-15
Gyrokinetic global particle-in-cell simulations for a small torus with a large aspect ratio ({epsilon}{sup -1}>{approx}7) indicate a k{sub perpendicular}{sup -{alpha}} spectrum for electrostatic turbulence. When electrons are treated kinetically, the simulation results fit {alpha} that grows from about 1 at the plasma core to about 3 at the plasma edge for the flux surface component of the wave vector perpendicular to the magnetic field, while for adiabatic electrons {alpha}=4 is found for all radii, in agreement with the Hasegawa-Mima model. The relation between spectra and transport is investigated through the formation of an internal transport barrier. The role of flow shear in suppressing turbulence is illustrated by spectral diagnostics. A strong dependence between the presence of small wavenumbers and transport is explicitly observed. The simulated spectra are compared to recent experimental results.
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.
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.
Holod, I.; Lin, Z.
2013-03-15
The fluid-kinetic hybrid electron model is verified in global gyrokinetic particle simulation of linear electromagnetic drift-Alfvenic instabilities in tokamak. In particular, we have recovered the {beta}-stabilization of the ion temperature gradient mode, transition to collisionless trapped electron mode, and the onset of kinetic ballooning mode as {beta}{sub e} (ratio of electron kinetic pressure to magnetic pressure) increases.
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.
Gyrokinetic and global fluid simulations of tokamak microturbulence and transport
Dimits, A.M.; Byers, J.A.; Williams, T.J.; Cohen, B.I.; Xu, W.Q.; Cohen, R.H.; Crotinger, J.A.; Shestakov, A.I.
1994-08-30
Results are presented from the first systematic nonlinear kinetic simulation study of the swings and parameter dependences of toroidal ion-temperature-gradient (ITG) turbulence and transport, and from the first such study that includes sheared toroidal flows. Key results include the observation of clear gyroBohm scaling of the turbulent transport and of a surprisingly weak dependence of the transport on toroidal flow shear. Based on the simulation results, a parameterization of the transport is given that includes the dependence on all of the relevant physical parameters. The transition from local to nonlocal transport as a function of the profile scale length has been investigated using two-dimensional global fluid simulations of dissipative drift-wave turbulence. Local gyroBohm scaling is observed, except at very short profile scale lengths.
On the definition of a kinetic equilibrium in global gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Angelino, P.; Bottino, A.; Hatzky, R.; Jolliet, S.; Sauter, O.; Tran, T. M.; Villard, L.
2006-05-01
Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and E ×B zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric E ×B flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of E ×B flows. In addition, a revised δf scheme is introduced and compared to the standard δf method.
On the definition of a kinetic equilibrium in global gyrokinetic simulations
Angelino, P.; Bottino, A.; Hatzky, R.; Jolliet, S.; Sauter, O.; Tran, T.M.; Villard, L.
2006-05-15
Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and ExB zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric ExB flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of ExB flows. In addition, a revised {delta}f scheme is introduced and compared to the standard {delta}f method.
Comparisons between global and local gyrokinetic simulations of an ASDEX Upgrade H-mode plasma
NASA Astrophysics Data System (ADS)
Navarro, Alejandro Bañón; Told, Daniel; Jenko, Frank; Görler, Tobias; Happel, Tim
2016-04-01
We investigate by means of local and global nonlinear gyrokinetic GENE simulations an ASDEX Upgrade H-mode plasma. We find that for the outer core positions (i.e., ρ tor ≈ 0.5 - 0.7 ), nonlocal effects are important. For nominal input parameters local simulations over-predict the experimental heat fluxes by a large factor, while a good agreement is found with global simulations. This was a priori not expected, since the values of 1 / ρ ⋆ were large enough that global and local simulations should have been in accordance. Nevertheless, due to the high sensitivity of the heat fluxes with respect to the input parameters, it is still possible to match the heat fluxes in local simulations with the experimental and global results by varying the ion temperature gradient within the experimental uncertainties. In addition to that, once an agreement in the transport quantities between local (flux-matched) and global simulations is achieved, an agreement for other quantities, such as density and temperature fluctuations, is also found. The case presented here clearly shows that even in the presence of global size-effects, the local simulation approach is still a valid and accurate approach.
Flux- and gradient-driven global gyrokinetic simulation of tokamak turbulence
Goerler, Tobias; Jenko, Frank; Marcus, Patrick; Merz, Florian; Told, Daniel; Lapillonne, Xavier; Brunner, Stephan; Aghdam, Sohrab Khosh; McMillan, Ben F.; Sauter, Olivier; Villard, Laurent; Dannert, Tilman
2011-05-15
The Eulerian gyrokinetic turbulence code gene has recently been extended to a full torus code. Moreover, it now provides Krook-type sources for gradient-driven simulations where the profiles are maintained on average as well as localized heat sources for a flux-driven type of operation. Careful verification studies and benchmarks are performed successfully. This setup is applied to address three related transport issues concerning nonlocal effects. First, it is confirmed that in gradient-driven simulations, the local limit can be reproduced--provided that finite aspect ratio effects in the geometry are treated carefully. In this context, it also becomes clear that the profile widths (not the device width) may constitute a more appropriate measure for finite-size effects. Second, the nature and role of heat flux avalanches are discussed in the framework of both local and global, flux- and gradient-driven simulations. Third, simulations dedicated to discharges with electron internal barriers are addressed.
Quasisteady and steady states in global gyrokinetic particle-in-cell simulations
Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Bottino, A.; Angelino, P.
2009-05-15
Collisionless delta-f gyrokinetic particle-in-cell simulations suffer from the entropy paradox, in which the entropy grows linearly in time while low-order moments are saturated. As a consequence, these simulations do not reach a steady state and are unsuited to make quantitative predictions. A solution to this issue is the introduction of artificial dissipation. The notion of steady state in gyrokinetic simulations is studied by deriving an evolution equation for the fluctuation entropy and applying it to the global collisionless particle-in-cell code ORB5 [S. Jolliet et al., Comput. Phys. Commun. 177, 409 (2007)]. It is shown that a recently implemented noise-control algorithm [B. F. McMillan et al., Phys. Plasmas 15, 052308 (2008)] based on a W-stat provides the necessary dissipation to reach a steady state. The two interesting situations of decaying and driven turbulence are considered. In addition, it is shown that a separate heating algorithm, not based on a W-stat, does not lead to a statistical steady state.
Gyrokinetic particle simulation model
Lee, W.W.
1986-07-01
A new type of particle simulation model based on the gyrophase-averaged Vlasov and Poisson equations is presented. The reduced system, in which particle gyrations are removed from the equations of motion while the finite Larmor radius effects are still preserved, is most suitable for studying low frequency microinstabilities in magnetized plasmas. It is feasible to simulate an elongated system (L/sub parallel/ >> L/sub perpendicular/) with a three-dimensional grid using the present model without resorting to the usual mode expansion technique, since there is essentially no restriction on the size of ..delta..x/sub parallel/ in a gyrokinetic plasma. The new approach also enables us to further separate the time and spatial scales of the simulation from those associated with global transport through the use of multiple spatial scale expansion. Thus, the model can be a very efficient tool for studying anomalous transport problems related to steady-state drift-wave turbulence in magnetic confinement devices. It can also be applied to other areas of plasma physics.
Gyrokinetic large eddy simulations
Morel, P.; Navarro, A. Banon; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.
2011-07-15
The large eddy simulation approach is adapted to the study of plasma microturbulence in a fully three-dimensional gyrokinetic system. Ion temperature gradient driven turbulence is studied with the GENE code for both a standard resolution and a reduced resolution with a model for the sub-grid scale turbulence. A simple dissipative model for representing the effect of the sub-grid scales on the resolved scales is proposed and tested. Once calibrated, the model appears to be able to reproduce most of the features of the free energy spectra for various values of the ion temperature gradient.
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.
Global gyrokinetic simulations of the H-mode tokamak edge pedestal
Wan, Weigang; Parker, Scott E.; Chen, Yang; Groebner, Richard J.; Yan, Zheng; Pankin, Alexei Y.; Kruger, Scott E.
2013-05-15
Global gyrokinetic simulations of DIII-D H-mode edge pedestal show two types of instabilities may exist approaching the onset of edge localized modes: an intermediate-n, high frequency mode which we identify as the “kinetic peeling ballooning mode (KPBM),” and a high-n, low frequency mode. Our previous study [W. Wan et al., Phys. Rev. Lett. 109, 185004 (2012)] has shown that when the safety factor profile is flattened around the steep pressure gradient region, the high-n mode is clearly kinetic ballooning mode and becomes the dominant instability. Otherwise, the KPBM dominates. Here, the properties of the two instabilities are studied by varying the density and temperature profiles. It is found that the KPBM is destabilized by density and ion temperature gradient, and the high-n mode is mostly destabilized by electron temperature gradient. Nonlinear simulations with the KPBM saturate at high levels. The equilibrium radial electric field (E{sub r}) reduces the transport. The effect of the parallel equilibrium current is found to be weak.
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.
High frequency gyrokinetic particle simulation
Kolesnikov, R. A.; Lee, W. W.; Qin, H.; Startsev, E.
2007-07-15
The gyrokinetic approach for arbitrary frequency dynamics in magnetized plasmas is explored, using the gyrocenter-gauge kinetic theory. Contrary to low-frequency gyrokinetics, which views each particle as a rigid charged ring, arbitrary frequency response of a particle is described by a quickly changing Kruskal ring. This approach allows the separation of gyrocenter and gyrophase responses and thus allows for, in many situations, larger time steps for the gyrocenter push than for the gyrophase push. The gyrophase response which determines the shape of Kruskal rings can be described by a Fourier series in gyrophase for some problems, thus allowing control over the cyclotron harmonics at which the plasma responds. A computational algorithm for particle-in-cell simulation based on this concept has been developed. An example of the ion Bernstein wave is used to illustrate its numerical properties, and comparison with a direct Lorentz-force approach is presented.
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.
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)
Bass, E. M.; Waltz, R. E.
2012-10-01
In ITER, convection of fusion-produced alpha particles by energetic particle (EP)-driven Alfv'en eigenmodes (AEs) risks wall damage and loss of alpha heating needed for ignition. We examine beam-excited AEs and induced quasilinear transport in a DIII-D AE experiment using the gyrokinetic code GYRO [1]. Global, linear eigenvalue simulations show reverse-shear AEs (RSAEs), toroidal AEs, and beta-induced AEs interacting over one (equilibrium time scale) RSAE frequency sweep. Eigenfunction modifications over MHD, including a poloidal twist and broad AE footprint observed in electron cyclotron emission imaging [2], show the value of a kinetic approach. Under a simple quasilinear saturation assumption, a sequence of comparatively inexpensive local simulations quantitatively recreates some global features, notably the quasilinear transport footprint. Accordingly, we present here a stiff EP transport model where AEs limit the EP density gradient to the local stability threshold, and a TGLF-driven quasilinear model elsewhere. The model gives some``worst case'' predictions of the AE-limited alpha profile in ITER.[4pt] [1] J. Candy and R.E. Waltz, Phys. Rev. Lett. 91, 045001 (2003). [2] B.J. Tobias, et al., Phys. Rev. Lett. 106, 075003 (2011).
Gyrokinetic Simulations of ETG and ITG Turbulence
Dimits, A; Nevins, W; Shumaker, D; Hammett, G; Dannert, T; Jenko, F; Dorland, W; Leboeuf, J; Rhodes, T; Candy, J; Estrada-Mila, C
2006-10-03
Published gyrokinetic continuum-code simulations indicated levels of the electron thermal conductivity {chi}{sub e} due to electron-temperature-gradient (ETG) turbulence large enough to be significant in some tokamaks, while subsequent global particle-in-cell (PIC) simulations gave significantly lower values. We have carried out an investigation of this discrepancy. We have reproduced the key features of the aforementioned PIC simulations using the flux-tube gyrokinetic PIC code, PG3EQ, thereby eliminating global effects and as the cause of the discrepancy. We show that the late-time low-transport state in both of these sets of PIC simulations is a result of discrete particle noise, which is a numerical artifact. Thus, the low value of {chi}{sub e} along with conclusions about anomalous transport drawn from these particular PIC simulations are unjustified. In our attempts to benchmark PIC and continuum codes for ETG turbulence at the plasma parameters used above, both produce very large intermittent transport. We have therefore undertaken benchmarks at an alternate reference point, magnetic shear s=0.1 instead of s=0.796, and have found that PIC and continuum codes reproduce the same transport levels. Scans in the magnetic shear show an abrupt transition to a high-{chi}{sub e} state as the shear is increased above s=0.4. When nonadiabatic ions are used, this abrupt transition is absent, and {chi}{sub e} increases gradually reaching values consistent with transport analyses of DIII-D, JET, and JT60-U discharges. New results on the balances of zonal-flow driving and damping terms in late-time quasi-steady ITG turbulence and on real-geometry gyrokinetic simulations of shaped DIII-D discharges are also reported.
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.
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.
Intercode comparison of gyrokinetic global electromagnetic modes
NASA Astrophysics Data System (ADS)
Görler, T.; Tronko, N.; Hornsby, W. A.; Bottino, A.; Kleiber, R.; Norscini, C.; Grandgirard, V.; Jenko, F.; Sonnendrücker, E.
2016-07-01
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.
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.
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.
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.
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.
Cummings, Julian C.
2013-05-15
This project was a collaboration between researchers at the California Institute of Technology and the University of California, Irvine to investigate the utility of a global field-aligned mesh and gyrokinetic field solver for simulations of the tokamak plasma edge region. Mesh generation software from UC Irvine was tested with specific tokamak edge magnetic geometry scenarios and the quality of the meshes and the solutions to the gyrokinetic Poisson equation were evaluated.
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.
Chowdhury, J.; Wan, Weigang; Chen, Yang; Parker, Scott E.; Groebner, Richard J.; Holland, C.; Howard, N. T.
2014-11-15
The δ f particle-in-cell code GEM is used to study the transport “shortfall” problem of gyrokinetic simulations. In local simulations, the GEM results confirm the previously reported simulation results of DIII-D [Holland et al., Phys. Plasmas 16, 052301 (2009)] and Alcator C-Mod [Howard et al., Nucl. Fusion 53, 123011 (2013)] tokamaks with the continuum code GYRO. Namely, for DIII-D the simulations closely predict the ion heat flux at the core, while substantially underpredict transport towards the edge; while for Alcator C-Mod, the simulations show agreement with the experimental values of ion heat flux, at least within the range of experimental error. Global simulations are carried out for DIII-D L-mode plasmas to study the effect of edge turbulence on the outer core ion heat transport. The edge turbulence enhances the outer core ion heat transport through turbulence spreading. However, this edge turbulence spreading effect is not enough to explain the transport underprediction.
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.
Parallel magnetic field perturbations in gyrokinetic simulations
Joiner, N.; Hirose, A.; Dorland, W.
2010-07-15
At low beta it is common to neglect parallel magnetic field perturbations on the basis that they are of order beta{sup 2}. This is only true if effects of order beta are canceled by a term in the nablaB drift also of order beta[H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 (1977)]. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)] to investigate whether the compressional magnetic field perturbation B{sub ||} is required for accurate gyrokinetic simulations at low beta for microinstabilities commonly found in tokamaks. The kinetic ballooning mode (KBM) demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient (ETG) driven modes do not typically exhibit this behavior; the effects of B{sub ||} are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with eta{sub e}. The effect of B{sub ||} on the ETG instability is shown to depend on the normalized pressure gradient beta{sup '} at constant beta.
NASA Astrophysics Data System (ADS)
Banon Navarro, Alejandro
2015-11-01
Worldwide, gyrokinetic codes are used to predict the dominant micro-instabilities as well as the resulting anomalous transport in fusion experiments. A careful verification and validation of these codes is crucial to develop confidence in the model and improving the predictive capabilities of the numerical simulations. To date, the validation of gyrokinetic simulations versus experiments is mainly done at a macroscopic level, namely, by comparing turbulent heat fluxes. This is usually achieved by varying the profile gradients within the experimental error bars until a match with the experimental heat fluxes is obtained. However, since the turbulent fluxes are caused by plasma fluctuations on microscopic scales, it is also necessary to validate gyrokinetic codes on a microscopic level. We will describe a recent step in this direction by presenting simulation results with the gyrokinetic code GENE for an ASDEX Upgrade discharge. In particular, after flux-matched simulations are achieved, density fluctuations measured by means of Doppler reflectometry are compared with results of gyrokinetic simulations. We will also show that density and temperature fluctuation amplitudes and even the fluctuation spectra can be very sensitive to small changes in the profile gradients. This implies that a match of gyrokinetic simulations with experiment measurements for these quantities can be very difficult to achieve. However, it is observed that cross-phases between different quantities are robust to changes in this parameter, indicating that cross-phases could be a better observable for comparisons with experimental measurements.
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.
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 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.
Comparisons of gyrofluid and gyrokinetic simulations
Parker, S.E.; Dorland, W.; Santoro, R.A.; Beer, M.A.; Liu, Q.P.; Lee, W.W.; Hammett, G.W.
1994-03-01
The gyrokinetic and gyrofluid models show the most promise for large scale simulations of tokamak microturbulence. This paper discusses detailed comparisons of these two complementary approaches. Past comparisons with linear theory have been fairly good, therefore the emphasis here is on nonlinear comparisons. Simulations include simple two dimensional slab test cases, turbulent three dimensional slab cases, and toroidal cases, each modeling the nonlinear evolution of the ion temperature gradient instability. There is good agreement in both turbulent and coherent nonlinear slab comparisons in terms of the ion heat flux, both in magnitude and scaling with magnetic shear. However, the nonlinear saturation level for {vert_bar}{Phi}{vert_bar} in the slab comparisons show differences of approximately 40%. Preliminary toroidal comparisons show agreement within 50%, in terms of ion heat flux and saturation level.
Gyrokinetic Simulations of the ITER Pedestal
NASA Astrophysics Data System (ADS)
Kotschenreuther, Mike
2015-11-01
It has been reported that low collisionality pedestals for JET parameters are strongly stable to Kinetic Ballooning Modes (KBM), and it is, as simulations with GENE show, the drift-tearing modes that produce the pedestal transport. It would seem, then, that gyrokinetic simulations may be a powerful, perhaps, indispensable tool for probing the characteristics of the H-mode pedestal in ITER especially since projected ITER pedestals have the normalized gyroradius ρ* smaller than the range of present experimental investigation; they do lie, however, within the regime of validity of gyrokinetics. Since ExB shear becomes small as ρ* approaches zero, strong drift turbulence will eventually be excited. Finding an answer to the question whether the ITER ρ* is small enough to place it in the high turbulence regime compels serious investigation. We begin with MHD equilibria (including pedestal bootstrap current) constructed using VMEC. Plasma profile shapes, very close to JET experimental profiles, are scaled to values expected on ITER (e.g., a 4 keV pedestal). The equilibrium ExB shear is computed using a neoclassical formula for the radial electric field. As with JET, the ITER pedestal is found to be strongly stable to KBM. Preliminary nonlinear simulations with GENE show that the turbulent drift transport is strong for ITER; the electrostatic transport has a highly unfavorable scaling from JET to ITER, going from being highly sub-dominant to electromagnetic transport on JET, to dominant on ITER. At burning plasma parameters, pedestals in spherical tokamak H-modes may have much stronger velocity shear, and hence more favorable transport; preliminary investigations will be reported. This research supported by U.S. Department of Energy, Office of Fusion Energy Science: Grant No. DE-FG02-04ER-54742.
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).
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.
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.
Gyrokinetic particle simulation of neoclassical transport
Lin, Z.; Tang, W.M.; Lee, W.W.
1995-02-01
A time varying weighting ({delta} f) scheme for gyrokinetic particle simulation is applied to a steady state, multi-species 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 in these multispecies simulations 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 sheared flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory of Hinton and Wong. 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, the present work demonstrates a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes.
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.
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}.
Gyrokinetic Simulation of Residual Stress from Diamagnetic Velocity Shears
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
2010-11-01
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the parallel velocity (and parallel velocity itself) vanishes. Previously [1] we demonstrated with gyrokinetic (GYRO) simulations that TAM pinching from the diamagnetic level shear in the ExB velocity could provide the residual stress needed for spontaneous toroidal rotation. Here we show that the shear in the diamagnetic velocities themselves provide comparable residual stress (and level of stabilization). The sign of the residual stress, quantified by the ratio of TAM flow to ion power flow (M/P), depends on the signs of the various velocity shears as well as ion (ITG) versus electron (TEM) mode directed turbulence. The residual stress from these temperature and density gradient diamagnetic velocity shears is demonstrated in global gyrokinetic simulation of ``null'' rotation DIIID discharges by matching M/P profiles within experimental error. 8pt [1] R.E. Waltz, G.M. Staebler, J. Candy, and F.L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009).
Visual interrogation of gyrokinetic particle simulations
NASA Astrophysics Data System (ADS)
Jones, Chad; Ma, Kwan-Liu; Sanderson, Allen; Myers, Lee Roy, Jr.
2007-07-01
Gyrokinetic particle simulations are critical to the study of anomalous energy transport associated with plasma microturbulence in magnetic confinement fusion experiments. The simulations are conducted on massively parallel computers and produce large quantities of particles, variables, and time steps, thus presenting a formidable challenge to data analysis tasks. We present two new visualization techniques for scientists to improve their understanding of the time-varying, multivariate particle data. One technique allows scientists to examine correlations in multivariate particle data with tightly coupled views of the data in both physical space and variable space, and to visually identify and track features of interest. The second technique, built into SCIRun, allows scientists to perform range-based queries over a series of time slices and visualize the resulting particles using glyphs. The ability to navigate the multiple dimensions of the particle data, as well as query individual or a collection of particles, enables scientists to not only validate their simulations but also discover new phenomena in their data.
Edge gyrokinetic theory and continuum simulations
NASA Astrophysics Data System (ADS)
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.
2007-08-01
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 plateau 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.
Gyrokinetic particle simulation of a field reversed configuration
NASA Astrophysics Data System (ADS)
Fulton, D. P.; Lau, C. K.; Holod, I.; Lin, Z.; Dettrick, S.
2016-01-01
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.
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.
ADVANCES IN COMPREHENSIVE GYROKINETIC SIMULATIONS OF TRANSPORT IN TOKAMAKS
WALTZ RE; CANDY J; HINTON FL; ESTRADA-MILA C; KINSEY JE
2004-10-01
A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite {beta}, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}{sub *}) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or a globally with physical profile variation. Rohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, plasma pinches and impurity flow, and simulations at fixed flow rather than fixed gradient are illustrated and discussed.
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.
ADVANCES IN COMPREHENSIVE GYROKINETIC SIMULATIONS OF TRANSPORT IN TOKAMAKS
WALTZ,R.E; CANDY,J; HINTON,F.L; ESTRADA-MILA,C; KINSEY,J.E
2004-10-01
A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite {beta}, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}{sub *}) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or globally with physical profile variation. Bohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, are illustrated.
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 simulation of driftwave instability in field-reversed configuration
NASA Astrophysics Data System (ADS)
Fulton, D. P.; Lau, C. K.; Schmitz, L.; Holod, I.; Lin, Z.; Tajima, T.; Binderbauer, M. W.
2016-05-01
Following the recent remarkable progress in magnetohydrodynamic (MHD) stability control in the C-2U advanced beam driven field-reversed configuration (FRC), turbulent transport has become one of the foremost obstacles on the path towards an FRC-based fusion reactor. Significant effort has been made to expand kinetic simulation capabilities in FRC magnetic geometry. The recently upgraded Gyrokinetic Toroidal Code (GTC) now accommodates realistic magnetic geometry from the C-2U experiment at Tri Alpha Energy, Inc. and is optimized to efficiently handle the FRC's magnetic field line orientation. Initial electrostatic GTC simulations find that ion-scale instabilities are linearly stable in the FRC core for realistic pressure gradient drives. Estimated instability thresholds from linear GTC simulations are qualitatively consistent with critical gradients determined from experimental Doppler backscattering fluctuation data, which also find ion scale modes to be depressed in the FRC core. Beyond GTC, A New Code (ANC) has been developed to accurately resolve the magnetic field separatrix and address the interaction between the core and scrape-off layer regions, which ultimately determines global plasma confinement in the FRC. The current status of ANC and future development targets are discussed.
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.
NASA Astrophysics Data System (ADS)
McClenaghan, J.; Lin, Z.; Holod, I.; Deng, W.; Wang, Z.
2014-12-01
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.
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.
Status of edge gyrokinetic turbulence simulation in XGC1
NASA Astrophysics Data System (ADS)
Ku, Seung-Hoe; Chang, C. S.; Zorin, D.; Greengard, L.; Adams, M.; Cummings, J.; Worley, P.; D'Azevedo, E.; Lee, W.; Parker, S.; Chen, Y.; Lin, Z.
2007-11-01
Gyrokinetic simulation of a tokamak edge plasma is one of the highest priority research items for ITER and the magnetic fusion program. Due to the complex physical modeling required in the edge plasma (closed and open magnetic field lines with the magnetic separatrix in between, the importance of neoclassical physics, the material wall boundary, steep pressure gradients, a non-Maxwellian distribution function, and the neutral particle physics), most of the gyrokinetic simulation activities have so far been focused on the core plasmas. The status of the gyrokinetic edge turbulence simulation in the XGC1 particle code in the SciDAC Prototype FSP Center for Plasma Edge Simulation (CPES) will be reported. XGC1 includes the above mentioned edge complexities with full- f/delta-f particle technology on an unstructured mesh. Special physics/math/CS features will be discussed. Our current electrostatic turbulence/neoclassical capabilities will be presented and verified. Plans for incorporating full electromagnetic turbulence will also be discussed.
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.
2013-01-15
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{sub Parallel-To }, {mu}) 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{sub Parallel-To} and {mu} 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. 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.; 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.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
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.
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.
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.
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.
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.
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)
Qi, Lei; Kwon, Jaemin; Hahm, T. S.; Jo, Gahyung
2016-06-01
Nonlinear bounce-averaged kinetic theory [B. H. Fong and T. S. Hahm, Phys. Plasmas 6, 188 (1999)] is used for magnetically trapped electron dynamics for the purpose of achieving efficient gyrokinetic simulations of Trapped Electron Mode (TEM) and Ion Temperature Gradient mode with trapped electrons (ITG-TEM) in shaped tokamak plasmas. The bounce-averaged kinetic equations are explicitly extended to shaped plasma equilibria from the previous ones for concentric circular plasmas, and implemented to a global nonlinear gyrokinetic code, Gyro-Kinetic Plasma Simulation Program (gKPSP) [J. M. Kwon et al., Nucl. Fusion 52, 013004 (2012)]. Verification of gKPSP with the bounce-averaged kinetic trapped electrons in shaped plasmas is successfully carried out for linear properties of the ITG-TEM mode and Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)]. Physics responsible for stabilizing effects of elongation on both ITG mode and TEM is identified using global gKPSP simulations. These can be understood in terms of magnetic flux expansion, leading to the effective temperature gradient R / L T ( 1 - E ') [P. Angelino et al., Phys. Rev. Lett. 102, 195002 (2009)] and poloidal wave length contraction at low field side, resulting in the effective poloidal wave number kθρi/κ.
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.
Gyrokinetic particle simulations of reversed shear Alfven eigenmode excited by antenna and fast ions
Deng Wenjun; Holod, Ihor; Xiao Yong; Lin Zhihong; Wang Xin; Zhang Wenlu
2010-11-15
Global gyrokinetic particle simulations of reversed shear Alfven eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode amplitude eventually saturates due to the thermal ion damping. The damping rates measured from the antenna excitation and from the initial perturbation simulation agree very well. The RSAE excited by fast ions shows an exponential growth. The finite Larmor radius effects of the fast ions are found to significantly reduce the growth rate. With kinetic thermal ions and electron pressure, the mode frequency increases due to the elevation of the Alfven continuum by the geodesic compressibility. The nonperturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic (MHD) theory. The gyrokinetic simulations have been benchmarked with extended hybrid MHD-gyrokinetic simulations.
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.
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.
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.
Effects of the magnetic equilibrium on gyrokinetic simulations of tokamak microinstabilities
Wan, Weigang; Chen, Yang; Parker, Scott E.; Groebner, Richard J.
2015-06-15
The general geometry of the experimental tokamak magnetic equilibrium is implemented in the global gyrokinetic simulation code GEM. Compared to the general geometry, the well used Miller parameterization of the magnetic equilibrium is a good approximation in the core region and up to the top of the pedestal. Linear simulations indicate that results with the two geometries agree for r/a ≤ 0.9. However, in the edge region, the instabilities are sensitive to the magnetic equilibrium in both the L-mode and the H-mode plasmas. A small variation of the plasma shaping parameters leads to large changes to the edge instability.
Pullback transformation in gyrokinetic electromagnetic simulations
Mishchenko, Alexey Könies, Axel; Kleiber, Ralf; Cole, Michael
2014-09-15
It is shown that a considerable mitigation of the cancellation problem can be achieved by a slight modification of the simulation scheme. The new scheme is verified, simulating a Toroidal Alfvén Eigenmode in tokamak geometry at low perpendicular mode numbers, the so-called “MHD limit.” Also, an electromagnetic drift mode has been successfully simulated in a stellarator.
Using a local gyrokinetic code to study global ion temperature gradient modes in tokamaks
NASA Astrophysics Data System (ADS)
Abdoul, P. A.; Dickinson, D.; Roach, C. M.; Wilson, H. R.
2015-06-01
In this paper the global eigenmode structures of linear ion temperature gradient (ITG) modes in tokamak plasmas are obtained using a novel technique which combines results from the local gyrokinetic code GS2 with analytical theory to reconstruct global properties. Local gyrokinetic calculations are performed for a range of radial flux surfaces, x, and ballooning phase angles, p, to map out the local complex mode frequency, Ω0(x, p) = ω0(x, p) + iγ0(x, p) for a single toroidal mode number, n. Taylor expanding Ω0 about a reference surface at x = 0, and employing the Fourier-ballooning representation leads to a second order ODE for the amplitude envelope, A(p), which describes how the local results are combined to form the global mode. The equilibrium profiles impact on the variation of Ω0(x, p) and hence influence the global mode structure. The simulations presented here are based upon a global extension to the CYCLONE base case and employ the circular Miller equilibrium model. In an equilibrium with radially varying profiles of a/LT and a/Ln, peaked at x = 0, and with all other equilibrium profiles held constant, including ηi = Ln/LT, Ω0(x, p) is found to have a stationary point. The reconstructed global mode sits at the outboard mid-plane of the tokamak, with global growth rate, γ ∼ Max[γ0]. Including the radial variation of other equilibrium profiles like safety factor and magnetic shear, leads to a mode that peaks away from the outboard mid-plane, with a reduced global growth rate. Finally, the influence of toroidal flow shear has also been investigated through the introduction of a Doppler shift, {ω0}\\to {ω0}-nΩ φ\\prime x , where Ωϕ is the equilibrium toroidal flow, and a prime denotes the radial derivative. The equilibrium profile variations introduce an asymmetry into the global growth rate spectrum with respect to the sign of Ω φ\\prime , such that the maximum growth rate is achieved with non-zero shearing, consistent with recent global
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.
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 simulation of the collisional micro-tearing mode instability
NASA Astrophysics Data System (ADS)
Startsev, Edward; Lee, Wei-Li; Wang, Weixing
2015-11-01
An application of recently developed perturbative particle simulation scheme for finite- β plasmas in the presence of background inhomogeneities is presented. Originally, using similar scheme, we were able to simulate shear-Alfven waves, finite- β modified drift waves and ion temperature gradient modes using a simple gyrokinetic particle code based on realistic fusion plasma parameters. Recently, we have successfully used the scheme for simulation of linear tearing and drift-tearing modes, in both collisionless semi-collisional regimes in slab geometry with sheared magnetic field. Here, we present further development of this scheme for the simulation of linear semi-collisional micro-tearing mode driven by electron temperature gradient in high-aspect ratio cylindrical cross-section tokamak using the modified turbulence code GTS. Research supported by the U. S. Department of Energy.
Nonlinear Full-f Edge Gyrokinetic Turbulence Simulations
NASA Astrophysics Data System (ADS)
Xu, X. Q.; Dimits, A. M.; Umansky, M. V.
2008-11-01
TEMPEST is a nonlinear full-f 5D electrostatic gyrokinetic code for simulations of neoclassical and turbulent transport for tokamak plasmas. Given an initial density perturbation, 4D TEMPEST simulations show that the kinetic GAM exists in the edge in the form of outgoing waves [1], its radial scale is set by plasma profiles, and the ion temperature inhomogeneity is necessary for GAM radial propagation. From an initial Maxwellian distribution with uniform poloidal profiles on flux surfaces, the 5D TEMPEST simulations in a flux coordinates with Boltzmann electron model in a circular geometry show the development of neoclassical equilibrium, the generation of the neoclassical electric field due to neoclassical polarization, and followed by a growth of instability due to the spatial gradients. 5D TEMPEST simulations of kinetic GAM turbulent generation, radial propagation, and its impact on transport will be reported. [1] X. Q. Xu, Phys. Rev. E., 78 (2008).
Gyrokinetic theory and simulation of angular momentum transport
Waltz, R. E.; Staebler, G. M.; Candy, J.; Hinton, F. L.
2007-12-15
A gyrokinetic theory of turbulent toroidal angular momentum transport as well as modifications to neoclassical poloidal rotation from turbulence is formulated starting from the fundamental six-dimensional kinetic equation. The gyro-Bohm scaled transport is evaluated from toroidal delta-f gyrokinetic simulations using the GYRO code [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. The simulations recover two pinch mechanisms in the radial transport of toroidal angular momentum: The slab geometry ExB shear pinch [Dominguez and Staebler, Phys. Fluids B 5, 387 (1993)] and the toroidal geometry 'Coriolis' pinch [Peeters, Angioni, and Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. The pinches allow the steady state null stress (or angular momentum transport flow) condition required to understand intrinsic (or spontaneous) toroidal rotation in heated tokamak without an internal source of torque [Staebler, Kinsey, and Waltz, Bull. Am. Phys. Soc. 46, 221 (2001)]. A predicted turbulent shift in the neoclassical poloidal rotation [Staebler, Phys. Plasmas 11, 1064 (2004)] appears to be small at the finite relative gyroradius (rho-star) of current experiments.
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.
Simulating Gyrokinetic/fluid hybrid electromagnetic modes in the total-f gyrokinetic code XGC1
NASA Astrophysics Data System (ADS)
Lang, Jianying; Hager, Robert; Ku, Seung-Hoe; Chang, Choong-Seock
2015-11-01
XGC1 code has been extended to include the electronmagnetic capability using the hybrid model with gyrokinetic ions and fluid electrons. This feature will enable a more complete description of the MHD/fluid type mode activities including ELMs and low-n tearing modes. Their interaction with the kinetic neoclassical and microturbulence dynamics needs to be simulated together. Evolution of the background profile should also be captured self-consistently. We report recent development and verification of this hybrid model in the limit of small delta-B. The code has been verified for Alfven waves and ITG/KBM transition, and low-n resistive tearing modes. The KBM capability of XGC1 has been verified against the published results from Gyro, GEM, GS2, Gene, and GTC. Detailed verification of resistive tearing modes and kink modes in the toroidal geometry will be also presented. An implicit method is implemented in XGC1 to bypass the Courant condition caused by fast Alfven oscillations. Work supported by US DOE OFES and OASCR.
Gyrokinetic full-torus simulations of ohmic tokamak plasmas in circular limiter configuration
NASA Astrophysics Data System (ADS)
Korpilo, T.; Gurchenko, A. D.; Gusakov, E. Z.; Heikkinen, J. A.; Janhunen, S. J.; Kiviniemi, T. P.; Leerink, S.; Niskala, P.; Perevalov, A. A.
2016-06-01
The gyrokinetic full 5D particle distribution code ELMFIRE has been extended to simulate circular tokamak plasmas from the magnetic axis to the limiter scrape-off-layer. The predictive power of the code in the full-torus configuration is tested via its ability to reproduce experimental steady-state profiles in FT-2 ohmic L-mode plasmas. The results show that the experimental profile solution is not reproduced numerically due to the difficulty of obtaining global power balance. This is verified by cross-comparison of ELMFIRE code versions, which shows also the impact of boundary conditions and grid resolution on turbulent transport.
Gyrokinetic simulations of off-axis minimum-q profile corrugations
Waltz, R.E.; Austin, M.E.; Burrell, K.H.; Candy, J.
2006-05-15
Quasiequilibrium radial 'profile corrugations' in the electron temperature gradient are found at lowest-order singular surfaces in global gyrokinetic code simulations of both monotonic-q and off-axis minimum-q discharges. The profile corrugations in the temperature and density gradients are time-averaged components of zonal flows. The m/n=2/1 electron temperature gradient corrugation is measurably large and appears to trigger an internal transport barrier as the off-axis minimum-q=2 surfaces enter the plasma.
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.
Transport and discrete particle noise in gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Jenkins, Thomas; Lee, W. W.
2006-10-01
We present results from our recent investigations regarding the effects of discrete particle noise on the long-time behavior and transport properties of gyrokinetic particle-in-cell simulations. It is found that the amplitude of nonlinearly saturated drift waves is unaffected by discreteness-induced noise in plasmas whose behavior is dominated by a single mode in the saturated state. We further show that the scaling of this noise amplitude with particle count is correctly predicted by the fluctuation-dissipation theorem, even though the drift waves have driven the plasma from thermal equilibrium. As well, we find that the long-term behavior of the saturated system is unaffected by discreteness-induced noise even when multiple modes are included. Additional work utilizing a code with both total-f and δf capabilities is also presented, as part of our efforts to better understand the long- time balance between entropy production, collisional dissipation, and particle/heat flux in gyrokinetic plasmas.
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.
Electron heat transport from stochastic fields in gyrokinetic simulations
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-15
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as {beta}{sub e} is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of {beta}{sub e}. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, d{sub m}[A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
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
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.
Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode
NASA Astrophysics Data System (ADS)
Zhang, H. S.; Liu, Y. Q.; Lin, Z.; Zhang, W. L.
2016-04-01
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.
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.
Database-driven web interface automating gyrokinetic simulations for validation
NASA Astrophysics Data System (ADS)
Ernst, D. R.
2010-11-01
We are developing a web interface to connect plasma microturbulence simulation codes with experimental data. The website automates the preparation of gyrokinetic simulations utilizing plasma profile and magnetic equilibrium data from TRANSP analysis of experiments, read from MDSPLUS over the internet. This database-driven tool saves user sessions, allowing searches of previous simulations, which can be restored to repeat the same analysis for a new discharge. The website includes a multi-tab, multi-frame, publication quality java plotter Webgraph, developed as part of this project. Input files can be uploaded as templates and edited with context-sensitive help. The website creates inputs for GS2 and GYRO using a well-tested and verified back-end, in use for several years for the GS2 code [D. R. Ernst et al., Phys. Plasmas 11(5) 2637 (2004)]. A centralized web site has the advantage that users receive bug fixes instantaneously, while avoiding the duplicated effort of local compilations. Possible extensions to the database to manage run outputs, toward prototyping for the Fusion Simulation Project, are envisioned. Much of the web development utilized support from the DoE National Undergraduate Fellowship program [e.g., A. Suarez and D. R. Ernst, http://meetings.aps.org/link/BAPS.2005.DPP.GP1.57.
Gyrokinetic particle simulations of kinetic ballooning mode in tokamak pedestal
NASA Astrophysics Data System (ADS)
Holod, Ihor
2014-10-01
The pedestal height and width in tokamak H-mode operation are widely believed to be constrained by mesoscale peeling-ballooning modes and microscopic kinetic ballooning modes (KBM). However, direct evidences of the KBM turbulence in pedestal are very limited. The role of the drift-Alfvenic microturbulence during the pedestal recovery period is not clear. Here we use gyrokinetic toroidal code (GTC) to study the edge instability of a DIII-D discharge #131997 using realistic geometry and plasma profiles and focusing on the pedestal region with steep pressure gradient. First, electrostatic simulations find a reactive trapped electron mode with an unusual eigenmode structure, which peaks at the poloidal angle θ = +/- π /2. The electron collisions decrease the growth rate by about one-half. Next, the plasma pressure is scanned in GTC electromagnetic simulations to identify the boundary for the KBM onset. At the finite electron beta an electromagnetic instability is found with KBM characteristics. The linear growth rate increases with βe and the mode propagation is in the ion diamagnetic direction. Nonlinear simulations of the KBM turbulence will also be presented. Work supported by DOE Grant DE-SC0010416, and in collaborations with GTC team.
Energy conserving continuum algorithms for kinetic & gyrokinetic simulations of plasmas
NASA Astrophysics Data System (ADS)
Hakim, A.; Hammett, G. W.; Shi, E.; Stoltzfus-Dueck, T.
2015-11-01
We present high-order, energy conserving, continuum algorithms for the solution of gyrokinetic equations for use in edge turbulence simulations. The distribution function is evolved with a discontinuous Galerkin scheme, while the fields are evolved with a continuous finite-element method. These algorithms work for a general, possibly non-canonical, Poisson bracket operator and conserve energy exactly. Benchmark simulations with ETG turbulence in 3X/2V are shown, as well as initial applications of the algorithms to turbulence in a simplified SOL geometry. Sheath boundary conditions with recycling and secondary electron emission are implemented, and a Lenard-Bernstein collision operator is included. Extension of these algorithms to full Vlasov-Maxwell equations are presented. It is shown that with a particular choice of numerical fluxes the total (particle+field) energy is conserved. Algorithms are implemented in a flexible and open-source framework, Gkeyll, which also includes fluid models, allowing potential hybrid simulations of various plasma problems. Supported by the Max-Planck/Princeton Center for Plasma Physics, and DOE Contract DE-AC02-09CH11466.
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.
Web Interface Connecting Gyrokinetic Turbulence Simulations with Tokamak Fusion Data
NASA Astrophysics Data System (ADS)
Suarez, A.; Ernst, D. R.
2005-10-01
We are developing a comprehensive interface to connect plasma microturbulence simulation codes with experimental data in the U.S. and abroad. This website automates the preparation and launch of gyrokinetic simulations utilizing plasma profile and magnetic equilibrium data. The functionality of existing standalone interfaces, such as GS2/PREP [D. R. Ernst et al., Phys. Plasmas 11(5) 2637 (2004)], in use for several years for the GS2 code [W. Dorland et al., Phys. Rev. Lett. 85(26) 5579 (2000)], will be extended to other codes, including GYRO [J. Candy / R.E. Waltz, J. Comput. Phys.186, (2003) 545]. Data is read from mdsplus and TRANSP [\\underline {http://w3.pppl.gov/transp}] and can be viewed using a java plotter, Webgraph, developed for this project by previous students Geoffrey Catto and Bo Feng. User sessions are tracked and saved to allow users to access their previous simulations, which can be used as templates for future work.
Full-f gyrokinetic simulation over a confinement time
Idomura, Yasuhiro
2014-02-15
A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., “Consequences of profile shearing on toroidal momentum transport,” Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the radial electric field shear but also on the radial electric field itself. Based on the toroidal angular momentum conservation, it is found that in the steady null momentum transport state, the turbulent residual stress is cancelled by the neoclassical counterpart, which is greatly enhanced in the presence of turbulent fluctuations.
Global particle-in-cell simulations of Alfvenic modes
Mishchenko, A.; Koenies, A.; Hatzky, R.
2008-11-01
Global linear gyro-kinetic particle-in-cell (PIC) simulations of electromagnetic modes in pinch and tokamak geometries are reported. The Toroidal Alfven Eigenmode and the Kinetic Ballooning Mode have been simulated. All plasma species have been treated kinetically (i.e. no hybrid fluid-kinetic or reduced-kinetic model has been applied). The main intention of the paper is to demonstrate that the global Alfven modes can be treated with the gyro-kinetic PIC method.
The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations
Hornsby, W. A. Migliano, P.; Buchholz, R.; Kroenert, L.; Weikl, A.; Peeters, A. G.; Zarzoso, D.; Poli, E.; Casson, F. J.
2015-02-15
Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η{sup 1∕7} scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.
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.
A new hybrid kinetic electron model for full-f gyrokinetic simulations
NASA Astrophysics Data System (ADS)
Idomura, Y.
2016-05-01
A new hybrid kinetic electron model is developed for electrostatic full-f gyrokinetic simulations of the ion temperature gradient driven trapped electron mode (ITG-TEM) turbulence at the ion scale. In the model, a full kinetic electron model is applied to the full-f gyrokinetic equation, the multi-species linear Fokker-Planck collision operator, and an axisymmetric part of the gyrokinetic Poisson equation, while in a non-axisymmetric part of the gyrokinetic Poisson equation, turbulent fluctuations are determined only by kinetic trapped electrons responses. By using this approach, the so-called ωH mode is avoided with keeping important physics such as the ITG-TEM, the neoclassical transport, the ambipolar condition, and particle trapping and detrapping processes. The model enables full-f gyrokinetic simulations of ITG-TEM turbulence with a reasonable computational cost. Comparisons between flux driven ITG turbulence simulations with kinetic and adiabatic electrons are presented. Although the similar ion temperature gradients with nonlinear upshift from linear critical gradients are sustained in quasi-steady states, parallel flows and radial electric fields are qualitatively different with kinetic electrons.
NASA Astrophysics Data System (ADS)
Wang, Weixing; Brian, B.; Ethier, S.; Chen, J.; Startsev, E.; Diamond, P. H.; Lu, Z.
2015-11-01
A non-diffusive momentum flux connecting edge momentum sources/sinks and core plasma flow is required to establish the off-axis peaked ion rotation profile typically observed in ECH-heated DIII-D plasmas without explicit external momentum input. The understanding of the formation of such profile structures provides an outstanding opportunity to test the physics of turbulence driving intrinsic rotation, and validate first-principles-based gyrokinetic simulation models. Nonlinear, global gyrokinetic simulations of DIII-D ECH plasmas indicate a substantial ITG fluctuation-induced residual stress generated around the region of peaked toroidal rotation, along with a diffusive momentum flux. The residual stress profile shows an anti-gradient, dipole structure, which is critical for accounting for the formation of the peaked rotation profile. It is showed that both turbulence intensity gradient and zonal flow ExB shear contribute to the generation of k// asymmetry needed for residual stress generation. By balancing the simulated residual stress and the momentum diffusion, a rotation profile is calculated. In general, the radial structure of core rotation profile is largely determined by the residual stress profile, while the amplitude of core rotation depends on the edge toroidal rotation velocity, which is determined by edge physics and used as a boundary condition in our model. The calculated core rotation profile is consistent with the experimental measurements. Also discussed is the modification of turbulence-generated Reynolds stress on poloidal rotation in those plasmas. Work supported by U.S. DOE Contract DE-AC02-09-CH11466.
Validation study of gyrokinetic simulation (GYRO) near the edge in Alcator C-Mod ohmic discharges
NASA Astrophysics Data System (ADS)
Sung, C.; White, A.; Howard, N.; Mikkelsen, D.; Holland, C.; Rice, J.; Reinke, M.; Gao, C.; Ennever, P.; Porkolab, M.; Churchill, R.; Theiler, C.; Walk, J.; Hughes, J.; Hubbard, A.; Greenwald, M.
2014-10-01
A validation study of local gyrokinetic simulations (GYRO) near the edge region (r / a ~ 0 . 85) has been performed for two C-Mod ohmic discharges, namely one that is in the Linear Ohmic Confinement (LOC) regime and the other one in the Saturated Ohmic Confinement (SOC) regime. Comparing the simulated heat fluxes and synthetic Te fluctuations with the experiments, it is found that GYRO can reproduce the ion heat flux and the Te fluctuation level measured by the Correlation ECE (CECE) diagnostic within their uncertainties, while the simulated electron heat flux is under-predicted. Furthermore, the synthetic Te spectral shape is not matched with the measured spectrum in both LOC/SOC discharges. We have also performed global simulations to consider the interaction of turbulence within the sampling volume of the CECE diagnostic, enabling us to evaluate the importance of global simulations in applying a synthetic CECE diagnostic in this study. The LOC/SOC transition physics will be also explored. Research supported by USDoE Awards DE-SC0006419, DE-FC02-99ER54512.
W.W. Lee
2003-09-17
Particle simulation has played an important role for the recent investigations on turbulence in magnetically confined plasmas. In this paper, theoretical and numerical properties of a gyrokinetic plasma as well as its relationship with magnetohydrodynamics (MHD) are discussed with the ultimate aim of simulating microturbulence in transport time scale using massively parallel computers.
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
Verification of Gyrokinetic (delta)f Simulations of Electron Temperature Gradient Turbulence
Nevins, W M; Parker, S E; Chen, Y; Candy, J; Dimits, A; Dorland, W; Hammett, G W; Jenko, F
2007-05-07
The GEM gyrokinetic {delta}f simulation code [Chen, 2003] [Chen, 2007] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [Nevins, 2006]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.
Gyrokinetic simulation studies on the energetic-particle-induced geodesic acoustic mode
NASA Astrophysics Data System (ADS)
Miki, Kazuhiro; Idomura, Yasuhiro
2014-10-01
Understanding of the energetic particles physics is of great interest in the future burning plasmas. Particularly, particle loss in the presence of EGAM may be critical for ITER. We thus need to know how EGAM is excited and interacts with turbulence. We here introduce energetic particles in a full-f gyrokinetic code (GT5D). (i) We find linear dynamics of the EGAM driven by bump-on-tail particle distributions. We examine flat-q, homogeneous, axisymmetric, electrostatic gyrokinetic simulations. Above a certain level of the beam intensity, an oscillatory mode grows with about a half of the standard GAM. The observed frequencies are consistent with the eigenmode analyses derived from the perturbed gyrokinetic equations. The theoretical analyses also indicate a bifurcation of the excited modes depending on q-value. Estimation of the finite-orbit-width effects can provide a size dependency of the EGAM growth rate. (ii) We find linear and nonlinear dynamics of the EGAM driven by slowing-down distributions. We examine the axisymmetric gyrokinetic simulations with DIII-D-like parameters. The observed growth rates and frequencies are consistent with results of other hybrid code. Furthermore, we will focus on nonlinear phase space dynamics, namely chirping mode. This work is supported by HPCI Strategic Program Field No.4: Next-Generation Industrial Innovations, funded by the MEXT, Japan.
Gyrokinetic Simulations of Impurity Seeded C-Mod Ohmic Plasmas
NASA Astrophysics Data System (ADS)
Porkolab, Miklos; Ennever, Paul; Rice, John; Rost, J. Chris; Davis, Evan; Ernst, Darin; Fiore, Catherine; Hubbard, Amanda; Hughes, Jerry; Terry, Jim; Tsujii, Naoto; Candy, Jeff; Staebler, Gary; Reinke, Matthew; Alcator C-Mod Team
2014-10-01
Ohmic plasmas on C-Mod were seeded with nitrogen to study the impact of dilution in the LOC (linear ohmic) and SOC (saturated ohmic) regimes. The seeding decreased ion diffusivity and caused the rotation to reverse in certain cases. TGLF, TGYRO, and global GYRO simulations were performed on these plasmas, simulating both the transport and the density fluctuations. TGYRO simulations using TGLF showed that the ion temperature profile only needed slight modification to get agreement with the heat flux, and the electron temperature profile needed almost no modification. However, when these TGYRO modified profiles were simulated with global GYRO the ion and electron fluxes were much lower than the experimental measurements and the TGLF simulated fluxes. The average of the TGYRO and experimental profiles gave ion fluxes that agreed with the experimental fluxes, and the density fluctuations agreed with PCI measurements. The electron flux from GYRO is below experimental levels, and since these plasmas have little TEM turbulence ETG simulations are being performed to make up the difference. Results will be presented. Work supported by US DOE awards DE-FG02-94-ER54235 and DE-FC02-99-ER54512.
Waltz, R. E.; Candy, J.; Petty, C. C.
2006-07-15
Global gyrokinetic simulations of DIII-D [M. A. Mahdavi and J. L. Luxon, in 'DIII-D Tokamak Special Issue', Fusion Sci. Technol. 48, 2 (2005)] L- and H-mode dimensionally similar discharge pairs are treated in detail. The simulations confirm the Bohm scaling of the well-matched L-mode pair. The paradoxical but experimentally apparent gyro-Bohm scaling of the H-mode pair at larger relative gyroradius (rho-star) and lower transport levels is due to poor profile similarity. Simulations of projected experimental plasma profiles with perfect similarity show both the L- and H-mode pairs to have Bohm scaling. A {rho}{sub *} stabilization rule for predicting the breakdown of gyro-Bohm scaling from simulations of a single discharge is presented.
NASA Astrophysics Data System (ADS)
Ishizawa, Akihiro; Watanabe, Tomo-Hiko; Sugama, Hideo; Maeyama, Shinya; Nunami, Masanori; Nakajima, Noriyoshi
2014-10-01
Turbulent transport in a high ion temperature discharge of Large Helical Device (LHD) is investigated by means of electromagnetic gyrokinetic simulations including kinetic electrons. A new electromagnetic gyrokinetic simulation code GKV+enables us to examine electron heat and particle fluxes as well as ion heat flux in finite beta heliotron/stellarator plasmas. This problem has not been previously explored because of numerical difficulties associated with complex three-dimensional magnetic structures as well as multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The turbulent fluxes, which are evaluated through a nonlinear simulation carried out in the K-super computer system, will be reported. This research uses computational resources of K at RIKEN Advanced Institute for Computational Science through the HPCI System Research project (Project ID: hp140044).
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
Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
2011-04-15
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium ExB velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or ''profile shear'' in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) ExB and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a ''null'' toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the ExB shear and parallel velocity (Coriolis force) pinching components from the larger ''diffusive'' parallel velocity shear driven component and
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
NASA Astrophysics Data System (ADS)
Imadera, K.; Kishimoto, Y.; Sen, S.; Vahala, G.
2016-02-01
The ion-temperature-driven modes are studied in the presence of radio frequency waves by the use of the Gyro-Kinetic simulation Code. It is shown that the radio frequency waves through the ponderomotive force can stabilise the ion-temperature-gradient instabilities and contrary to the usual belief no radio frequency wave-induced flow generation hypothesis is required. This might be a major way to create a transport barrier in the fusion energy generation.
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.
Nature of turbulent transport across sheared zonal flows: insights from gyro-kinetic simulations
Sanchez, Raul; Newman, David E; Leboeuf, Jean-Noel; Decyk, Viktor
2011-01-01
The traditional view regarding the reduction of turbulence-induced transport across a stable sheared flow invokes a reduction of the characteristic length scale in the direction perpendicular to the flow as a result of the shearing and stretching of eddies caused by the differential pull exerted in the direction of the flow. A reduced effective transport coefficient then suffices to capture the reduction, that can then be readily incorporated into a transport model. However, recent evidence from gyrokinetic simulations of the toroidal ion-temperature-gradient mode suggests that the dynamics of turbulent transport across sheared flows changes in a more fundamental manner, and that the use of reduced effective transport coefficients fails to capture the full dynamics that may exhibit both subdiffusion and non-Gaussian statistics. In this contribution, after briefly reviewing these results, we propose some candidates for the physical mechanisms responsible for endowing transport with such non-diffusive characteristics, backing these proposals with new numerical gyrokinetic data
Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection
NASA Astrophysics Data System (ADS)
Munoz Sepulveda, Patricio Alejandro; Büchner, Jörg; Kilian, Patrick; Told, Daniel; Jenko, Frank
2016-07-01
Fully kinetic Particle-in-Cell (PIC) simulations of (strong) guide-field reconnection can be computationally very demanding, due to the intrinsic stability and accuracy conditions required by this numerical method. One convenient approach to circumvent this issue is using gyrokinetic theory, an approximation of the Vlasov-Maxwell equations for strongly magnetized plasmas that eliminates the fast gyromotion, and thus reduces the computational cost. Although previous works have started to compare the features of reconnection between both approaches, a complete understanding of the differences is far from being complete. This knowledge is essential to discern the limitations of the gyrokinetic simulations of magnetic reconnection when applied to scenarios with moderate guide fields, such as the Solar corona, in contrast to most of the fusion/laboratory plasmas. We extend a previous work by our group, focused in the differences in the macroscopic flows, by analyzing the heating processes and non-thermal features developed by reconnection between both plasma approximations. We relate these processes by identifying some high-frequency cross-streaming instabilities appearing only in the fully kinetic approach. We characterize the effects of these phenonema such as anisotropic electron heating, beam formation and turbulence under different parameter regimes. And finally, we identify the conditions under which these instabilities tends to become negligible in the fully kinetic model, and thus a comparison with gyrokinetic theory becomes more reliable.
Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks
Swamy, Aditya K.; Ganesh, R.; Chowdhury, J.; Brunner, S.; Vaclavik, J.; Villard, L.
2014-08-15
Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient η{sub e}. Scans at different β values show an inverse relationship between the η{sub e} threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.
NASA Astrophysics Data System (ADS)
Howard, N. T.; Holland, C.; White, A. E.; Greenwald, M.; Candy, J.
2015-06-01
The first study using multi-scale (coupled ITG/TEM/ETG) gyrokinetic simulations at both reduced and realistic electron mass ratios, μ = (mD/me).5 = 20.0, 40.0 and 60.0, has been performed on a standard, Alcator C-Mod, L-mode discharge. Ion-scale (kθρs ∼ 1.0) and multi-scale (up to kθρe ∼ 0.8) gyrokinetic simulations are compared at different simulated mass ratios to investigate the fidelity of reduced electron mass ratio, multi-scale simulation through direct comparison with realistic mass ratio, multi-scale simulation. Detailed description of both the numerical setup and the turbulent scales required to obtain meaningful coupled ITG/TEM/ETG simulation is presented. Significant high-k driven (TEM/ETG) heat flux is found to exist at scales of approximately kθρe ∼ 0.1 at all mass ratios but can only be obtained by simulation capturing turbulence up to kθρe ∼ 1.0. At slightly reduced mass ratio, μ = 40.0, qualitative agreement with realistic mass simulation can be obtained in the studied discharge, consistent with intuition obtained from linear stability analysis. However, realistic electron mass is required for any robust quantitative comparison with experimental heat fluxes for the condition studied, as significant differences are observed at even slightly reduced electron mass ratio. The details of this numerical study are presented to provide a basis for future studies utilizing coupled ITG/TEM/ETG gyrokinetic simulation.
NASA Astrophysics Data System (ADS)
Tangri, Varun; Terry, P. W.; Waltz, R. E.
2011-05-01
A simple large-aspect-ratio (R0/r) circular equilibrium model is developed for low-beta reversed field pinch (RFP) geometry. The model is suitable for treating small scale instability and turbulent transport driven by ion temperature gradient (ITG) and related electron drift modes in gyrokinetic simulations. The equilibrium model is an RFP generalization of the common tokamak s-α model to small safety factor (q), where the poloidal field dominates the toroidal field. The model accommodates the RFP toroidal field reversal (where q vanishes) by generalizing the cylindrical force-free Bessel function model (BFM) [J. B. Taylor, Phys. Rev. Lett. 33, 1139 (1974)] to toroidal geometry. The global equilibrium can be described in terms of the RFP field reversal and pinch parameters [F ,Θ]. This new toroidal Bessel function model (TBFM) has been incorporated into the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J.Comput. Phys. 186, 545 (2003)] and used here to explore local electrostatic ITG adiabatic electron instability rates for typical low-q RFP parameters.
Tangri, Varun; Terry, P. W.; Waltz, R. E.
2011-05-15
A simple large-aspect-ratio (R{sub 0}/r) circular equilibrium model is developed for low-beta reversed field pinch (RFP) geometry. The model is suitable for treating small scale instability and turbulent transport driven by ion temperature gradient (ITG) and related electron drift modes in gyrokinetic simulations. The equilibrium model is an RFP generalization of the common tokamak s-{alpha} model to small safety factor (q), where the poloidal field dominates the toroidal field. The model accommodates the RFP toroidal field reversal (where q vanishes) by generalizing the cylindrical force-free Bessel function model (BFM) [J. B. Taylor, Phys. Rev. Lett. 33, 1139 (1974)] to toroidal geometry. The global equilibrium can be described in terms of the RFP field reversal and pinch parameters [F,{Theta}]. This new toroidal Bessel function model (TBFM) has been incorporated into the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J.Comput. Phys. 186, 545 (2003)] and used here to explore local electrostatic ITG adiabatic electron instability rates for typical low-q RFP parameters.
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.
Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST
NASA Astrophysics Data System (ADS)
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 (ψ,θ,γ,μ) 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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
2011-04-01
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium E ×B velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or "profile shear" in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) E ×B and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a "null" toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the E ×B shear and parallel velocity (Coriolis force) pinching components from the larger "diffusive" parallel velocity shear driven component and
A generalized gyrokinetic Poisson solver
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms.
Multiscale Nature of the Dissipation Range in Gyrokinetic Simulations of Alfvénic Turbulence.
Told, D; Jenko, F; TenBarge, J M; Howes, G G; Hammett, G W
2015-07-10
Nonlinear energy transfer and dissipation in Alfvén wave turbulence are analyzed in the first gyrokinetic simulation spanning all scales from the tail of the MHD range to the electron gyroradius scale. For typical solar wind parameters at 1 AU, about 30% of the nonlinear energy transfer close to the electron gyroradius scale is mediated by modes in the tail of the MHD cascade. Collisional dissipation occurs across the entire kinetic range k(⊥)ρ(I)≳1. Both mechanisms thus act on multiple coupled scales, which have to be retained for a comprehensive picture of the dissipation range in Alfvénic turbulence. PMID:26207474
Verification of gyrokinetic {delta}f simulations of electron temperature gradient turbulence
Nevins, W. M.; Parker, S. E.; Chen, Y.; Candy, J.; Dimits, A.; Dorland, W.; Hammett, G. W.; Jenko, F.
2007-08-15
The GEM gyrokinetic {delta}f simulation code [Y. Chen and S. Parker, J. Comput. Phys. 189, 463 (2003); and ibid.220, 839 (2007)] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [W. M. Nevins, J. Candy, S. Cowley, T. Dannert, A. Dimits, W. Dorland, C. Estrada-Mila, G. W. Hammett, F. Jenko, M. J. Pueschel, and D. E. Shumaker, Phys. Plasmas 13, 122306 (2006)]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.
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.
Storelli, A. Vermare, L.; Hennequin, P.; Gürcan, Ö. D.; Singh, Rameswar; Morel, P.; Dif-Pradalier, G.; Sarazin, Y.; Garbet, X.; Grandgirard, V.; Ghendrih, P.; Görler, T.
2015-06-15
In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.
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.
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.
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
Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence
Nevins, W M; Wang, E; Candy, J
2010-02-12
Analysis of the magnetic field structure from electromagnetic simulations of tokamak ion temperature gradient turbulence demonstrates that the magnetic field can be stochastic even at very low plasma pressure. The degree of magnetic stochasticity is quantified by evaluating the magnetic diffusion coefficient. We find that the magnetic stochasticity fails to produce a dramatic increase in the electron heat conductivity because the magnetic diffusion coefficient remains small.
Nonlinear Gyrokinetic Turbulence Simulations of the NSTX Spherical Torus
NASA Astrophysics Data System (ADS)
Peterson, J. Luc; Hammett, G. W.; Mikkelsen, D.; Kaye, S.; Mazzucato, E.; Bell, R.; Leblanc, B.; Yuh, H.; Smith, D.; Candy, J.; Waltz, R. E.; Belli, E. A.; Staebler, G. M.; Kinsey, J.
2010-11-01
The National Spherical Torus Experiment provides a unique environment for the study of electron turbulence and transport. We present nonlinear GYROootnotetextJ. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003). simulations of microturbulence in NSTX discharges and make comparisons between numerically simulated and experimentally measured levels of electron-scale turbulence. In particular we examine the effects of magnetic shear, ExB shearing and collisionality on turbulence driven by the Electron Temperature Gradient (ETG) mode, while paying attention to the roles of electromagnetic fluctuations, kinetic ions and realistic experimental NSTX parameters. We also investigate the interplay between electron turbulence and transport using the TGYROootnotetextJ. Candy et al., Phys. Plasmas 16, 060704 (2009). simulation suite. This work is supported by the SciDAC Center for the Study of Plasma Microturbulence, DOE Contract DE-AC02-09CH11466, and used the resources of the National Center for Computational Sciences at ORNL, under DOE Contract DE-AC05-00OR22725.
NASA Astrophysics Data System (ADS)
Oberparleiter, M.; Jenko, F.; Told, D.; Doerk, H.; Görler, T.
2016-04-01
Neoclassical and turbulent transport in tokamaks has been studied extensively over the past decades, but their possible interaction remains largely an open question. The two are only truly independent if the length scales governing each of them are sufficiently separate, i.e., if the ratio ρ* between ion gyroradius and the pressure gradient scale length is small. This is not the case in particularly interesting regions such as transport barriers. Global simulations of a collisional ion-temperature-gradient-driven microturbulence performed with the nonlinear global gyrokinetic code Gene are presented. In particular, comparisons are made between systems with and without neoclassical effects. In fixed-gradient simulations, the modified radial electric field is shown to alter the zonal flow pattern such that a significant increase in turbulent transport is observed for ρ*≳1 /300 . Furthermore, the dependency of the flux on the collisionality changes. In simulations with fixed power input, we find that the presence of neoclassical effects decreases the frequency and amplitude of intermittent turbulent transport bursts (avalanches) and thus plays an important role for the self-organisation behaviour.
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).
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.
Simulations of 4D edge transport and dynamics using the TEMPEST gyro-kinetic code
NASA Astrophysics Data System (ADS)
Rognlien, T. D.; Cohen, B. I.; Cohen, R. H.; Dorr, M. R.; Hittinger, J. A. F.; Kerbel, G. D.; Nevins, W. M.; Xiong, Z.; Xu, X. Q.
2006-10-01
Simulation results are presented for tokamak edge plasmas with a focus on the 4D (2r,2v) option of the TEMPEST continuum gyro-kinetic code. A detailed description of a variety of kinetic simulations is reported, including neoclassical radial transport from Coulomb collisions, electric field generation, dynamic response to perturbations by geodesic acoustic modes, and parallel transport on open magnetic-field lines. Comparison is made between the characteristics of the plasma solutions on closed and open magnetic-field line regions separated by a magnetic separatrix, and simple physical models are used to qualitatively explain the differences observed in mean flow and electric-field generation. The status of extending the simulations to 5D turbulence will be summarized. The code structure used in this ongoing project is also briefly described, together with future plans.
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.
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.
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
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.
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.
Singh, Rameswar; Brunner, S.; Ganesh, R.; Jenko, F.
2014-03-15
This paper presents effects of finite ballooning angles on linear ion temperature gradient (ITG) driven mode and associated heat and momentum flux in Gyrokinetic flux tube simulation GENE. It is found that zero ballooning angle is not always the one at which the linear growth rate is maximum. The ITG mode acquires a short wavelength (SW) branch (k{sub ⊥}ρ{sub i} > 1) when growth rates maximized over all ballooning angles are considered. However, the SW branch disappears on reducing temperature gradient showing characteristics of zero ballooning angle SWITG in case of extremely high temperature gradient. Associated heat flux is even with respect to ballooning angle and maximizes at nonzero ballooning angle while the parallel momentum flux is odd with respect to the ballooning angle.
NASA Astrophysics Data System (ADS)
Ernst, Darin; Long, A.; Basse, N.; Lin, L.; Porkolab, M.; Dorland, W.
2006-04-01
We have developed a synthetic diagnostic^1 for the GS2 gyrokinetic code for direct comparisons with phase contrast imaging (PCI) measurements of density fluctuations in Alcator C-Mod. The gyrokinetic simulation is carried out in a local, field line following flux-tube, while PCI measures density fluctuations along 32 chords passing vertically through the plasma cross-section.^2 Transforming from Clebsch to cartesian coordinates, and integrating appropriately over portions of the flux tube viewed by the diagnostic, yields a density fluctuation spectrum versus wavenumber kR in the major radius direction. To achieve vertical localization, we examine an ITB case in which the spectrum is dominated by a strong trapped electron mode, localized near the half-radius. The wavelength spectrum from the simulations, using the synthetic diagnostic, closely reproduces the PCI spectrum. Contributions from kψ, where B=∇αx∇ψ, downshift the GS2 kα spectrum to improve upon our previous raw comparison with the PCI kR spectrum.^3 ^1A. Long, D. R. Ernst et al., Bull. Am. Phys. Soc. 50(8) p. 153, GP1.48, also p. 235, LP1.37 http://www.psfc.mit.edu/research/alcator/pubs/APS/APS2005/ernst.pdf. ^2N. P. Basse et al., Phys. Plasmas 12, 052512 (2005). ^3D. R. Ernst et al., 2004 IAEA Fusion Energy Conference, IAEA-CN116/TH/4-1 http://www-naweb.iaea.org/napc/physics/fec/fec2004/datasets/TH4-1.html, see also Phys. Plasmas 11 (2004) 2637.
Gyrokinetic δ f simulation of collisionless and semi-collisional tearing mode instabilities
NASA Astrophysics Data System (ADS)
Wan, Weigang; Chen, Yang; Parker, Scott
2004-11-01
The evolution of collisionless and semi-collisional tearing mode instabilities is studied using a three-dimensional particle-in-cell simulation model that utilizes the δ f-method with the split-weight scheme to enhance the time step, and a novel algorithm(Y. Chen and S.E. Parker, J. Comput. Phys. 198), 463 (2003) to accurately solve the Ampere's equation for experimentally relevant β values, βfracm_im_e≫ 1. We use the model of drift-kinetic electrons and gyrokinetic ions. Linear simulation results are benchmarked with eigenmode analysis for the case of fixed ions. In small box simulations the ions response can be neglected but for large box simulations the ions response is important because the width of perturbed current is larger than ρ_i.The nonlinear dynamics of magnetic islands will be studied and the results will be compared with previous theoretical studiesfootnote J.F. Drake and Y. C. Lee, Phys. Rev. Lett. 39, 453 (1977) on the saturation level and the electron bounce frequency. A collision operator is included in the electron drift kinetic equation to study the simulation in the semi-collisional regime. The algebraical growth stage has been observed and compared quantitatively with theory. Our progress on three-dimensional simulations of tearing mode instabilities will be reported.
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)].
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.
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
NASA Astrophysics Data System (ADS)
Howard, N. T.; Holland, C.; White, A. E.; Greenwald, M.; Candy, J.; Creely, A. J.
2016-05-01
To better understand the role of cross-scale coupling in experimental conditions, a series of multi-scale gyrokinetic simulations were performed on Alcator C-Mod, L-mode plasmas. These simulations, performed using all experimental inputs and realistic ion to electron mass ratio ((mi/me)1/2 = 60.0), simultaneously capture turbulence at the ion ( kθρs˜O (1.0 ) ) and electron-scales ( kθρe˜O (1.0 ) ). Direct comparison with experimental heat fluxes and electron profile stiffness indicates that Electron Temperature Gradient (ETG) streamers and strong cross-scale turbulence coupling likely exist in both of the experimental conditions studied. The coupling between ion and electron-scales exists in the form of energy cascades, modification of zonal flow dynamics, and the effective shearing of ETG turbulence by long wavelength, Ion Temperature Gradient (ITG) turbulence. The tightly coupled nature of ITG and ETG turbulence in these realistic plasma conditions is shown to have significant implications for the interpretation of experimental transport and fluctuations. Initial attempts are made to develop a "rule of thumb" based on linear physics, to help predict when cross-scale coupling plays an important role and to inform future modeling of experimental discharges. The details of the simulations, comparisons with experimental measurements, and implications for both modeling and experimental interpretation are discussed.
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.
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.
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.
Gyrokinetic Vlasov-Poisson simulation in slab geometry using the conservative IDO scheme
NASA Astrophysics Data System (ADS)
Imadera, Kenji; Kishimoto, Yasuaki; Li, Jiquan; Saito, Daisuke; Utsumi, Takayuki
2008-11-01
We have introduced the IDO-CF (Conservative Form of Interpolated Differential Operator) scheme [1], which is one of the multi-moment schemes and has been applied to various CFD problems, in solving a Vlasov-Poisson system. The IDO scheme is found to be efficient in capturing a sharp domain interface like shock propagation, and in introducing dissipations like particle collision and also external source/sink terms. Furthermore, the IDO-CF scheme has exact mass conservation properties, so that we can apply it to the problems that need long time scale simulations. We first apply the scheme in studying the nonlinear Landau damping and two-stream instability. We have investigated the conservation property of the total mass, energy and entropy, and found that the IDO-CF scheme allows stable simulation over many bounce periods keeping higher accuracy than other multi-moment schemes. We have also developed a gyrokinetic full-f Vlasov code with the IDO-CF scheme in studying the slab ITG driven turbulence. [1] Y.Imai et al., J. Comput. Phys. 227, 2263(2008).
NASA Astrophysics Data System (ADS)
Matsuoka, Seikichi; Idomura, Yasuhiro; Satake, Shinsuke
2014-10-01
A magnetic field perturbation in tokamak plasmas plays a key role in determining the intrinsic rotation and velocity shear, since even a small perturbation can break the axisymmetry in the toroidal direction and induces the finite neoclassical toroidal viscosity (NTV). A simulation study for the NTV evaluation in an axisymmetric tokamak with a small resonant magnetic field perturbation using the full-f gyrokinetic Eulerian code GT5D is presented. The magnetic field perturbation is included in the particle orbit of GT5D only through the Hamiltonian by replacing the axisymmetric magnetic field with the sum of the axisymmetric field and the perturbation, which enables us to perform GT5D simulations without changing the symplectic structure of the single-particle Lagrangian constructed for the equilibrium (axisymmetric) magnetic field. Numerical results are benchmarked with those obtained by the neoclassical transport code, FORTEC-3D, which solves the drift kinetic equation by two-weight δf Monte Carlo method. The NTV of GT5D with a single-helicity perturbation is found to have a similar peaked profile around the resonant surface as that of FORTEC-3D.
Four-Dimensional Continuum Gyrokinetic Code: Neoclassical Simulation of Fusion Edge Plasmas
NASA Astrophysics Data System (ADS)
Xu, X. Q.
2005-10-01
We are developing a continuum gyrokinetic code, TEMPEST, to simulate edge plasmas. Our code represents velocity space via a grid in equilibrium energy and magnetic moment variables, and configuration space via poloidal magnetic flux and poloidal angle. The geometry is that of a fully diverted tokamak (single or double null) and so includes boundary conditions for both closed magnetic flux surfaces and open field lines. The 4-dimensional code includes kinetic electrons and ions, and electrostatic field-solver options, and simulates neoclassical transport. The present implementation is a Method of Lines approach where spatial finite-differences (higher order upwinding) and implicit time advancement are used. We present results of initial verification and validation studies: transition from collisional to collisionless limits of parallel end-loss in the scrape-off layer, self-consistent electric field, and the effect of the real X-point geometry and edge plasma conditions on the standard neoclassical theory, including a comparison of our 4D code with other kinetic neoclassical codes and experiments.
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
NASA Astrophysics Data System (ADS)
Merlo, G.; Brunner, S.; Sauter, O.; Camenen, Y.; Görler, T.; Jenko, F.; Marinoni, A.; Told, D.; Villard, L.
2015-05-01
The experimental observation made on the TCV tokamak of a significant confinement improvement in plasmas with negative triangularity (δ < 0) compared to those with standard positive triangularity has been interpreted in terms of different degrees of profile stiffness (Sauter et al 2014 Phys. Plasmas 21 055906) and/or different critical gradients. Employing the Eulerian gyrokinetic code GENE (Jenko et al 2000 Phys. Plasmas 7 1904), profile stiffness and critical gradients are studied under TCV relevant conditions. For the considered experimental discharges, trapped electron modes (TEMs) and electron temperature gradient (ETG) modes are the dominant microinstabilities, with the latter providing a significant contribution to the non-linear electron heat fluxes near the plasma edge. Two series of simulations with different levels of realism are performed, addressing the question of profile stiffness at various radial locations. Retaining finite collisionality, impurities and electromagnetic effects, as well as the physical electron-to-ion mass ratio are all necessary in order to approach the experimental flux measurements. However, flux-tube simulations are unable to fully reproduce the TCV results, pointing towards the need to carry out radially nonlocal (global) simulations, i.e. retaining finite machine size effects, in a future study. Some conclusions about the effect of triangularity can nevertheless be drawn based on the flux-tube results. In particular, the importance of considering the sensitivity to both temperature and density gradient is shown. The flux tube results show an increase of the critical gradients towards the edge, further enhanced when δ < 0, and they also appear to indicate a reduction of profile stiffness towards plasma edge.
Three-dimensional gyrokinetic simulation of the relaxation of a magnetized temperature filament
Sydora, R. D.; Morales, G. J.; Maggs, J. E.; Van Compernolle, B.
2015-10-15
An electromagnetic, 3D gyrokinetic particle code is used to study the relaxation of a magnetized electron temperature filament embedded in a large, uniform plasma of lower temperature. The study provides insight into the role played by unstable drift-Alfvén waves observed in a basic electron heat transport experiment [D. C. Pace et al., Phys. Plasmas 15, 122304 (2008)] in which anomalous cross-field transport has been documented. The simulation exhibits the early growth of temperature-gradient-driven, drift-Alfvén fluctuations that closely match the eigenmodes predicted by linear theory. At the onset of saturation, the unstable fluctuations display a spiral spatial pattern, similar to that observed in the laboratory, which causes the rearrangement of the temperature profile. After saturation of the linear instability, the system exhibits a markedly different behavior depending on the inclusion in the computation of modes without variation along the magnetic field, i.e., k{sub z} = 0. In their absence, the initial filament evolves into a broadened temperature profile, self-consistent with undamped, finite amplitude drift-Alfvén waves. But the inclusion of k{sub z} = 0 modes causes the destruction of the filament and damping of the drift-Alfvén modes leading to a final state consisting of undamped convective cells and multiple, smaller-scale filaments.
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.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
NASA Astrophysics Data System (ADS)
Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.
2016-06-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation - e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others - can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function - driven by ionization, charge exchange and wall loss - is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
NASA Astrophysics Data System (ADS)
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.
2015-06-01
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.
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.
NASA Astrophysics Data System (ADS)
Liu, Dongjian; Bao, Jian; Han, Tao; Wang, Jiaqi; Lin, Zhihong
2016-02-01
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 De2, where De is the electron skin depth. On the other hand, the growth rate of a double tearing mode is proportional to De in the parameter regime of fusion plasmas.
Gyrokinetic Simulations of Enhanced Alpha Transport by De-stabilized Alfvèn Turbulence
NASA Astrophysics Data System (ADS)
Bass, E. M.
2009-11-01
Alfvèn turbulence, destabilized by fusion-produced α-particles, is expected to greatly enhance transport of these hot fusion products. Previously, the gyrokinetic code GYRO [1] was used to simulate the convective transport of fusion alpha particles by electrostatic (β=0) ITG/TEM turbulence driven at low k (0
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
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.
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.
Global electromagnetic simulations of the outer core of an ASDEX Upgrade L-mode plasma
NASA Astrophysics Data System (ADS)
Abiteboul, J.; Görler, T.; Jenko, F.; Told, D.
2015-09-01
The outer core of a low confinement discharge performed at the ASDEX Upgrade tokamak is investigated using both global and local nonlinear gyrokinetic simulations. Previous work [Told et al., Phys. Plasmas 20, 122312 (2013)] had shown that local gyrokinetic simulations agree reasonably well with experimental results in terms of transport levels, with minor discrepancies that can be resolved within the uncertainties of the experimental profile. In the present work, the analysis of the same discharge is extended to include global gradient-driven simulations with the GENE code, taking into account the plasma profiles from mid-radius up to close to the separatrix. It is shown that the mean fluxes obtained assuming the local approximation are in general agreement with results from global simulations. Moreover, both types of simulations exhibit large-scale avalanche-like events, both in the ion and electron heat fluxes, with similar basic properties. However, analyzing the statistics of the fluxes reveals that intermittency is more important in the global case. Furthermore, even when averaging over turbulent time scales, radial corrugations in the ion temperature profile are identified in the global simulation. These corrugations are at most of the order of 1%, but correspond to up to 10% variations in the gradient. Thus, while the results on the mean fluxes support the validity of the local approximation, the presence of corrugated structures may pose a challenge for the direct validation of local gyrokinetic simulations against experiments.
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)
Howard, N. T.; Holland, C.; White, A. E.; Greenwald, M.; Candy, J.
2016-01-01
The transport of heat in laboratory and astrophysical plasmas is dominated by the complex nonlinear dynamics of plasma turbulence. In magnetically confined plasmas used for fusion energy research, turbulence is responsible for cross-field transport that limits the performance of tokamak reactors. We report a set of novel gyrokinetic simulations that capture ion and electron-scale turbulence simultaneously, revealing the dynamics of cross-scale energy transfer and zonal flow modification that give rise to heat losses. Multi-scale simulations are required to match experimental ion and electron heat fluxes and electron profile stiffness, establishing the applicability of the newly discovered physics to experiment. Importantly, these results provide a likely explanation for the loss of electron heat from tokamak plasmas, the ‘great unsolved problem’ (Bachelor et al (2007 Plasma Sci. Technol. 9 312-87)) in plasma turbulence and the projected dominant loss channel in ITER.
Gyrokinetic simulations of ion temperature gradient modes in the reversed field pinch
Predebon, I.; Guo, S. C.; Angioni, C.
2010-01-15
Linear gyrokinetic calculations are applied to the reversed field pinch configuration to investigate the occurrence of ion temperature gradient instabilities. The analysis shows this type of instability to be only marginally responsible for particle and energy transport. The required gradients could be reached only in correspondence to the temperature slopes arising at the boundary of the helical structure in the quasisingle helicity states. The dependence of the instability threshold on the relevant macroscopic quantities is considered. A discussion on the main differences in the driving mechanisms existing between the reversed field pinch and the tokamak configuration is addressed.
Energetically consistent collisional gyrokinetics
Burby, J. W.; Brizard, A. J.; Qin, H.
2015-10-01
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.
2015-10-15
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.
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.
NASA Astrophysics Data System (ADS)
Sampsell, M. B.; Bravenec, R. V.; Candy, J.; Ernst, D. R.; Alcator C-Mod Team Nevins
2004-11-01
Beam-emission spectroscopy (BES) on Alcator C-Mod has observed long wavelength broadband fluctuations and a `quasi-coherent mode' (the latter exclusive to enhanced D_α H modes) in the plasma edge. However, it has not observed broadband fluctuations at the top of the H-mode pedestal or farther in. In an attempt to understand this, we have run the GYRO gyrokinetic code [J. Candy, J. Comput. Phys. 186, 545 (2003)] for this region, applied `synthetic BES' to the fluctuating density output, and compared with the data. The synthetic BES is composed of i) an anti-aliasing filter in GYRO itself, ii) a conversion from density fluctuations to emissivity fluctuations, and iii) a spatial filter to model the finite viewing area of the diagnostic. We find significant attenuation of the density fluctuations. Transport results from GYRO are also compared to data to validate the simulations.
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
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. PMID:19044712
NASA Astrophysics Data System (ADS)
Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu
2016-07-01
The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me . In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me . The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where k →.B → =0 , consistent with previous analytical and simulation studies. Here, B → is the equilibrium magnetic field and k → is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at k →.B → ≠0 . In addition, the simulation results indicate that varying mi/me , the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.
Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu
2016-07-07
The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location wheremore » $$\\vec{k}$$• $$\\vec{B}$$ =0, consistent with previous analytical and simulation studies. Here, $$\\vec{B}$$ is the equilibrium magnetic field and $$\\vec{k}$$ is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at $$\\vec{k}$$ •$$\\vec{B}$$ ≠0. Additionally, the simulation results indicate that varying mi/me, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.« less
Gyrokinetic turbulence simulations of the pedestal region at various lithium doses in NSTX
NASA Astrophysics Data System (ADS)
Coury, Mireille; Guttenfelder, Walter; Mikkelsen, David R.; Canik, John M.; Diallo, Ahmed; Maingi, Rajesh
2015-11-01
It is shown that lithium-coated walls alter the pedestal structure by, for instance, improving the energy confinement and reducing recycling. Recent work shows improved discharge characteristics with increasing lithium doses in highly shaped discharges. Edge-localized modes triggered by large edge pressure and current gradients are altered, even suppressed with increasing lithium doses. In this work, the plasma edge characteristics under increasing lithium doses are investigated with GS2 gyrokinetic code. Using experimental discharges as input parameters, microinstabilities are investigated in the pedestal region and the effect of increasing lithium doses on these microinstabilities is discussed. This work is supported by U.S. Dept. of Energy under contract DE-AC02-09CH11466.
NASA Astrophysics Data System (ADS)
Nakata, Motoki; Honda, Mitsuru; Yoshida, Maiko; Urano, Hajime; Nunami, Masanori; Maeyama, Shinya; Watanabe, Tomo-Hiko; Sugama, Hideo
2016-08-01
Quantitative validation studies of flux-tube gyrokinetic Vlasov simulations on ion and electron heat transport are carried out for the JT-60U tokamak experiment. The ion temperature gradient (ITG) and/or trapped electron modes (TEM) driven turbulent transport and zonal flow generations are investigated for an L-mode plasma in the local turbulence limit with a sufficiently small normalized ion thermal gyroradius and weak mean radial electric fields. Nonlinear turbulence simulations by the GKV code successfully reproduce radial profiles of the ion and electron energy fluxes in the core region. The numerical results show that the TEM-driven zonal flow generation in the outer region is more significant than that in the core region with ITG- and ITG–TEM-dominated turbulence, leading to moderate transport shortfall of the ion energy flux. Error levels in the prediction of the ion and electron temperature gradient profiles in the core region are estimated as less than +/- 30% , based on a multiple flux matching technique, where the simulated ion and electron energy fluxes are simultaneously matched to the experimental values.
NASA Astrophysics Data System (ADS)
Hornsby, W. A.; Migliano, P.; Buchholz, R.; Grosshauser, S.; Weikl, A.; Zarzoso, D.; Casson, F. J.; Poli, E.; Peeters, A. G.
2016-01-01
The non-linear evolution of a magnetic island is studied using the Vlasov gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a self-consistently growing magnetic island, generated by a tearing unstable {{Δ }\\prime}>0 current profile, is considered. The turbulence is able to seed the magnetic island and bypass the linear growth phase by generating structures that are approximately an ion gyro-radius in width. The non-linear evolution of the island width and its rotation frequency, after this seeding phase, is found to be modified and is dependent on the value of the plasma beta and equilibrium pressure gradients. At low values of beta the island evolves largely independent of the turbulence, while at higher values the interaction has a dramatic effect on island growth, causing the island to grow exponentially at the growth rate of its linear phase, even though the island is larger than linear theory validity. The turbulence forces the island to rotate in the ion-diamagnetic direction as opposed to the electron diamagnetic direction in which it rotates when no turbulence is present. In addition, it is found that the mode rotation slows as the island grows in size.
Spong, D. A.; Bass, E. M.; Deng, W.; Heidbrink, W. W.; Lin, Z.; Tobias, B.; Van Zeeland, M. A.; Austin, M. E.; Domier, C. W.; Luhmann, N. C. Jr.
2012-08-15
A verification and validation study is carried out for a sequence of reversed shear Alfven instability time slices. The mode frequency increases in time as the minimum (q{sub min}) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (no. 142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL are compared. The experimental mode structure of the instability was measured using time-resolved two-dimensional electron cyclotron emission imaging. The three models reproduce the frequency upsweep event within {+-}10% of each other, and the average of the code predictions is within {+-}8% of the measurements; growth rates are predicted that are consistent with the observed spectral line widths. The mode structures qualitatively agree with respect to radial location and width, dominant poloidal mode number, ballooning structure, and the up-down asymmetry, with some remaining differences in the details. Such similarities and differences between the predictions of the different models and the experimental results are a valuable part of the verification/validation process and help to guide future development of the modeling efforts.
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.
Gyrokinetic microtearing turbulence.
Doerk, H; Jenko, F; Pueschel, M J; Hatch, D R
2011-04-15
The nonlinear dynamics of microtearing modes in standard tokamak plasmas are investigated by means of ab initio gyrokinetic simulations. The saturation levels of the magnetic field fluctuations can be understood in the framework of a balance between (small poloidal wave number) linear drive and small-scale dissipation. The resulting heat transport is dominated by the electron magnetic component, and the transport levels are found to be experimentally relevant. Microtearing modes thus constitute another candidate for explaining turbulent transport in such toroidal systems. PMID:21568567
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.
Kinsey, J. E.; Waltz, R. E.; Candy, J.
2007-10-15
Nonlinear gyrokinetic simulations with kinetic electron dynamics are used to study the effects of plasma shaping on turbulent transport and ExB shear in toroidal geometry including the presence of kinetic electrons using the GYRO code. Over 120 simulations comprised of systematic scans were performed around several reference cases in the local, electrostatic, collisionless limit. Using a parameterized local equilibrium model for shaped geometry, the GYRO simulations show that elongation {kappa} (and its gradient) stabilizes the energy transport from ion temperature gradient (ITG) and trapped electron mode (TEM) instabilities at fixed midplane minor radius. For scans around a reference set of parameters, the GYRO ion energy diffusivity, in gyro-Bohm units, approximately follows a {kappa}{sup -1} scaling which is qualitatively similar to recent experimental energy confinement scalings. Most of the {kappa} scaling is due to the shear in the elongation rather than the local {kappa} itself. The {kappa} scaling for the electrons is found to vary and can be stronger or weaker than {kappa}{sup -1} depending on the wavenumber where the transport peaks. The {kappa} scaling is weaker when the energy diffusivity peaks at low wavenumbers and is stronger when the peak occurs at high wavenumbers. The simulations also demonstrate a nonlinear upshift in the critical temperature gradient as the elongation increases due to an increase in the residual zonal flow amplitude. Triangularity is found to be slightly destabilizing and its effect is strongest for highly elongated plasmas. Finally, we find less ExB shear is needed to quench the transport at high elongation and low aspect ratio. A new linear ExB shear quench rule, valid for shaped tokamak geometry, is presented.
NASA Astrophysics Data System (ADS)
Muñoz, P. A.; Told, D.; Kilian, P.; Büchner, J.; Jenko, F.
2015-08-01
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 (bg). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (βi = 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 (bg ≳ 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 (bg ≳ 5). Kinetic PIC simulations using guide fields bg ≲ 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 (βi = 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 (bg ≲ 3).
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)
White, A. E.; Peebles, W. A.; Rhodes, T. L.; Schmitz, L.; Carter, T. A.; Hillesheim, J. C.; Doyle, E. J.; Zeng, L.; Holland, C. H.; Wang, G.; McKee, G. R.; Staebler, G. M.; Waltz, R. E.; DeBoo, J. C.; Petty, C. C.; Burrell, K. H.
2010-05-15
This paper presents new measurements of the cross-phase angle, alpha{sub n{sub eT{sub e}}}, between long-wavelength (k{sub t}hetarho{sub s}<0.5) density, n-tilde{sub e}, and electron temperature, T-tilde{sub e}, fluctuations in the core of DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak plasmas. The coherency and cross-phase angle between n-tilde{sub e} and T-tilde{sub e} are measured using coupled reflectometer and correlation electron cyclotron emission diagnostics that view the same plasma volume. In addition to the experimental results, two sets of local, nonlinear gyrokinetic turbulence simulations that are performed with the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are described. One set, called the pre-experiment simulations, was performed prior to the experiment in order to predict a change in alpha{sub n{sub eT{sub e}}} given experimentally realizable increases in the electron temperature, T{sub e}. In the experiment the cross-phase angle was measured at three radial locations (rho=0.55, 0.65, and 0.75) in both a 'Base' case and a 'High T{sub e}' case. The measured cross-phase angle is in good qualitative agreement with the pre-experiment simulations, which predicted that n-tilde{sub e} and T-tilde{sub e} would be out of phase. The pre-experiment simulations also predicted a decrease in cross-phase angle as T{sub e} is increased. Experimentally, this trend is observed at the inner two radial locations only. The second set of simulations, the postexperiment simulations, is carried out using local parameters taken from measured experimental profiles as input to GYRO. These postexperiment simulation results are in good quantitative agreement with the measured cross-phase angle, despite disagreements with transport fluxes. Directions for future modeling and experimental work are discussed.
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.
Gyrokinetic-ion drift-kinetic-electron simulation of the (m = 2, n = 1) cylindrical tearing mode
NASA Astrophysics Data System (ADS)
Chen, Y.; Chowdhury, J.; Maksimovic, N.; Parker, S. E.; Wan, W.
2016-05-01
Particle-in-cell simulations of (m =2 ,n =1 ) tearing mode in cylindrical plasmas are carried out with kinetic electrons using the split-weight control-variate algorithm [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)]. Radially, global simulation shows global mode structure in agreement with reduced-magnetohydrodynamic eigenmode calculation. Simulations of the tearing layer are verified with analytic results for the collisionless, semi-collisional, and drift-tearing mode.
Transport in gyrokinetic tokamaks
Mynick, H.E.; Parker, S.E.
1995-01-01
A comprehensive study of transport in full-volume gyrokinetic (gk) simulations of ion temperature gradient driven turbulence in core tokamak plasmas is presented. Though this ``gyrokinetic tokamak`` is much simpler than experimental tokamaks, such simplicity is an asset, because a dependable nonlinear transport theory for such systems should be more attainable. Toward this end, we pursue two related lines of inquiry. (1) We study the scalings of gk tokamaks with respect to important system parameters. In contrast to real machines, the scalings of larger gk systems (a/{rho}{sub s} {approx_gt} 64) with minor radius, with current, and with a/{rho}{sub s} are roughly consistent with the approximate theoretical expectations for electrostatic turbulent transport which exist as yet. Smaller systems manifest quite different scalings, which aids in interpreting differing mass-scaling results in other work. (2) With the goal of developing a first-principles theory of gk transport, we use the gk data to infer the underlying transport physics. The data indicate that, of the many modes k present in the simulation, only a modest number (N{sub k} {approximately} 10) of k dominate the transport, and for each, only a handful (N{sub p} {approximately} 5) of couplings to other modes p appear to be significant, implying that the essential transport physics may be described by a far simpler system than would have been expected on the basis of earlier nonlinear theory alone. Part of this analysis is the inference of the coupling coefficients M{sub kpq} governing the nonlinear mode interactions, whose measurement from tokamak simulation data is presented here for the first time.
Evidence of a New Instability in Gyrokinetic Simulations of LAPD Plasmas
NASA Astrophysics Data System (ADS)
Terry, P. W.; Pueschel, M. J.; Rossi, G.; Jenko, F.; Told, D.; Carter, T. A.
2015-11-01
Recent experiments at the LArge Plasma Device (LAPD) have focused on structure formation driven by density and temperature gradients. A central difference relative to typical, tokamak-like plasmas stems from the linear geometry and absence of background magnetic shear. At sufficiently high β, strong excitation of parallel (compressional) magnetic fluctuations was observed. Here, linear and nonlinear simulations with the
Gyrokinetic simulations of 2D magnetic reconnection turbulence in guide fields
NASA Astrophysics Data System (ADS)
Terry, P. W.; Pueschel, M. J.; Jenko, F.; Zweibel, E.; Zhdankin, V.; Told, D.
2012-10-01
Following the analyses in [M.J. Pueschel et al., Phys. Plasmas 18, 112102 (2011)], a study of turbulence in driven reconnection is commenced, with a sinusoidal current sheet providing the drive through a Krook-type operator in a bi-periodic box. Simulations with the Gene code cover all relevant physical parameters, allowing for encompassing comparisons with expectations from linear simulations. A central observed feature are coherent circular current structures which may be identified as plasmoids. These objects move randomly in the plane perpendicular to the guide field, and may either disappear again after some time or instead merge with one another---the setup can thus be described as turbulence driven by reconnection, but simultaneously creating its own reconnection. Such merger events are associated with large bursts in the heating rate jE, and display strong non-Maxwellian components of the distribution function in parallel velocity space. The plasmoid energetics are studied, as are their ability to produce populations of fast particles. Statistics of such populations are used to facilitate direct comparisons with astrophysical scenarios of energetic particle production.
NASA Astrophysics Data System (ADS)
Happel, Tim; Bañón Navarro, Alejandro; Conway, Garrard; Görler, Tobias; Jenko, Frank; Ryter, Francois; Stroth, Ulrich; ASDEX Upgrade Team
2014-10-01
Core plasma turbulence determines transport properties and impacts on the efficiency of a fusion reactor. Gyrokinetic codes are developed to predict dominant instabilities and the turbulence level, which causes the observed particle and heat losses. A careful validation of these codes is mandatory to improve the reliability of predictions. To this end, core turbulence is investigated in ASDEX Upgrade by means of Doppler reflectometry, which provides the perpendicular velocity of turbulent structures and their fluctuation level. H-mode discharges have been performed in which ECRH is used to drive the turbulence from the ITG turbulence regime towards the TEM regime. In general, the turbulence level increases from core towards the edge. With increasing R /LTe , core large scale structures show larger fluctuation amplitudes while their phase velocity is altered with respect to that of small structures. Results are compared with gyrokinetic simulations with the GENE code. Linear results show a transition from ITG towards TEM turbulence close to the radial ECRH deposition location. After matching of heat fluxes to results from power balance analysis, the radial trend in the turbulence level is reproduced. The response to additional heating is opposite to the experimental findings.
2D properties of core turbulence on DIII-D and comparison to gyrokinetic simulations
Shafer, Morgan W; Fonck, R. J.; McKee, G. R.; Holland, Chris; White, A. E.; Schlossberg, D J
2012-01-01
Quantitative 2D characteristics of localized density fluctuations are presented over the range of 0.3 < r/a < 0.9 in L-mode plasmas on DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. Broadband density fluctuations increase in amplitude from (n) over tilde/n < 0.5% in the deep core to (n) over tilde/n similar to 2.5% near the outer region. The observed Doppler-shift due to the E x B velocity matches well with the measured turbulence group and phase velocities (in toroidally rotating neutral beam heated plasmas). Turbulence decorrelation rates are found to be similar to 200 kHz at the edge and to decrease toward the core (0.45 < r/a < 0.9) where they approach the E x B shearing rate (similar to 50 kHz). Radial and poloidal correlation lengths are found to scale with the ion gyroradius and exhibit an asymmetric poloidally elongated eddy structure. The ensemble-averaged turbulent eddy structure changes its tilt with respect to the radial-poloidal coordinates in the core, consistent with an E x B shear mechanism. The 2D spatial correlation and wavenumber spectra [S(k(r); k(theta))] are presented and compared to nonlinear flux-tube GYRO simulations at two radii, r/a = 0.5 and r/a = 0.75, showing reasonable overall agreement, but the GYRO spectrum exhibits a peak at finite kr for r/a = 0.75 that is not observed experimentally; E x B shear may cause this discrepancy. (C) 2012 American Institute of Physics.
Simulating Global Climate Summits
ERIC Educational Resources Information Center
Vesperman, Dean P.; Haste, Turtle; Alrivy, Stéphane
2014-01-01
One of the most persistent and controversial issues facing the global community is climate change. With the creation of the UN Framework Convention on Climate Change (UNFCCC) in 1992 and the Kyoto Protocol (1997), the global community established some common ground on how to address this issue. However, the last several climate summits have failed…
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.
Global particle-in-cell simulations of plasma pressure effects on Alfvenic modes
Mishchenko, Alexey; Koenies, Axel; Hatzky, Roman
2011-01-15
Global linear gyrokinetic particle-in-cell simulations of electromagnetic modes in realistic tokamak geometry are reported. The effect of plasma pressure on Alfvenic modes is studied. It is shown that the fast-particle pressure can considerably affect the shear Alfven wave continuum structure and hence the toroidicity-induced gap in the continuum. It is also found that the energetic ions can substantially reduce the growth rate of the ballooning modes (and perhaps completely stabilize them in a certain parameter range). Ballooning modes are found to be the dominant instabilities if the bulk-plasma pressure gradient is large enough.
Coury, M.; Guttenfelder, W.; Mikkelsen, D. R.; Canik, J. M.; Canal, G. P.; Diallo, A.; Kaye, S.; Kramer, G. J.; Maingi, R.
2016-06-30
Linear (local) gyrokinetic predictions of edge microinstabilities in highly shaped, lithiated and non-lithiated NSTX discharges are reported using the gyrokinetic code GS2. Microtearing modes dominate the non-lithiated pedestal top. The stabilization of these modes at the lithiated pedestal top enables the electron temperature pedestal to extend further inwards, as observed experimentally. Kinetic ballooning modes are found to be unstable mainly at the mid-pedestal of both types of discharges, with un- stable trapped electron modes nearer the separatrix region. At electron wavelengths, ETG modes are found to be unstable from mid-pedestal outwards for ηe, exp ~2.2 with higher growth rates formore » the lithiated discharge. Near the separatrix, the critical temperature gradient for driving ETG modes is reduced in the presence of lithium, re ecting the reduction of the lithiated density gradients observed experimentally. A preliminary linear study in the edge of non-lithiated discharges shows that the equilibrium shaping alters the electrostatic modes stability, found more unstable at high plasma shaping.« less
Energy Science and Technology Software Center (ESTSC)
2015-10-29
GFS is a simulation engine that is used for the characterization of Accelerator performance parameters based on the machine layout, configuration and noise sources. It combines extensively tested Feedback models with a longitudinal phase space tracking simulator along with the interaction between the two via beam-based feedback using a computationally efficient simulation engine. The models include beam instrumentation, considerations on loop delays for in both the R and beam-based feedback loops, as well as themore » ability to inject noise (both correlated and uncorrelated) at different points of the machine including a full characterization of the electron gun performance parameters.« less
Carlos Serrano, Lawrence Doolittle
2015-10-29
GFS is a simulation engine that is used for the characterization of Accelerator performance parameters based on the machine layout, configuration and noise sources. It combines extensively tested Feedback models with a longitudinal phase space tracking simulator along with the interaction between the two via beam-based feedback using a computationally efficient simulation engine. The models include beam instrumentation, considerations on loop delays for in both the R and beam-based feedback loops, as well as the ability to inject noise (both correlated and uncorrelated) at different points of the machine including a full characterization of the electron gun performance parameters.
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.
A Gyrokinetic Approach to Low Frequency Anisotropy-Driven Instabilities in the Solar Wind
NASA Astrophysics Data System (ADS)
Johnson, J.; Porazik, P.
2014-12-01
Observational surveys of temperature anisotropy in the solar wind indicate that anisotropy is bounded over a wide range of plasma beta and the anisotropy bounds appear to be predominately controlled by wave-particle interactions associated with mirror and oblique firehose instabilities. We present a reduced kinetic description that exploits gyrosymmetry (a symmetry associated with the gyromotion), providing an efficient, self-consistent approach that can be utilized in global models of the solar wind. We discuss the underlying physics of the mirror and firehose instabilities that allow for a reduced gyrokinetic description, and we verify the approach through comparisons of theory and simulations using gyrokinetic, hybrid, and fully kinetic descriptions. We present simulations showing the nonlinear development and saturation of the mirror instability and explain the amplitude and structure of the nonlinear state in terms of particle trapping. We also consider the nonlinear development of the oblique firehose instability and the associated wave spectra.
Global Simulation of Aviation Operations
NASA Technical Reports Server (NTRS)
Sridhar, Banavar; Sheth, Kapil; Ng, Hok Kwan; Morando, Alex; Li, Jinhua
2016-01-01
The simulation and analysis of global air traffic is limited due to a lack of simulation tools and the difficulty in accessing data sources. This paper provides a global simulation of aviation operations combining flight plans and real air traffic data with historical commercial city-pair aircraft type and schedule data and global atmospheric data. The resulting capability extends the simulation and optimization functions of NASA's Future Air Traffic Management Concept Evaluation Tool (FACET) to global scale. This new capability is used to present results on the evolution of global air traffic patterns from a concentration of traffic inside US, Europe and across the Atlantic Ocean to a more diverse traffic pattern across the globe with accelerated growth in Asia, Australia, Africa and South America. The simulation analyzes seasonal variation in the long-haul wind-optimal traffic patterns in six major regions of the world and provides potential time-savings of wind-optimal routes compared with either great circle routes or current flight-plans if available.
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.
NASA Astrophysics Data System (ADS)
Neiser, Tom; Jenko, Frank; Schmitz, Lothar; Told, Daniel; Banon Navarro, Alejandro; Carter, Troy; Yan, Zheng; McKee, George
2015-11-01
A prerequisite for the development of a self-consistent theoretical description of the L-H transition is the ability to quantitatively characterize near-edge L-mode plasmas. It is shown here for the first time that regimes exist in the L-mode near-edge that appear to be dominated by sub-ion-scale turbulence driven by electron temperature gradient (ETG) modes. These are results of gyrokinetic simulations of a DIII-D L-mode discharge in the near edge region (r/a = 0.8) with the GENE code (www.genecode.org). Instructed by a linear analysis, we performed nonlinear simulations of ITG and ETG turbulence, pointing to a dominance of ETG turbulence regarding the anomalous radial heat flux. Direct comparison with experimental data is encouraging. Respective multi-scale simulations, covering both ion and electron scales are underway and will be presented. Implications for L-H transition modeling will also be discussed. Work supported by the US Department of Energy (DOE) under DE-FG02-08ER54984 and DE-FC02-04ER54698, as well as NERSC, a DOE Office of Science User Facility supported under Contract No. DE-AC02-05CH11231.
Spong, Donald A; Bass, Eric; Deng, Wenjun; Heidbrink, W.; Lin, Zhihong; Tobias, Ben; Van Zeeland, Michael; Austin, M. E.; Domier, C. W.; Luhmann, N.C.
2012-01-01
A verification and validation study is carried out for a sequence of reversed shear Alfven instability time slices. The mode frequency increases in time as the minimum (q{sub min}) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (No.142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL are compared. The experimental mode structure of the instability was measured using time-resolved two-dimensional electron cyclotron emission imaging. The three models reproduce the frequency upsweep event within {+-}10% of each other, and the average of the code predictions is within {+-}8% of the measurements; growth rates are predicted that are consistent with the observed spectral line widths. The mode structures qualitatively agree with respect to radial location and width, dominant poloidal mode number, ballooning structure, and the up-down asymmetry, with some remaining differences in the details. Such similarities and differences between the predictions of the different models and the experimental results are a valuable part of the verification/validation process and help to guide future development of the modeling efforts.
Global gyrokinetic simulations of trapped-electron mode and trapped-ion mode microturbulence
NASA Astrophysics Data System (ADS)
Drouot, T.; Gravier, E.; Reveille, T.; Sarrat, M.; Collard, M.; Bertrand, P.; Cartier-Michaud, T.; Ghendrih, P.; Sarazin, Y.; Garbet, X.
2015-08-01
This paper presents a reduced kinetic model, which describes simultaneously trapped-ion (TIM) and trapped-electron (TEM) driven modes. Interestingly, the model enables the study of a full f problem for ion and electron trapped particles at very low numerical cost. The linear growth rate obtained with the full f nonlinear code Trapped Element REduction in Semi Lagrangian Approach is successfully compared with analytical predictions. Moreover, nonlinear results show some basic properties of collisionless TEM and TIM turbulence in tokamaks. A competition between streamer-like structures and zonal flows is observed for TEM and TIM turbulence. Zonal flows are shown to play an important role in suppressing the nonlinear transport and strongly depend on the temperature ratio Te/Ti .
Global Health Simulation During Residency
Rosenman, Jane R.; Fischer, Philip R.; Arteaga, Grace M.; Hulyalkar, Manasi; Butteris, Sabrina M.; Pitt, Michael B.
2016-01-01
Resident participation in international health electives (IHEs) has been shown to be beneficial, yet not all residents have the opportunity to participate. We sought to determine whether participating in simulated global health cases, via the standardized Simulation Use for Global Away Rotations (SUGAR) curriculum, was useful for all pediatric residents, not merely those planning to go on an IHE. Pediatric residents in our program took part in 2 SUGAR cases and provided feedback via an online survey. Thirty-six of 40 residents participated (90%); 72% responded to the survey. Three of 10 residents not previously planning to work in resource-limited settings indicated participation in SUGAR made them more likely to do so. Nearly all residents (88%) felt SUGAR should be part of the residency curriculum. All felt better prepared for working cross-culturally. While designed to prepare trainees for work in resource-limited settings, SUGAR may be beneficial for all residents. PMID:27583300
Global Health Simulation During Residency.
Rosenman, Jane R; Fischer, Philip R; Arteaga, Grace M; Hulyalkar, Manasi; Butteris, Sabrina M; Pitt, Michael B
2016-01-01
Resident participation in international health electives (IHEs) has been shown to be beneficial, yet not all residents have the opportunity to participate. We sought to determine whether participating in simulated global health cases, via the standardized Simulation Use for Global Away Rotations (SUGAR) curriculum, was useful for all pediatric residents, not merely those planning to go on an IHE. Pediatric residents in our program took part in 2 SUGAR cases and provided feedback via an online survey. Thirty-six of 40 residents participated (90%); 72% responded to the survey. Three of 10 residents not previously planning to work in resource-limited settings indicated participation in SUGAR made them more likely to do so. Nearly all residents (88%) felt SUGAR should be part of the residency curriculum. All felt better prepared for working cross-culturally. While designed to prepare trainees for work in resource-limited settings, SUGAR may be beneficial for all residents. PMID:27583300
Global Simulations of Magnetotail Reconnection
NASA Technical Reports Server (NTRS)
Kuznetsova, M. M.; Hesse, M.; Rastatter, L.; Toth, G.; Gombosi, T.
2007-01-01
There is a growing number of observational evidences of dynamic quasi-periodical magnetosphere response to continuously southward interplan etary magnetic field (IMF). However, traditional global MHD simulatio ns with magnetic reconnection supported by numerical dissipation and ad hoc anomalous resistivity driven by steady southward IMF often prod uce only quasi-steady configurations with almost stationary near-eart h neutral line. This discrepancy can be explained by the assumption that global MHD simulations significantly underestimate the reconnectio n rate in the magnetotail during substorm expansion phase. Indeed, co mparative studies of magnetic reconnection in small scale geometries demonstrated that traditional resistive MHD did not produce the fast r econnection rates observed in kinetic simulations. The major approxim ation of the traditional MHD approach is an isotropic fluid assumption) with zero off-diagonal pressure tensor components. The approximatio n, however, becomes invalid in the diffusion region around the reconn ection site where ions become unmagnetized and experience nongyrotropic behaviour. Deviation from gyrotropy in particle distribution functi on caused by kinetic effects manifests itself in nongyrotropic pressu re tensor with nonzero off-diagonal components. We use the global MHD code BATS-R-US and replace ad hoc parameters such as "critical curren t density" and "anomalous resistivity" with a physically motivated di ssipation model. The key element of the approach is to identify diffusion regions where the isotropic fluid MHD approximation is not applic able. We developed an algorithm that searches for locations of magnet otail reconnection sites. The algorithm takes advantage of block-based domain-decomposition technique employed by the BATS-R-US. Boundaries of the diffusion region around each reconnection site are estimated from the gyrotropic orbit threshold condition, where the ion gyroradius is equal to the distance to the
NASA Astrophysics Data System (ADS)
Sung, C.; White, A.; Howard, N.; Mikkelsen, D.; Rice, J.; Reinke, M.; Gao, C.; Ennever, P.; Porkolab, M.; Churchill, R.; Theiler, C.; Hubbard, A.; Greenwald, M.
2013-10-01
Long wavelength electron temperature fluctuations (kyρs < 0 . 3) near the edge (r / a ~ 0 . 85) are reduced across the ohmic confinement transition from Linear Ohmic Confinement(LOC) regime to Saturated Ohmic Confinement(SOC) regime in Alcator C-Mod. Linear stability analysis shows that the dominant mode of long wavelength turbulence near the edge is changed from Trapped Electron Mode(TEM) to Ion Temperature Gradient(ITG) mode while the dominant mode is not changed deeper in the core (r / a ~ 0 . 5). This indicates that local turbulence changes near the edge might be responsible for the change of global energy confinement in ohmic plasmas. Further study using nonlinear gyrokinetic simulations is being performed to clarify the relation between the change of local turbulence and global ohmic energy confinement. Through nonlinear gyrokinetic simulation (GYRO), we will investigate the change of fluctuating quantities (T~ , ñ , ϕ~) and their phase relations across ohmic confinement transitions, and relate them to the change of energy transport. A synthetic CECE diagnostic for C-Mod has been developed, and it will be used to validate the gyrokinetic simulations. Research supported by USDoE awards DE-SC0006419, DE-FC02-99ER54512.
Transport of momentum in full f gyrokinetics
Parra, Felix I.; Catto, Peter J.
2010-05-15
Full f electrostatic gyrokinetic formulations employ two gyrokinetic equations, one for ions and the other for electrons, and quasineutrality to obtain the ion and electron distribution functions and the electrostatic potential. We demonstrate with several examples that the long wavelength radial electric field obtained with full f approaches is extremely sensitive to errors in the ion and electron density since small deviations in density give rise to large, nonphysical deviations in the conservation of toroidal angular momentum. For typical tokamak values, a relative error of 10{sup -7} in the ion or electron densities is enough to obtain the incorrect toroidal rotation. Based on the insights gained with the examples considered, three simple tests to check transport of toroidal angular momentum in full f simulations are proposed.
Heikkinen, J. A.; Nora, M.
2011-02-15
Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J=
Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
Hatch, D. R.; Terry, P. W.; Jenko, F.; Merz, F.; Nevins, W. M.
2011-03-18
In the context of toroidal gyrokinetic simulations, it is shown that a hierarchy of damped modes is excited in the nonlinear turbulent state. These modes exist at the same spatial scales as the unstable eigenmodes that drive the turbulence. The larger amplitude subdominant modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Modes with increasingly fine-scale structure are excited to decreasing amplitudes. In aggregate, damped modes define a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems.
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)
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.
Intrinsic rotation with gyrokinetic models
Parra, Felix I.; Barnes, Michael; Catto, Peter J.; Calvo, Ivan
2012-05-15
The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed.
Confronting Global Issues: A Multipurpose IR Simulation
ERIC Educational Resources Information Center
Shellman, Stephen M.; Turan, Kursad
2006-01-01
This article describes an international relations simulation that focuses on threats of transnational insurgent organizations, the future of the Iraqi regime, and the effect of globalization on foreign policies. It contains both the Simulation Director's Guide and the Participant's Guide. The guides explain the steps taken to run the simulation…
Leerink, S.; Heikkinen, J. A.; Janhunen, S. J.; Kiviniemi, T. P.; Nora, M.; Ogando, F.
2008-09-15
The ELMFIRE gyrokinetic simulation code has been used to perform full f simulations of the FT-2 tokamak. The dynamics of the radial electric field and the creation of poloidal velocity in the presence of turbulence are presented.
The theory of gyrokinetic turbulence: A multiple-scales approach
NASA Astrophysics Data System (ADS)
Plunk, Gabriel Galad
gradient (ETG)) which rules out the possibility that ultra-fine streamers could produce significant transport, (3) a demonstration that the variation in the phasing of the primary mode (which depend on the values, of the equilibrium scale lengths of the system) effects the strength of the secondary instability, distinguishing the gyrokinetic model from a previous gyrofluid model, (4) parameter scans for the mean-scale gradient lengths which suggest a possible role of secondary instabilities in the Dimits shift and the formation of electron internal transport barriers (ITB) in tokamaks, (5) a formulation of the theory for fully gyrokinetic ions and electrons in order to explore the transition between ETG and ITG scales and (6) demonstrate the existence of a mechanism for the saturation of long-wavelength ETG modes in this ETG-ITG transition range (modes which have been demonstrated in simulations not to saturate when employing the ETG Boltzmann-ion gyrokinetic system). The final project is an application of the methods from inertial range understanding of fluid turbulence, to describe the stationary state of fully developed two-dimensional gyrokinetic turbulence. This work explores the relatively new idea of a phase-space cascade, whereby fine scales are nonlinearly generated in both position space and velocity space, and ultimately smoothed by collisional entropy production. This process constitutes the thermodynamic balance which occurs in the true steady state of a turbulent plasma, including those found in fusion devices. The results of this work include (1) exact third order relations (in analogy to Kolmogorov's four-fifths law), (2) phenomenological scaling theories for the forward and inverse cascades, (3) a detailed description of the relationship of the two-dimensional gyrokinetic cascade to the Charney-Hasegawa-Mima and two-dimensional Navier-Stokes cascades, (4) a Hankel transform formalism for treating velocity scales in the distribution function and (4) power
The isotope effect in turbulent transport control by GAMs. Observation and gyrokinetic modeling
NASA Astrophysics Data System (ADS)
Gurchenko, A. D.; Gusakov, E. Z.; Niskala, P.; Altukhov, A. B.; Esipov, L. A.; Kiviniemi, T. P.; Korpilo, T.; Kouprienko, D. V.; Lashkul, S. I.; Leerink, S.; Perevalov, A. A.; Irzak, M. A.
2016-04-01
A comparative investigation of the isotope effect in multi-scale anomalous transport phenomena is performed both experimentally by highly localized turbulence diagnostics in comparable hydrogen and deuterium FT-2 tokamak discharges and theoretically with the help of global gyrokinetic modeling. Substantial excess of the geodesic acoustic mode (GAM) amplitude, radial wavelength and correlation length in a wide spatial region of deuterium discharge resulting in stronger modulation of drift-wave turbulence level is demonstrated by both approaches. A larger turbulence radial correlation length is found at LFS in D-discharge in experiment and a stronger modulation of gyrokinetic particles and energy fluxes is shown there by the gyrokinetic code. The gyrokinetic modeling demonstrated comparable levels of drift wave density and electric field fluctuations in hydrogen and deuterium discharges. Nevertheless, the mean value of the ion energy and particle anomalous flux provided by modeling shows the systematic isotope effect at all radii.
Global Positioning System Simulator Field Operational Procedures
NASA Technical Reports Server (NTRS)
Kizhner, Semion; Quinn, David A.; Day, John H. (Technical Monitor)
2002-01-01
Global Positioning System (GPS) simulation is an important activity in the development or qualification of GPS signal receivers for space flight. Because a GPS simulator is a critical resource it is highly desirable to develop a set of field operational procedures to supplement the basic procedures provided by most simulator vendors. Validated field procedures allow better utilization of the GPS simulator in the development of new test scenarios and simulation operations. These procedures expedite simulation scenario development while resulting in scenarios that are more representative of the true design, as well as enabling construction of more complex simulations than previously possible, for example, spacecraft maneuvers. One difficulty in the development of a simulation scenario is specifying various modes of test vehicle motion and associated maneuvers requiring that a user specify some (but not all) of a few closely related simulation parameters. Currently this can only be done by trial and error. A stand-alone procedure that implements the simulator maneuver motion equations and solves for the motion profile transient times, jerk and acceleration would be of considerable value. Another procedure would permit the specification of some configuration parameters that would determine the simulated GPS signal composition. The resulting signal navigation message, for example, would force the receiver under test to use only the intended C-code component of the simulated GPS signal. A representative class of GPS simulation-related field operational procedures is described in this paper. These procedures were developed and used in support of GPS integration and testing for many successful spacecraft missions such as SAC-A, EO-1, AMSAT, VCL, SeaStar, sounding rockets, and by using the industry standard Spirent Global Simulation Systems Incorporated (GSSI) STR series simulators.
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.
Saturation of gyrokinetic turbulence through damped eigenmodes.
Hatch, D R; Terry, P W; Jenko, F; Merz, F; Nevins, W M
2011-03-18
In the context of toroidal gyrokinetic simulations, it is shown that a hierarchy of damped modes is excited in the nonlinear turbulent state. These modes exist at the same spatial scales as the unstable eigenmodes that drive the turbulence. The larger amplitude subdominant modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Modes with increasingly fine-scale structure are excited to decreasing amplitudes. In aggregate, damped modes define a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems. PMID:21469869
Global magnetohydrodynamic simulations on multiple GPUs
NASA Astrophysics Data System (ADS)
Wong, Un-Hong; Wong, Hon-Cheng; Ma, Yonghui
2014-01-01
Global magnetohydrodynamic (MHD) models play the major role in investigating the solar wind-magnetosphere interaction. However, the huge computation requirement in global MHD simulations is also the main problem that needs to be solved. With the recent development of modern graphics processing units (GPUs) and the Compute Unified Device Architecture (CUDA), it is possible to perform global MHD simulations in a more efficient manner. In this paper, we present a global magnetohydrodynamic (MHD) simulator on multiple GPUs using CUDA 4.0 with GPUDirect 2.0. Our implementation is based on the modified leapfrog scheme, which is a combination of the leapfrog scheme and the two-step Lax-Wendroff scheme. GPUDirect 2.0 is used in our implementation to drive multiple GPUs. All data transferring and kernel processing are managed with CUDA 4.0 API instead of using MPI or OpenMP. Performance measurements are made on a multi-GPU system with eight NVIDIA Tesla M2050 (Fermi architecture) graphics cards. These measurements show that our multi-GPU implementation achieves a peak performance of 97.36 GFLOPS in double precision.
SciDAC Center for Plasma Edge Simulation
Lin, Zhihong
2013-12-17
This project with a total funding of $592,998 for six years has partially supported four postdoctoral researchers at the University of California, Irvine (UCI). The UCI team has formulated electrostatic and electromagnetic global gyrokinetic particle simulation models with kinetic electrons, implemented these models in the edge code XGC1, performed benchmark between GTC and XGC1, developed computational tools for gyrokinetic particle simulation in tokamak edge geometry, and initiated preparatory study of edge turbulence using GTC code. The research results has been published in 12 papers and presented at many international and national conferences.
Global Hybrid Simulations of the Bow Shock
NASA Astrophysics Data System (ADS)
Omidi, N.; Blanco-Cano, X.; Russell, C. T.
2005-08-01
This paper summarizes recent results from global hybrid (kinetic ions, fluid electrons) simulations of bow shocks or waves associated with solar wind interaction with magnetic dipoles of various strength. By virtue of resolving ion temporal and spatial scales, global hybrid simulations account for collissionless dissipational processes at and upstream of the shock and their effects on the macrostructure of the bow shock, ion foreshock and the magnetosheath. The results demonstrate that as the level of magnetization increases and the dipole becomes a more effective obstacle, the quasi-perpendicular part of the bow shock forms first and that formation of quasi-parallel part of the bow shock is tied to the generation of oblique magnetosonic waves which steepen to form shocklets in the upstream region.
ERIC Educational Resources Information Center
Lawless, Kimberly A.; Brown, Scott W.
2015-01-01
GlobalEd 2 (GE2) is a set of technology-mediated, problem-based learning (PBL) simulations for middle-grade students, that capitalises on the multidisciplinary nature of the social sciences as an expanded curricular space for students to learn and apply scientific literacies and concepts, while simultaneously also enriching their understanding of…
Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas
Artun, M.; Tang, W.M.
1994-03-01
The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.
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.
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.
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.
The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code
NASA Astrophysics Data System (ADS)
Jiang, Peng; Lin, Zhihong; Ihor, Holod; Xiao, Chijie
2016-02-01
The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code (GTC). The ion and electron density profiles become partially flattened inside the islands. The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side, which do not move along the perturbed magnetic field lines. When the fraction of trapped particles decreases, the density profile at the low field becomes more flattened. supported by National Special Research Program of China for ITER (Nos. 2013GB111000 and 2014GB107004), China Scholarship Council (No. 2011601098), U.S. DOE Grants DE-SC0010416 and DE-FG02-07ER54916
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
Equilibrium fluctuation energy of gyrokinetic plasma
Krommes, J.A.; Lee, W.W.; Oberman, C.
1985-11-01
The thermal equilibrium electric field fluctuation energy of the gyrokinetic model of magnetized plasma is computed, and found to be smaller than the well-known result
Simulations of global electrostatic microinstabilities in ASDEX Upgrade discharges
NASA Astrophysics Data System (ADS)
Bottino, A.; Peeters, A. G.; Sauter, O.; Vaclavik, J.; Villard, L.
2004-01-01
Electrostatic microinstabilities in ion internal barrier (ITB) and H-mode discharges of the ASDEX Upgrade tokamak [O. Gruber, R. Arslanbekov, C. Atanasiu et al., Nucl. Fusion 41, 1369 (2001)] have been investigated with a full radius gyrokinetic code. The code models linear stability and includes the effect of an equilibrium radial electric field and trapped electrons. In order to simulate plasmas in experimental conditions [k⊥ρL˜O(1)], the long wavelength approximation in the quasineutrality equation has been replaced by a Padé expansion of the modified Bessel function. Results show that the E×B flow, induced by the radial electric field, changes the linear stability of the dominant ion temperature gradient modes. The electrostatic potential eddies are tilted by the sheared flow thus reducing the radial extent and the growth rate of modes. However, the finite value of the flow has a stabilizing effect too; the most unstable modes are shifted away from the unfavorable curvature region leading to lower linear growth rates. In addition to this at least two other mechanisms give an important contribution to the stabilization in the ITB region; the reverse shear profile itself and, to a lesser degree, the local value of the temperature ratio, τ=Te/Ti.