Field theory and a structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

Xiao, Jianyuan; Qin, Hong

doi:10.1088/1741-4326/ab38dc

Field theory and a structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

Journal Article · Mon Sep 09 00:00:00 EDT 2019 · Nuclear Fusion

DOI:https://doi.org/10.1088/1741-4326/ab38dc· OSTI ID:1660945

Xiao, Jianyuan ^[1]; Qin, Hong ^[2]

Univ. of Science and Technology of China, Hefei (China)
Univ. of Science and Technology of China, Hefei (China); Princeton Univ., NJ (United States)

A field theory and the associated structure-preserving geometric particle-in-cell (PIC) algorithm are developed to study low frequency electrostatic perturbations with fully kinetic ions and adiabatic electrons in magnetized plasmas. The algorithm is constructed by geometrically discretizing the field theory using discrete exterior calculus, high-order Whitney interpolation forms, and non-canonical Hamiltonian splitting method. The discretization preserves the non-canonical symplectic structure of the particle-field system, as well as the electromagnetic gauge symmetry. As a result, the algorithm is charge-conserving and possesses long-term conservation properties. Because drift wave turbulence and anomalous transport intrinsically involve multi time-scales, simulation studies using fully kinetic particles demand algorithms with long-term accuracy and fidelity. The structure-preserving geometric PIC algorithm developed adequately serves this purpose. The algorithm has been implemented in the code, tested and benchmarked using the examples of ion Bernstein waves and drift waves. We apply the algorithm to study the ion temperature gradient (ITG) instability and turbulence in a 2D slab geometry. Simulation results show that at the early stage of the turbulence, the energy diffusion is between the Bohm scaling and gyro-Bohm scaling. Finally, at later time, the observed diffusion is closer to the gyro-Bohm scaling, and density blobs generated by the rupture of unstable modes are the prominent structures of the fully developed ITG turbulence.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE; National Key Research and Development Program; National Natural Science Foundation of China (NNSFC); China Postdoctoral Science Foundation; Fundamental Research Funds for the Central Universities

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1660945

Alternate ID(s):: OSTI ID: 22929962

Journal Information:: Nuclear Fusion, Journal Name: Nuclear Fusion Journal Issue: 10 Vol. 59; ISSN 0029-5515

Publisher:: IOP ScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (98)

Partially Linearized Algorithms in Gyrokinetic Particle Simulation Dimits, A. M.; Lee, W. W. Journal of Computational Physics, Vol. 107, Issue 2 https://doi.org/10.1006/jcph.1993.1146	journal	August 1993
Stability and Transport in Magnetic Confinement Systems Weiland, Jan Springer Series on Atomic, Optical, and Plasma Physics https://doi.org/10.1007/978-1-4614-3743-7	book	January 2012
KAM theorem of symplectic algorithms for Hamiltonian systems Shang, Zai-jiu Numerische Mathematik, Vol. 83, Issue 3 https://doi.org/10.1007/s002110050460	journal	September 1999
Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs Marsden, Jerrold E.; Patrick, George W.; Shkoller, Steve Communications in Mathematical Physics, Vol. 199, Issue 2 https://doi.org/10.1007/s002200050505	journal	December 1998
Symplectic integrators with adaptive time step applied to runaway electron dynamics Shi, Yanyan; Sun, Yajuan; He, Yang Numerical Algorithms, Vol. 81, Issue 4 https://doi.org/10.1007/s11075-018-0636-6	journal	January 2019
Gyrokinetic particle simulation model Lee, W. W. Journal of Computational Physics, Vol. 72, Issue 1 https://doi.org/10.1016/0021-9991(87)90080-5	journal	September 1987
A symplectic integration algorithm for separable Hamiltonian functions Candy, J.; Rozmus, W. Journal of Computational Physics, Vol. 92, Issue 1 https://doi.org/10.1016/0021-9991(91)90299-Z	journal	January 1991
Fourth-order symplectic integration Forest, Etienne; Ruth, Ronald D. Physica D: Nonlinear Phenomena, Vol. 43, Issue 1 https://doi.org/10.1016/0167-2789(90)90019-L	journal	May 1990
Construction of higher order symplectic integrators Yoshida, Haruo Physics Letters A, Vol. 150, Issue 5-7 https://doi.org/10.1016/0375-9601(90)90092-3	journal	November 1990
The symplecticity of multi-step methods Tang, Yi-Fa Computers & Mathematics with Applications, Vol. 25, Issue 3 https://doi.org/10.1016/0898-1221(93)90146-M	journal	February 1993
Multisymplecticity of the centred box discretization for hamiltonian PDEs with m ≥ 2 space dimensions Hong, Jialin; Qin, Meng-Zhao Applied Mathematics Letters, Vol. 15, Issue 8 https://doi.org/10.1016/S0893-9659(02)00077-0	journal	November 2002
Explicit high-order gauge-independent symplectic algorithms for relativistic charged particle dynamics Xiao, Jianyuan; Qin, Hong Computer Physics Communications, Vol. 241 https://doi.org/10.1016/j.cpc.2019.04.003	journal	August 2019
Variational formulation of particle algorithms for kinetic plasma simulations Evstatiev, E. G.; Shadwick, B. A. Journal of Computational Physics, Vol. 245 https://doi.org/10.1016/j.jcp.2013.03.006	journal	July 2013
Volume-preserving algorithms for charged particle dynamics He, Yang; Sun, Yajuan; Liu, Jian Journal of Computational Physics, Vol. 281 https://doi.org/10.1016/j.jcp.2014.10.032	journal	January 2015
Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational Ellison, C. L.; Burby, J. W.; Qin, H. Journal of Computational Physics, Vol. 301 https://doi.org/10.1016/j.jcp.2015.09.007	journal	November 2015
Higher order volume-preserving schemes for charged particle dynamics He, Yang; Sun, Yajuan; Liu, Jian Journal of Computational Physics, Vol. 305 https://doi.org/10.1016/j.jcp.2015.10.032	journal	January 2016
Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems Chen, Qiang; Qin, Hong; Liu, Jian Journal of Computational Physics, Vol. 349 https://doi.org/10.1016/j.jcp.2017.08.033	journal	November 2017
Hamiltonian gyrokinetic Vlasov–Maxwell system Burby, J. W.; Brizard, A. J.; Morrison, P. J. Physics Letters A, Vol. 379, Issue 36 https://doi.org/10.1016/j.physleta.2015.06.051	journal	September 2015
Explicit K -symplectic algorithms for charged particle dynamics He, Yang; Zhou, Zhaoqi; Sun, Yajuan Physics Letters A, Vol. 381, Issue 6 https://doi.org/10.1016/j.physleta.2016.12.031	journal	February 2017
A lattice Maxwell system with discrete space–time symmetry and local energy–momentum conservation Xiao, Jianyuan; Qin, Hong; Shi, Yuan Physics Letters A, Vol. 383, Issue 9 https://doi.org/10.1016/j.physleta.2018.12.010	journal	February 2019
Gauge-free electromagnetic gyrokinetic theory Burby, J. W.; Brizard, A. J. Physics Letters A, Vol. 383, Issue 18 https://doi.org/10.1016/j.physleta.2019.04.019	journal	June 2019
Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic co-ordinates Brizard, A. Journal of Plasma Physics, Vol. 41, Issue 3 https://doi.org/10.1017/S0022377800014070	journal	June 1989
Monte Carlo particle-in-cell methods for the simulation of the Vlasov–Maxwell gyrokinetic equations Bottino, A.; Sonnendrücker, E. Journal of Plasma Physics, Vol. 81, Issue 5 https://doi.org/10.1017/S0022377815000574	journal	July 2015
Discrete mechanics and variational integrators Marsden, J. E.; West, M. Acta Numerica, Vol. 10 https://doi.org/10.1017/S096249290100006X	journal	May 2001
GEMPIC: geometric electromagnetic particle-in-cell methods Kraus, Michael; Kormann, Katharina; Morrison, Philip J. Journal of Plasma Physics, Vol. 83, Issue 4 https://doi.org/10.1017/s002237781700040x	journal	July 2017
Gyrocenter-gauge kinetic theory Qin, H.; Tang, W. M.; Lee, W. W. Physics of Plasmas, Vol. 7, Issue 11 https://doi.org/10.1063/1.1309031	journal	November 2000
Construction of multisymplectic schemes of any finite order for modified wave equations Sun, Ya Juan; Qin, Meng Zhao Journal of Mathematical Physics, Vol. 41, Issue 11 https://doi.org/10.1063/1.1316062	journal	November 2000
Pullback transformations in gyrokinetic theory Qin, H.; Tang, W. M. Physics of Plasmas, Vol. 11, Issue 3 https://doi.org/10.1063/1.1640626	journal	March 2004
Anomalous Diffusion Arising from Microinstabilities in a Plasma Drummond, William E.; Rosenbluth, Marshall N. Physics of Fluids, Vol. 5, Issue 12 https://doi.org/10.1063/1.1706559	journal	January 1962
Universal Instability in Complex Field Geometries Krall, Nicholas A.; Rosenbluth, Marshall N. Physics of Fluids, Vol. 8, Issue 8 https://doi.org/10.1063/1.1761444	journal	January 1965
Higher-Order Corrections to the Chew-Goldberger-Low Theory Frieman, Edward Physics of Fluids, Vol. 9, Issue 8 https://doi.org/10.1063/1.1761881	journal	January 1966
Instabilities due to Temperature Gradients in Complex Magnetic Field Configurations Coppi, B. Physics of Fluids, Vol. 10, Issue 3 https://doi.org/10.1063/1.1762151	journal	January 1967
Geometric gyrokinetic theory for edge plasmas Qin, H.; Cohen, R. H.; Nevins, W. M. Physics of Plasmas, Vol. 14, Issue 5 https://doi.org/10.1063/1.2472596	journal	May 2007
Variational symplectic algorithm for guiding center dynamics and its application in tokamak geometry Qin, Hong; Guan, Xiaoyin; Tang, William M. Physics of Plasmas, Vol. 16, Issue 4 https://doi.org/10.1063/1.3099055	journal	April 2009
Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme Squire, J.; Qin, H.; Tang, W. M. Physics of Plasmas, Vol. 19, Issue 8 https://doi.org/10.1063/1.4742985	journal	August 2012
Global gyrokinetic simulations of the H-mode tokamak edge pedestal Wan, Weigang; Parker, Scott E.; Chen, Yang Physics of Plasmas, Vol. 20, Issue 5 https://doi.org/10.1063/1.4803890	journal	May 2013
Why is Boris algorithm so good? Qin, Hong; Zhang, Shuangxi; Xiao, Jianyuan Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4818428	journal	August 2013
A variational multi-symplectic particle-in-cell algorithm with smoothing functions for the Vlasov-Maxwell system Xiao, Jianyuan; Liu, Jian; Qin, Hong Physics of Plasmas, Vol. 20, Issue 10 https://doi.org/10.1063/1.4826218	journal	October 2013
Canonicalization and symplectic simulation of the gyrocenter dynamics in time-independent magnetic fields Zhang, Ruili; Liu, Jian; Tang, Yifa Physics of Plasmas, Vol. 21, Issue 3 https://doi.org/10.1063/1.4867669	journal	March 2014
Variational formulation of macro-particle plasma simulation algorithms Shadwick, B. A.; Stamm, A. B.; Evstatiev, E. G. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4874338	journal	May 2014
Variational integration for ideal magnetohydrodynamics with built-in advection equations Zhou, Yao; Qin, Hong; Burby, J. W. Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4897372	journal	October 2014
Volume-preserving algorithm for secular relativistic dynamics of charged particles Zhang, Ruili; Liu, Jian; Qin, Hong Physics of Plasmas, Vol. 22, Issue 4 https://doi.org/10.1063/1.4916570	journal	April 2015
Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulationsa) Deng, Zhao; Waltz, R. E. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4917176	journal	May 2015
Variational symplectic particle-in-cell simulation of nonlinear mode conversion from extraordinary waves to Bernstein waves Xiao, Jianyuan; Liu, Jian; Qin, Hong Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4930118	journal	September 2015
Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems Xiao, Jianyuan; Qin, Hong; Liu, Jian Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4935904	journal	November 2015
Hamiltonian time integrators for Vlasov-Maxwell equations He, Yang; Qin, Hong; Sun, Yajuan Physics of Plasmas, Vol. 22, Issue 12 https://doi.org/10.1063/1.4938034	journal	December 2015
Particle-in-cell δf gyrokinetic simulations of the microtearing mode Chowdhury, J.; Chen, Yang; Wan, Weigang Physics of Plasmas, Vol. 23, Issue 1 https://doi.org/10.1063/1.4940333	journal	January 2016
Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations He, Yang; Sun, Yajuan; Qin, Hong Physics of Plasmas, Vol. 23, Issue 9 https://doi.org/10.1063/1.4962573	journal	September 2016
Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems Xiao, Jianyuan; Qin, Hong; Morrison, Philip J. Physics of Plasmas, Vol. 23, Issue 11 https://doi.org/10.1063/1.4967276	journal	November 2016
Lorentz covariant canonical symplectic algorithms for dynamics of charged particles Wang, Yulei; Liu, Jian; Qin, Hong Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4972824	journal	December 2016
A family of new explicit, revertible, volume-preserving numerical schemes for the system of Lorentz force Tu, Xiongbiao; Zhu, Beibei; Tang, Yifa Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4972878	journal	December 2016
Finite-dimensional collisionless kinetic theory Burby, J. W. Physics of Plasmas, Vol. 24, Issue 3 https://doi.org/10.1063/1.4976849	journal	March 2017
Structure and structure-preserving algorithms for plasma physics Morrison, P. J. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982054	journal	April 2017
Explicit symplectic methods for solving charged particle trajectories Zhou, Zhaoqi; He, Yang; Sun, Yajuan Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4982743	journal	May 2017
Local energy conservation law for a spatially-discretized Hamiltonian Vlasov-Maxwell system Xiao, Jianyuan; Qin, Hong; Liu, Jian Physics of Plasmas, Vol. 24, Issue 6 https://doi.org/10.1063/1.4986097	journal	June 2017
Low frequency fully kinetic simulation of the toroidal ion temperature gradient instability Sturdevant, B. J.; Chen, Y.; Parker, S. E. Physics of Plasmas, Vol. 24, Issue 8 https://doi.org/10.1063/1.4999945	journal	August 2017
Toroidal regularization of the guiding center Lagrangian Burby, J. W.; Ellison, C. L. Physics of Plasmas, Vol. 24, Issue 11 https://doi.org/10.1063/1.5004429	journal	November 2017
Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5011681	journal	May 2018
Degenerate variational integrators for magnetic field line flow and guiding center trajectories Ellison, C. L.; Finn, J. M.; Burby, J. W. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5022277	journal	May 2018
Ion temperature‐gradient‐driven modes and anomalous ion transport in tokamaks Romanelli, F. Physics of Fluids B: Plasma Physics, Vol. 1, Issue 5 https://doi.org/10.1063/1.859023	journal	May 1989
Considerations of ion‐temperature‐gradient‐driven turbulence Cowley, S. C.; Kulsrud, R. M.; Sudan, R. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 10 https://doi.org/10.1063/1.859913	journal	October 1991
A fully nonlinear characteristic method for gyrokinetic simulation Parker, S. E.; Lee, W. W. Physics of Fluids B: Plasma Physics, Vol. 5, Issue 1 https://doi.org/10.1063/1.860870	journal	January 1993
Gyrofluid turbulence models with kinetic effects Dorland, W.; Hammett, G. W. Physics of Fluids B: Plasma Physics, Vol. 5, Issue 3 https://doi.org/10.1063/1.860934	journal	March 1993
Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria Frieman, E. A. Physics of Fluids, Vol. 25, Issue 3 https://doi.org/10.1063/1.863762	journal	January 1982
Nonlinear gyrokinetic equations Dubin, Daniel H. E. Physics of Fluids, Vol. 26, Issue 12 https://doi.org/10.1063/1.864113	journal	January 1983
Gyrokinetic approach in particle simulation Lee, W. W. Physics of Fluids, Vol. 26, Issue 2 https://doi.org/10.1063/1.864140	journal	January 1983
Nonlinear gyrokinetic equations for tokamak microturbulence Hahm, T. S. Physics of Fluids, Vol. 31, Issue 9 https://doi.org/10.1063/1.866544	journal	September 1988
Generalized weighting scheme for δ f particle‐simulation method Hu, Genze; Krommes, John A. Physics of Plasmas, Vol. 1, Issue 4 https://doi.org/10.1063/1.870745	journal	April 1994
Nondimensional transport scaling in DIII‐D: Bohm versus gyro‐Bohm resolved Petty, C. C.; Luce, T. C.; Burrell, K. H. Physics of Plasmas, Vol. 2, Issue 6 https://doi.org/10.1063/1.871259	journal	June 1995
Gyrokinetic theory for arbitrary wavelength electromagnetic modes in tokamaks Qin, H.; Tang, W. M.; Rewoldt, G. Physics of Plasmas, Vol. 5, Issue 4 https://doi.org/10.1063/1.872633	journal	April 1998
Large-scale gyrokinetic turbulence simulations: Effects of profile variation Parker, Scott E.; Kim, Charlson; Chen, Yang Physics of Plasmas, Vol. 6, Issue 5 https://doi.org/10.1063/1.873429	journal	May 1999
Comparisons and physics basis of tokamak transport models and turbulence simulations Dimits, A. M.; Bateman, G.; Beer, M. A. Physics of Plasmas, Vol. 7, Issue 3 https://doi.org/10.1063/1.873896	journal	March 2000
Microinstability theory in tokamaks Tang, W. M. Nuclear Fusion, Vol. 18, Issue 8 https://doi.org/10.1088/0029-5515/18/8/006	journal	August 1978
Gyrokinetic simulations of ETG and ITG turbulence Dimits, A. M.; Nevins, W. M.; Shumaker, D. E. Nuclear Fusion, Vol. 47, Issue 8 https://doi.org/10.1088/0029-5515/47/8/012	journal	July 2007
Nonlinear interplay of TEM and ITG turbulence and its effect on transport Merz, F.; Jenko, F. Nuclear Fusion, Vol. 50, Issue 5 https://doi.org/10.1088/0029-5515/50/5/054005	journal	April 2010
Linearized gyro-kinetics Catto, P. J. Plasma Physics, Vol. 20, Issue 7 https://doi.org/10.1088/0032-1028/20/7/011	journal	July 1978
Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria Ellison, C. Leland; Finn, J. M.; Qin, H. Plasma Physics and Controlled Fusion, Vol. 57, Issue 5 https://doi.org/10.1088/0741-3335/57/5/054007	journal	April 2015
Symplectic integration of Hamiltonian systems Channell, P. J.; Scovel, C. Nonlinearity, Vol. 3, Issue 2 https://doi.org/10.1088/0951-7715/3/2/001	journal	May 1990
Variational approach to low-frequency kinetic-MHD in the current coupling scheme Burby, Joshua W.; Tronci, Cesare Plasma Physics and Controlled Fusion, Vol. 59, Issue 4 https://doi.org/10.1088/1361-6587/aa5c5b	journal	March 2017
Structure-preserving geometric particle-in-cell methods for Vlasov-Maxwell systems Xiao, Jianyuan; Qin, Hong; Liu, Jian Plasma Science and Technology, Vol. 20, Issue 11 https://doi.org/10.1088/2058-6272/aac3d1	journal	September 2018
Effective-action approach to wave propagation in scalar QED plasmas Shi, Yuan; Fisch, Nathaniel J.; Qin, Hong Physical Review A, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevA.94.012124	journal	July 2016
Formation of current singularity in a topologically constrained plasma Zhou, Yao; Huang, Yi-Min; Qin, Hong Physical Review E, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevE.93.023205	journal	February 2016
Explicit symplectic algorithms based on generating functions for charged particle dynamics Zhang, Ruili; Qin, Hong; Tang, Yifa Physical Review E, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevE.94.013205	journal	July 2016
Simulations of relativistic quantum plasmas using real-time lattice scalar QED Shi, Yuan; Xiao, Jianyuan; Qin, Hong Physical Review E, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevE.97.053206	journal	May 2018
Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields Qin, Hong; Guan, Xiaoyin Physical Review Letters, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevLett.100.035006	journal	January 2008
Global Gyrokinetic Simulation of Tokamak Edge Pedestal Instabilities Wan, Weigang; Parker, Scott E.; Chen, Yang Physical Review Letters, Vol. 109, Issue 18 https://doi.org/10.1103/PhysRevLett.109.185004	journal	November 2012
Diffusion of Plasma Across a Magnetic Field Taylor, J. B. Physical Review Letters, Vol. 6, Issue 6 https://doi.org/10.1103/PhysRevLett.6.262	journal	March 1961
Fluid moment models for Landau damping with application to the ion-temperature-gradient instability Hammett, Gregory W.; Perkins, Francis W. Physical Review Letters, Vol. 64, Issue 25 https://doi.org/10.1103/PhysRevLett.64.3019	journal	June 1990
Magnetic-field scaling of dimensionally similar tokamak discharges Waltz, R. E.; DeBoo, J. C.; Rosenbluth, M. N. Physical Review Letters, Vol. 65, Issue 19 https://doi.org/10.1103/PhysRevLett.65.2390	journal	November 1990
Gyrokinetic simulation of ion temperature gradient driven turbulence in 3D toroidal geometry Parker, S. E.; Lee, W. W.; Santoro, R. A. Physical Review Letters, Vol. 71, Issue 13 https://doi.org/10.1103/PhysRevLett.71.2042	journal	September 1993
Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks Dimits, A. M.; Williams, T. J.; Byers, J. A. Physical Review Letters, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevLett.77.71	journal	July 1996
Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence Rogers, B. N.; Dorland, W.; Kotschenreuther, M. Physical Review Letters, Vol. 85, Issue 25 https://doi.org/10.1103/PhysRevLett.85.5336	journal	December 2000
Particle simulation of plasmas Dawson, John M. Reviews of Modern Physics, Vol. 55, Issue 2 https://doi.org/10.1103/RevModPhys.55.403	journal	April 1983
Drift waves and transport Horton, W. Reviews of Modern Physics, Vol. 71, Issue 3 https://doi.org/10.1103/RevModPhys.71.735	journal	April 1999
A Can0nical Integrati0n Technique Ruth, Ronald D. IEEE Transactions on Nuclear Science, Vol. 30, Issue 4 https://doi.org/10.1109/TNS.1983.4332919	journal	August 1983
Turbulent Transport Reduction by Zonal Flows: Massively Parallel Simulations Lin, Z. Science, Vol. 281, Issue 5384 https://doi.org/10.1126/science.281.5384.1835	journal	September 1998
Plasma Physics via Computer Simulation Birdsall, C. K.; Langdon, A. B. https://doi.org/10.1887/0750301171	book	January 1991
Fully Kinetic Simulation of Ion-Temperature-Gradient Instabilities in Tokamaks Hu, Youjun; Miecnikowski, Matthew; Chen, Yang Plasma, Vol. 1, Issue 1 https://doi.org/10.3390/plasma1010010	journal	May 2018

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