A hybrid gyrokinetic ion and isothermal electron fluid code for astrophysical plasma. (English) Zbl 1391.76872

Summary: This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) [A. A. Schekochihin et al., “Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magentized weakly collisional plasmas”, Astrophys. J. Suppl. Ser. 182, No. 1, 310–377 (2009; doi:10.1088/0067-0049/182/1/310)]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into AstroGK, an Eulerian \(\delta f\) gyrokinetics code specialized to a slab geometry [R. Numata et al., J. Comput. Phys. 229, No. 24, 9347–9372 (2010; Zbl 1204.85021)]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant-Friedrichs-Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs \(\sim 2 \sqrt{m_i / m_e} \sim 100\) times faster than AstroGK with a single ion species and kinetic electrons where \(m_i / m_e\) is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron-ion temperature ratio and plasma beta.


76X05 Ionized gas flow in electromagnetic fields; plasmic flow
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics


Zbl 1204.85021
Full Text: DOI arXiv


[1] Rutherford, P. H.; Frieman, E., Drift instabilities in general magnetic field configurations, Phys. Fluids, 11, 3, 569-585, (1968)
[2] Taylor, J.; Hastie, R., Stability of general plasma equilibria-i formal theory, Phys. Fluids, 10, 5, 479, (1968) · Zbl 0159.29602
[3] Catto, P. J., Linearized gyro-kinetics, Plasma Phys., 20, 7, 719, (1978)
[4] Frieman, E.; Chen, L., Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria, Phys. Fluids, 25, 3, 502-508, (1982) · Zbl 0506.76133
[5] Brizard, A.; Hahm, T., Foundations of nonlinear gyrokinetic theory, Rev. Mod. Phys., 79, 2, 421, (2007) · Zbl 1205.76309
[6] Dimits, A. M.; Bateman, G.; Beer, M.; Cohen, B.; Dorland, W.; Hammett, G.; Kim, C.; Kinsey, J.; Kotschenreuther, M.; Kritz, A., Comparisons and physics basis of tokamak transport models and turbulence simulations, Phys. Plasmas, 7, 3, 969-983, (2000)
[7] Garbet, X.; Idomura, Y.; Villard, L.; Watanabe, T., Gyrokinetic simulations of turbulent transport, Nucl. Fusion, 50, 4, (2010)
[8] Howes, G. G.; Cowley, S. C.; Dorland, W.; Hammett, G. W.; Quataert, E.; Schekochihin, A. A., Astrophysical gyrokinetics: basic equations and linear theory, Astrophys. J., 651, 1, 590, (2006)
[9] Schekochihin, A.; Cowley, S.; Dorland, W.; Hammett, G.; Howes, G.; Quataert, E.; Tatsuno, T., Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas, Astrophys. J. Suppl. Ser., 182, 1, 310, (2009)
[10] Howes, G.; Dorland, W.; Cowley, S.; Hammett, G.; Quataert, E.; Schekochihin, A.; Tatsuno, T., Kinetic simulations of magnetized turbulence in astrophysical plasmas, Phys. Rev. Lett., 100, 6, (2008)
[11] Howes, G. G.; TenBarge, J. M.; Dorland, W.; Quataert, E.; Schekochihin, A. A.; Numata, R.; Tatsuno, T., Gyrokinetic simulations of solar wind turbulence from ion to electron scales, Phys. Rev. Lett., 107, 3, (2011)
[12] TenBarge, J.; Podesta, J.; Klein, K.; Howes, G., Interpreting magnetic variance anisotropy measurements in the solar wind, Astrophys. J., 753, 2, 107, (2012)
[13] Told, D.; Jenko, F.; TenBarge, J.; Howes, G.; Hammett, G., Multiscale nature of the dissipation range in gyrokinetic simulations of alfvénic turbulence, Phys. Rev. Lett., 115, 2, (2015)
[14] Navarro, A. B.; Teaca, B.; Told, D.; Groselj, D.; Crandall, P.; Jenko, F., Structure of plasma heating in gyrokinetic alfvénic turbulence, Phys. Rev. Lett., 117, 24, (2016)
[15] Howes, G. G., A prospectus on kinetic heliophysics, Phys. Plasmas, 24, 5, (2017)
[16] Bourouaine, S.; Howes, G. G., The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence, J. Plasma Phys., 83, 3, (2017)
[17] Klein, K. G.; Howes, G. G.; TenBarge, J. M., Diagnosing collisionless energy transfer using field-particle correlations: gyrokinetic turbulence, preprint
[18] Snyder, P. B., Gyrofluid theory and simulation of electromagnetic turbulence and transport in tokamak plasmas, (1999), Princeton University, Ph.D. thesis
[19] Snyder, P.; Hammett, G., A Landau fluid model for electromagnetic plasma microturbulence, Phys. Plasmas, 8, 7, 3199-3216, (2001)
[20] Sgro, A.; Nielson, C., Hybrid model studies of ion dynamics and magnetic field diffusion during pinch implosions, Phys. Fluids, 19, 1, 126-133, (1976)
[21] Byers, J.; Cohen, B.; Condit, W.; Hanson, J., Hybrid simulations of quasineutral phenomena in magnetized plasma, J. Comput. Phys., 27, 3, 363-396, (1978)
[22] Hewett, D.; Nielson, C., A multidimensional quasineutral plasma simulation model, J. Comput. Phys., 29, 2, 219-236, (1978) · Zbl 0388.76108
[23] Hewett, D., A global method of solving the electron-field equations in a zero-inertia-electron-hybrid plasma simulation code, J. Comput. Phys., 38, 3, 378-395, (1980) · Zbl 0462.76107
[24] Harned, D. S., Quasineutral hybrid simulation of macroscopic plasma phenomena, J. Comput. Phys., 47, 3, 452-462, (1982) · Zbl 0493.76122
[25] Matthews, A. P., Current advance method and cyclic leapfrog for 2d multispecies hybrid plasma simulations, J. Comput. Phys., 112, 1, 102-116, (1994) · Zbl 0801.76057
[26] Liewer, P. C.; Velli, M.; Goldstein, B. E., Alfvén wave propagation and ion cyclotron interactions in the expanding solar wind: one-dimensional hybrid simulations, Phys. Rev. Lett., 106, A12, (2001)
[27] Hellinger, P.; Trávníček, P.; Mangeney, A.; Grappin, R., Hybrid simulations of the expanding solar wind: temperatures and drift velocities, Geophys. Res. Lett., 30, 5, (2003)
[28] Hellinger, P.; Trávníček, P., Magnetosheath compression: role of characteristic compression time, alpha particle abundance, and alpha/proton relative velocity, J. Geophys. Res. Space Phys., 110, A4, (2005)
[29] Kunz, M. W.; Stone, J. M.; Bai, X.-N., Pegasus: a new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics, J. Comput. Phys., 259, 154-174, (2014) · Zbl 1349.82149
[30] Kunz, M. W.; Stone, J. M.; Quataert, E., Magnetorotational turbulence and dynamo in a collisionless plasma, Phys. Rev. Lett., 117, 23, (2016)
[31] Cerri, S.; Franci, L.; Califano, F.; Landi, S.; Hellinger, P., Plasma turbulence at ion scales: a comparison between particle in cell and Eulerian hybrid-kinetic approaches, J. Plasma Phys., 83, 2, (2017)
[32] Groselj, D.; Cerri, S. S.; Navarro, A. B.; Willmott, C.; Told, D.; Loureiro, N. F.; Califano, F.; Jenko, F., Fully-kinetic versus reduced-kinetic modelling of collisionless plasma turbulence, preprint
[33] Valentini, F.; Trávníček, P.; Califano, F.; Hellinger, P.; Mangeney, A., A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma, J. Comput. Phys., 225, 1, 753-770, (2007) · Zbl 1343.76051
[34] Lin, Z.; Chen, L., A fluid-kinetic hybrid electron model for electromagnetic simulations, Phys. Plasmas, 8, 5, 1447-1450, (2001)
[35] Chen, Y.; Parker, S., A gyrokinetic ion zero electron inertia fluid electron model for turbulence simulations, Phys. Plasmas, 8, 2, 441-446, (2001)
[36] Snyder, P.; Hammett, G., Electromagnetic effects on plasma microturbulence and transport, Phys. Plasmas, 8, 3, 744-749, (2001)
[37] Parker, S. E.; Chen, Y.; Kim, C. C., Electromagnetic gyrokinetic-ion drift-fluid-electron hybrid simulation, Comput. Phys. Commun., 127, 1, 59-70, (2000) · Zbl 1040.76528
[38] Abel, I.; Cowley, S., Multiscale gyrokinetics for rotating tokamak plasmas: ii. reduced models for electron dynamics, New J. Phys., 15, 2, (2013)
[39] Hinton, F.; Rosenbluth, M.; Waltz, R., Reduced equations for electromagnetic turbulence in tokamaks, Phys. Plasmas, 10, 1, 168-178, (2003)
[40] Hager, R.; Lang, J.; Chang, C.-S.; Ku, S.; Chen, Y.; Parker, S. E.; Adams, M. F., Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the xgc code, Phys. Plasmas, 24, 5, (2017)
[41] Numata, R.; Howes, G. G.; Tatsuno, T.; Barnes, M.; Dorland, W., Astrogk: astrophysical gyrokinetics code, J. Comput. Phys., 229, 24, 9347-9372, (2010) · Zbl 1204.85021
[42] Kotschenreuther, M.; Rewoldt, G.; Tang, W., Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities, Comput. Phys. Commun., 88, 2, 128-140, (1995) · Zbl 0923.76198
[43] Dorland, W.; Jenko, F.; Kotschenreuther, M.; Rogers, B., Electron temperature gradient turbulence, Phys. Rev. Lett., 85, 26, 5579, (2000)
[44] Tatsuno, T.; Dorland, W.; Schekochihin, A.; Plunk, G.; Barnes, M.; Cowley, S.; Howes, G., Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence, Phys. Rev. Lett., 103, 1, (2009)
[45] Tatsuno, T.; Barnes, M.; Dorland, W.; Numata, R.; Plunk, G.; Cowley, S.; Howes, G.; Schekochihin, A., Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence, J. Plasma Fusion Res., 9, 509-516, (2010)
[46] Tatsuno, T.; Plunk, G.; Barnes, M.; Dorland, W.; Howes, G.; Numata, R., Freely decaying turbulence in two-dimensional electrostatic gyrokinetics, Phys. Plasmas, 19, 12, (2012)
[47] Plunk, G.; Tatsuno, T., Energy transfer and dual cascade in kinetic magnetized plasma turbulence, Phys. Rev. Lett., 106, 16, (2011)
[48] Numata, R.; Dorland, W.; Howes, G. G.; Loureiro, N. F.; Rogers, B. N.; Tatsuno, T., Gyrokinetic simulations of the tearing instability, Phys. Plasmas, 18, 11, (2011)
[49] Kobayashi, S.; Rogers, B. N.; Numata, R., Gyrokinetic simulations of collisionless reconnection in turbulent non-uniform plasmas, Phys. Plasmas, 21, 4, (2014)
[50] Numata, R.; Loureiro, N., Ion and electron heating during magnetic reconnection in weakly collisional plasmas, J. Plasma Phys., 81, 02, (2015)
[51] Zocco, A.; Loureiro, N.; Dickinson, D.; Numata, R.; Roach, C., Kinetic microtearing modes and reconnecting modes in strongly magnetised slab plasmas, Plasma Phys. Control. Fusion, 57, 6, (2015)
[52] Abel, I.; Barnes, M.; Cowley, S.; Dorland, W.; Schekochihin, A., Linearized model Fokker-Planck collision operators for gyrokinetic simulations. i. theory, Phys. Plasmas, 15, 12, (2008)
[53] Barnes, M.; Abel, I.; Dorland, W.; Ernst, D.; Hammett, G.; Ricci, P.; Rogers, B.; Schekochihin, A.; Tatsuno, T., Linearized model Fokker-Planck collision operators for gyrokinetic simulations. ii. numerical implementation and tests, Phys. Plasmas, 16, 7, (2009)
[54] Y. Kawazura, M. Barnes, A.A. Schekochihin, in preparation.
[55] Courant, R.; Friedrichs, K.; Lewy, H., On the partial difference equations of mathematical physics, IBM J., 11, 2, 215-234, (1967) · Zbl 0145.40402
[56] Beam, R. M.; Warming, R. F., An implicit finite-difference algorithm for hyperbolic systems in conservation-law form, J. Comput. Phys., 22, 1, 87-110, (1976) · Zbl 0336.76021
[57] Orszag, S. A., On the elimination of aliasing in finite-difference schemes by filtering high-wavenumber components, J. Atmos. Sci., 28, 6, 1074, (1971)
[58] TenBarge, J.; Howes, G. G.; Dorland, W.; Hammett, G. W., An oscillating Langevin antenna for driving plasma turbulence simulations, Comput. Phys. Commun., 185, 2, 578-589, (2014) · Zbl 1348.76087
[59] Goldreich, P.; Sridhar, S., Toward a theory of interstellar turbulence. 2: strong alfvenic turbulence, Astrophys. J., 438, 763-775, (1995)
[60] Orszag, S. A.; Tang, C.-M., Small-scale structure of two-dimensional magnetohydrodynamic turbulence, J. Fluid Mech., 90, 01, 129-143, (1979)
[61] Biskamp, D.; Welter, H., Dynamics of decaying two-dimensional magnetohydrodynamic turbulence, Phys. Fluids, B Plasma Phys., 1, 10, 1964-1979, (1989)
[62] Loureiro, N.; Dorland, W.; Fazendeiro, L.; Kanekar, A.; Mallet, A.; Vilelas, M.; Zocco, A., Viriato: a Fourier-Hermite spectral code for strongly magnetized fluid-kinetic plasma dynamics, Comput. Phys. Commun., 206, 45-63, (2016) · Zbl 1375.76129
[63] Li, T. C.; Howes, G. G.; Klein, K. G.; TenBarge, J. M., Energy dissipation and Landau damping in two-and three-dimensional plasma turbulence, Astrophys. J. Lett., 832, 2, L24, (2016)
[64] Schekochihin, A.; Cowley, S.; Dorland, W.; Hammett, G.; Howes, G.; Plunk, G.; Quataert, E.; Tatsuno, T., Gyrokinetic turbulence: a nonlinear route to dissipation through phase space, Plasma Phys. Control. Fusion, 50, 12, (2008)
[65] Plunk, G.; Cowley, S.; Schekochihin, A.; Tatsuno, T., Two-dimensional gyrokinetic turbulence, J. Fluid Mech., 664, 407-435, (2010) · Zbl 1221.76108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.