Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

Hakim, Ammar H.; Mandell, Noah R.; Bernard, T. N.; Francisquez, M.; Hammett, G. W.; Shi, E. L.

doi:10.1063/1.5141157

Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

Journal Article · Tue Apr 07 00:00:00 EDT 2020 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5141157· OSTI ID:1668050

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Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Univ., NJ (United States)
General Atomics, San Diego, CA (United States); Univ. of Texas, Austin, TX (United States)
MIT Plasma Science and Fusion Center, Cambridge, MA (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Here, we present algorithms and results from Gkeyll, a full-f continuum, electromagnetic gyrokinetic code, designed to study turbulence in the edge region of fusion devices. The edge is computationally very challenging, requiring robust algorithms that can handle large-amplitude fluctuations and stable interactions with plasma sheaths. We present an energy-conserving high-order discontinuous Galerkin scheme that solves gyrokinetic equations in Hamiltonian form. Efficiency is improved by a careful choice of basis functions and automatically generated computation kernels. Previous verification tests were performed in the straight-field-line large plasma device [Shi et al., J. Plasma Phys. 83, 905830304 (2017)] and the Texas Helimak, a simple magnetized torus [Bernard et al., Phys. Plasmas 26, 042301 (2019)], including the effect of end-plate biasing on turbulence. Results for the scrape-off layer for NSTX parameters with a model helical magnetic geometry with bad curvature have been obtained [Shi et al., Phys. Plasmas 26, 012307 (2019)]. In this paper, we present algorithms for the two formulations of electromagnetic gyrokinetics: the Hamiltonian and the symplectic. We describe each formulation and show results of benchmark tests. Although our scheme works for the Hamiltonian formulation, the presence of spurious numerical modes for high-β and large $$k^2_⊥ρ^2_s$$ regimes shows that the symplectic formulation is more robust. We then review our recent algorithm for the symplectic formulation [Mandell et al., J. Plasma Phys. 86, 905860109 (2020)], along with example application of this new capability. Maintaining positivity of the distribution function can be challenging, and we describe a new and novel exponential recovery based algorithm to address this.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466; FC02-08ER54966; FG02-04ER54742; FG02-95ER54309; FG02-97ER25308

OSTI ID:: 1668050

Alternate ID(s):: OSTI ID: 1608504

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 4 Vol. 27; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (44)

Electron Physics in 3-D Two-Fluid 10-Moment Modeling of Ganymede's Magnetosphere Wang, Liang; Germaschewski, Kai; Hakim, Ammar Journal of Geophysical Research: Space Physics, Vol. 123, Issue 4 https://doi.org/10.1002/2017JA024761	journal	April 2018
Nonlinear Dynamics in the Tokamak Edge Scott, B. D.; Kendl, A.; Ribeiro, T. Contributions to Plasma Physics, Vol. 50, Issue 3-5 https://doi.org/10.1002/ctpp.201010039	journal	May 2010
The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V Cockburn, Bernardo; Shu, Chi-Wang Journal of Computational Physics, Vol. 141, Issue 2 https://doi.org/10.1006/jcph.1998.5892	journal	April 1998
A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows Liu, Jian-Guo; Shu, Chi-Wang Journal of Computational Physics, Vol. 160, Issue 2 https://doi.org/10.1006/jcph.2000.6475	journal	May 2000
The Serendipity Family of Finite Elements Arnold, Douglas N.; Awanou, Gerard Foundations of Computational Mathematics, Vol. 11, Issue 3 https://doi.org/10.1007/s10208-011-9087-3	journal	March 2011
Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities Kotschenreuther, Mike; Rewoldt, G.; Tang, W. M. Computer Physics Communications, Vol. 88, Issue 2-3 https://doi.org/10.1016/0010-4655(95)00035-E	journal	August 1995
Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I Arakawa, Akio Journal of Computational Physics, Vol. 1, Issue 1 https://doi.org/10.1016/0021-9991(66)90015-5	journal	August 1966
A δf particle method for gyrokinetic simulations with kinetic electrons and electromagnetic perturbations Chen, Yang; Parker, Scott E. Journal of Computational Physics, Vol. 189, Issue 2 https://doi.org/10.1016/S0021-9991(03)00228-6	journal	August 2003
A numerical instability in an ADI algorithm for gyrokinetics Belli, E. A.; Hammett, G. W. Computer Physics Communications, Vol. 172, Issue 2 https://doi.org/10.1016/j.cpc.2005.06.007	journal	November 2005
A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm Chen, G.; Chacón, L. Computer Physics Communications, Vol. 197 https://doi.org/10.1016/j.cpc.2015.08.008	journal	December 2015
A high resolution wave propagation scheme for ideal Two-Fluid plasma equations Hakim, A.; Loverich, J.; Shumlak, U. Journal of Computational Physics, Vol. 219, Issue 1 https://doi.org/10.1016/j.jcp.2006.03.036	journal	November 2006
Electromagnetic gyrokinetic PIC simulation with an adjustable control variates method Hatzky, R.; Könies, A.; Mishchenko, A. Journal of Computational Physics, Vol. 225, Issue 1 https://doi.org/10.1016/j.jcp.2006.12.019	journal	July 2007
Discontinuous Galerkin algorithms for fully kinetic plasmas Juno, J.; Hakim, A.; TenBarge, J. Journal of Computational Physics, Vol. 353 https://doi.org/10.1016/j.jcp.2017.10.009	journal	January 2018
Plasma-material boundary conditions for discontinuous Galerkin continuum-kinetic simulations, with a focus on secondary electron emission Cagas, Petr; Hakim, Ammar; Srinivasan, Bhuvana Journal of Computational Physics, Vol. 406 https://doi.org/10.1016/j.jcp.2019.109215	journal	April 2020
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. Journal of Plasma Physics, Vol. 83, Issue 3 https://doi.org/10.1017/S002237781700037X	journal	May 2017
Effect of a weak ion collisionality on the dynamics of kinetic electrostatic shocks Sundström, Andréas; Juno, James; TenBarge, Jason M. Journal of Plasma Physics, Vol. 85, Issue 1 https://doi.org/10.1017/S0022377819000023	journal	February 2019
Electromagnetic full- gyrokinetics in the tokamak edge with discontinuous Galerkin methods Mandell, N. R.; Hakim, A.; Hammett, G. W. Journal of Plasma Physics, Vol. 86, Issue 1 https://doi.org/10.1017/S0022377820000070	journal	February 2020
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems Cockburn, Bernardo; Shu, Chi-Wang Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261 https://doi.org/10.1023/A:1012873910884	journal	September 2001
Global Ten‐Moment Multifluid Simulations of the Solar Wind Interaction with Mercury: From the Planetary Conducting Core to the Dynamic Magnetosphere Dong, Chuanfei; Wang, Liang; Hakim, Ammar Geophysical Research Letters, Vol. 46, Issue 21 https://doi.org/10.1029/2019GL083180	journal	November 2019
An Extended MHD Study of the 16 October 2015 MMS Diffusion Region Crossing TenBarge, J. M.; Ng, J.; Juno, J. Journal of Geophysical Research: Space Physics, Vol. 124, Issue 11 https://doi.org/10.1029/2019JA026731	journal	November 2019
Gyrokinetic turbulence simulations with kinetic electrons Chen, Yang; Parker, Scott Physics of Plasmas, Vol. 8, Issue 5 https://doi.org/10.1063/1.1351828	journal	May 2001
Conventional δf-particle simulations of electromagnetic perturbations with finite elements Mishchenko, Alexey; Hatzky, Roman; Könies, Axel Physics of Plasmas, Vol. 11, Issue 12 https://doi.org/10.1063/1.1812275	journal	December 2004
Model Fokker-Planck Equation for a Plasma and Its Solution Dougherty, J. P. Physics of Fluids, Vol. 7, Issue 11 https://doi.org/10.1063/1.2746779	journal	January 1964
Intermittent convective transport carried by propagating electromagnetic filamentary structures in nonuniformly magnetized plasma Xu, G. S.; Naulin, V.; Fundamenski, W. Physics of Plasmas, Vol. 17, Issue 2 https://doi.org/10.1063/1.3302535	journal	February 2010
Finite-β simulation of microinstabilities Startsev, Edward A.; Lee, W. W. Physics of Plasmas, Vol. 21, Issue 2 https://doi.org/10.1063/1.4863847	journal	February 2014
Pullback transformation in gyrokinetic electromagnetic simulations Mishchenko, Alexey; Könies, Axel; Kleiber, Ralf Physics of Plasmas, Vol. 21, Issue 9 https://doi.org/10.1063/1.4895501	journal	September 2014
Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection Wang, Liang; Hakim, Ammar H.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 1 https://doi.org/10.1063/1.4906063	journal	January 2015
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse Shi, E. L.; Hakim, A. H.; Hammett, G. W. Physics of Plasmas, Vol. 22, Issue 2 https://doi.org/10.1063/1.4907160	journal	February 2015
Continuum kinetic and multi-fluid simulations of classical sheaths Cagas, P.; Hakim, A.; Juno, J. Physics of Plasmas, Vol. 24, Issue 2 https://doi.org/10.1063/1.4976544	journal	February 2017
Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code Hager, Robert; Lang, Jianying; Chang, C. S. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4983320	journal	May 2017
Simulations of anti-parallel reconnection using a nonlocal heat flux closure Ng, Jonathan; Hakim, Ammar; Bhattacharjee, A. Physics of Plasmas, Vol. 24, Issue 8 https://doi.org/10.1063/1.4993195	journal	August 2017
Nonlinear saturation of the Weibel instability Cagas, P.; Hakim, A.; Scales, W. Physics of Plasmas, Vol. 24, Issue 11 https://doi.org/10.1063/1.4994682	journal	November 2017
A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons Bao, J.; Lin, Z.; Lu, Z. X. Physics of Plasmas, Vol. 25, Issue 2 https://doi.org/10.1063/1.5016432	journal	February 2018
Full- f gyrokinetic simulation of turbulence in a helical open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. Physics of Plasmas, Vol. 26, Issue 1 https://doi.org/10.1063/1.5074179	journal	January 2019
Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak Bernard, T. N.; Shi, E. L.; Gentle, K. W. Physics of Plasmas, Vol. 26, Issue 4 https://doi.org/10.1063/1.5085457	journal	April 2019
Collisional effects on kinetic electromagnetic modes and associated quasilinear transport Rewoldt, G.; Tang, W. M.; Hastie, R. J. Physics of Fluids, Vol. 30, Issue 3 https://doi.org/10.1063/1.866332	journal	January 1987
Gyrokinetic field theory Sugama, H. Physics of Plasmas, Vol. 7, Issue 2 https://doi.org/10.1063/1.873832	journal	February 2000
Three-dimensional computation of drift Alfvén turbulence Scott, B. Plasma Physics and Controlled Fusion, Vol. 39, Issue 10 https://doi.org/10.1088/0741-3335/39/10/010	journal	October 1997
Low Mach-number collisionless electrostatic shocks and associated ion acceleration Pusztai, I.; TenBarge, J. M.; Csapó, A. N. Plasma Physics and Controlled Fusion, Vol. 60, Issue 3 https://doi.org/10.1088/1361-6587/aaa2cc	journal	January 2018
Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments Zhang, Xiangxiong; Shu, Chi-Wang Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 467, Issue 2134 https://doi.org/10.1098/rspa.2011.0153	journal	May 2011
Plasma Oscillations with Diffusion in Velocity Space Lenard, A.; Bernstein, Ira B. Physical Review, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRev.112.1456	journal	December 1958
Foundations of nonlinear gyrokinetic theory Brizard, A. J.; Hahm, T. S. Reviews of Modern Physics, Vol. 79, Issue 2 https://doi.org/10.1103/RevModPhys.79.421	journal	April 2007
Hamiltonian theory of guiding-center motion Cary, John R.; Brizard, Alain J. Reviews of Modern Physics, Vol. 81, Issue 2 https://doi.org/10.1103/RevModPhys.81.693	journal	May 2009
Temperature-dependent Saturation of Weibel-type Instabilities in Counter-streaming Plasmas Skoutnev, V.; Hakim, A.; Juno, J. The Astrophysical Journal, Vol. 872, Issue 2 https://doi.org/10.3847/2041-8213/ab0556	journal	February 2019

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