Pegasus: a new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics. (English) Zbl 1349.82149

Summary: We describe Pegasus, a new hybrid-kinetic particle-in-cell code tailored for the study of astrophysical plasma dynamics. The code incorporates an energy-conserving particle integrator into a stable, second-order-accurate, three-stage predictor-predictor-corrector integration algorithm. The constrained transport method is used to enforce the divergence-free constraint on the magnetic field. A \(\delta f\) scheme is included to facilitate a reduced-noise study of systems in which only small departures from an initial distribution function are anticipated. The effects of rotation and shear are implemented through the shearing-sheet formalism with orbital advection. These algorithms are embedded within an architecture similar to that used in the popular astrophysical magnetohydrodynamics code Athena, one that is modular, well-documented, easy to use, and efficiently parallelized for use on thousands of processors. We present a series of tests in one, two, and three spatial dimensions that demonstrate the fidelity and versatility of the code.


82D10 Statistical mechanics of plasmas
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
Full Text: DOI arXiv


[1] Sharma, P.; Hammett, G. W.; Quataert, E.; Stone, J. M., Shearing box simulations of the MRI in a collisionless plasma, Astrophys. J., 637, 952-967, (February 2006)
[2] Kunz, M. W.; Bogdanović, T.; Reynolds, C. S.; Stone, J. M., Buoyancy instabilities in a weakly collisional intracluster medium, Astrophys. J., 754, 122, (August 2012)
[3] Byers, J. A.; Cohen, B. I.; Condit, W. C.; Hanson, J. D., Hybrid simulations of quasineutral phenomena in magnetized plasma, J. Comput. Phys., 27, 363-396, (June 1978)
[4] Hewett, D. W.; Nielson, C. W., A multidimensional quasineutral plasma simulation model, J. Comput. Phys., 29, 219-236, (November 1978)
[5] Winske, D.; Omidi, N., Hybrid codes: methods and applications, (Matsumoto, H.; Omura, Y., Computer Space Plasma Physics: Simulation Techniques and Software, (1993), TERRAPUB), 103-160
[6] Lipatov, A. S., The hybrid multiscale simulation technology: an introduction with application to astrophysical and laboratory plasmas, (2002), Springer Berlin · Zbl 1015.76001
[7] Winske, D.; Yin, L.; Omidi, N.; Karimabadi, H.; Quest, K., Hybrid simulation codes: past, present and future - A tutorial, (Büchner, J.; Dum, C.; Scholer, M., Space Plasma Simulation, Lecture Notes in Physics, vol. 615, (2003), Springer-Verlag Berlin), 136-165
[8] Stone, J. M.; Gardiner, T. A.; Teuben, P.; Hawley, J. F.; Simon, J. B., Athena: A new code for astrophysical MHD, Astrophys. J. Suppl. Ser., 178, 137-177, (September 2008)
[9] Goldreich, P.; Lynden-Bell, D., II. spiral arms as sheared gravitational instabilities, Mon. Not. R. Astron. Soc., 130, 125, (1965)
[10] Hawley, J. F.; Gammie, C. F.; Balbus, S. A., Local three-dimensional magnetohydrodynamic simulations of accretion disks, Astrophys. J., 440, 742, (February 1995)
[11] Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C., A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma, Mon. Not. R. Astron. Soc., 413, 7-38, (May 2011)
[12] Takizuka, T.; Abe, H., A binary collision model for plasma simulation with a particle code, J. Comput. Phys., 25, 205-219, (November 1977)
[13] Dimits, A. M.; Cohen, B. I., Collision operators for partially linearized particle simulation codes, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., 49, 709-721, (January 1994)
[14] Miller, R. H.; Combi, M. R., A Coulomb collision algorithm for weighted particle simulations, Geophys. Res. Lett., 21, 1735-1738, (August 1994)
[15] Jones, M., A grid-based Coulomb collision model for PIC codes, J. Comput. Phys., 123, 169-181, (January 1996)
[16] Manheimer, W. M.; Lampe, M.; Joyce, G., Langevin representation of Coulomb collisions in PIC simulations, J. Comput. Phys., 138, 563-584, (December 1997)
[17] Larson, D. J., A Coulomb collision model for PIC plasma simulation, J. Comput. Phys., 188, 123-138, (June 2003)
[18] Chen, Y.; Parker, S. E., Coarse-graining phase space in δf particle-in-cell simulations, Phys. Plasmas, 14, 8, 082301, (August 2007)
[19] Sherlock, M., A Monte-Carlo method for Coulomb collisions in hybrid plasma models, J. Comput. Phys., 227, 2286-2292, (February 2008)
[20] Lemons, D. S.; Winske, D.; Daughton, W.; Albright, B., Small-angle Coulomb collision model for particle-in-cell simulations, J. Comput. Phys., 228, 1391-1403, (March 2009)
[21] Hellinger, P.; Trávníček, P. M., Langevin representation of Coulomb collisions for bi-Maxwellian plasmas, J. Comput. Phys., 229, 5432-5439, (August 2010)
[22] Krommes, J. A.; Hu, G., The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox, Phys. Plasmas, 1, 3211-3238, (October 1994)
[23] Krommes, J. A., Thermostatted δf, Phys. Plasmas, 6, 1477-1494, (May 1999)
[24] Boris, J. P., Relativistic plasma simulation-optimization of a hybrid code, (Proc. Fourth Conf. Num. Sim. Plasmas, (1970), Naval Res. Lab), 3-67
[25] Bai, X.-N.; Stone, J. M., Particle-gas dynamics with athena: method and convergence, Astrophys. J. Suppl. Ser., 190, 297-310, (October 2010)
[26] Birdsall, C. K.; Langdon, A. B., Plasma physics via computer simulations, (1991), McGraw-Hill New York
[27] Lehe, R.; Parrish, I. J.; Quataert, E., The heating of test particles in numerical simulations of alfvénic turbulence, Astrophys. J., 707, 404-419, (December 2009)
[28] Parker, S. E.; Lee, W. W., A fully nonlinear characteristic method for gyrokinetic simulation, Phys. Fluids, B Plasma Phys., 5, 77-86, (January 1993)
[29] Hu, G.; Krommes, J. A., Generalized weighting scheme for delta f particle-simulation method, Phys. Plasmas, 1, 863-874, (April 1994)
[30] Denton, R. E.; Kotschenreuther, M., δf algorithm, J. Comput. Phys., 119, 283-294, (January 1995)
[31] Belova, E. V.; Denton, R. E.; Chan, A. A., Hybrid simulations of the effects of energetic particles on low-frequency MHD waves, J. Comput. Phys., 136, 324-336, (September 1997)
[32] Belova, E. V.; Jardin, S. C.; Ji, H.; Yamada, M.; Kulsrud, R., Numerical study of tilt stability of prolate field-reversed configurations, Phys. Plasmas, 7, 4996-5006, (December 2000)
[33] Cheng, J.; Parker, S. E.; Chen, Y.; Uzdensky, D. A., A second-order semi-implicit δf method for hybrid simulation, J. Comput. Phys., 245, 364-375, (July 2013)
[34] 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, 753-770, (July 2007)
[35] Tristan, O. Buneman, The 3-d electromagnetic particle code, (Matsumoto, H.; Omura, Y., Computer Space Plasma Physics: Simulation Techniques and Software, (1993), TERRAPUB), 67-84
[36] Spitkovsky, A., Simulations of relativistic collisionless shocks: shock structure and particle acceleration, (Bulik, T.; Rudak, B.; Madejski, G., Astrophysical Sources of High Energy Particles and Radiation, American Institute of Physics Conference Series, vol. 801, (November 2005)), 345-350
[37] Brackbill, J. U.; Barnes, D. C., The effect of nonzero product of magnetic gradient and B on the numerical solution of the magnetohydrodynamic equations, J. Comput. Phys., 35, 426-430, (May 1980)
[38] Ramshaw, J. D., A method for enforcing the solenoidal condition on magnetic field in numerical calculations, J. Comput. Phys., 52, 592, (December 1983)
[39] Evans, C. R.; Hawley, J. F., Simulation of magnetohydrodynamic flows - A constrained transport method, Astrophys. J., 332, 659-677, (September 1988)
[40] Harned, D. S., Quasineutral hybrid simulation of macroscopic plasma phenomena, J. Comput. Phys., 47, 452-462, (September 1982)
[41] Horowitz, E. J.; Shumaker, D. E.; Anderson, D. V., QN3D: A three-dimensional quasi-neutral hybrid particle-in-cell code with applications to the tilt mode instability in field reserved configurations, J. Comput. Phys., 84, 279, (October 1989)
[42] Gargaté, L.; Bingham, R.; Fonseca, R. A.; Silva, L. O., Dhybrid: A massively parallel code for hybrid simulations of space plasmas, Comput. Phys. Commun., 176, 419-425, (March 2007)
[43] Müller, J.; Simon, S.; Motschmann, U.; Schüle, J.; Glassmeier, K.-H.; Pringle, G. J., A.I.K.E.F.: adaptive hybrid model for space plasma simulations, Comput. Phys. Commun., 182, 946-966, (April 2011)
[44] Stone, J. M.; Norman, M. L., ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II. the magnetohydrodynamic algorithms and tests, Astrophys. J. Suppl. Ser., 80, 791, (June 1992)
[45] Gardiner, T. A.; Stone, J. M., An unsplit Godunov method for ideal MHD via constrained transport, J. Comput. Phys., 205, 509-539, (May 2005)
[46] Gardiner, T. A.; Stone, J. M., An unsplit Godunov method for ideal MHD via constrained transport in three dimensions, J. Comput. Phys., 227, 4123-4141, (April 2008)
[47] Swift, D., Use of a hybrid code for global-scale plasma simulation, J. Comput. Phys., 126, 109-121, (June 1996)
[48] Omelchenko, Y. A.; Karimabadi, H., HYPERS: A unidimensional asynchronous framework for multiscale hybrid simulations, J. Comput. Phys., 231, 1766-1780, (February 2012)
[49] Yee, K., Numerical solution of initial boundary value problems involving maxwellʼs equations in isotropic media, IEEE Trans. Antennas Propag., 14, 302-307, (May 1966)
[50] Masset, F., FARGO: A fast Eulerian transport algorithm for differentially rotating disks, Astron. Astrophys. Suppl. Ser., 141, 165-173, (January 2000)
[51] Gammie, C. F., Nonlinear outcome of gravitational instability in cooling, gaseous disks, Astrophys. J., 553, 174-183, (May 2001)
[52] Johnson, B. M.; Guan, X.; Gammie, C. F., Orbital advection by interpolation: A fast and accurate numerical scheme for super-fast MHD flows, Astrophys. J. Suppl. Ser., 177, 373-387, (July 2008)
[53] Stone, J. M.; Gardiner, T. A., Implementation of the shearing box approximation in athena, Astrophys. J. Suppl. Ser., 189, 142-155, (July 2010)
[54] Umurhan, O. M.; Regev, O., Hydrodynamic stability of rotationally supported flows: linear and nonlinear 2D shearing box results, Astron. Astrophys., 427, 855-872, (December 2004)
[55] Lesur, G.; Longaretti, P.-Y., On the relevance of subcritical hydrodynamic turbulence to accretion disk transport, Astron. Astrophys., 444, 25-44, (December 2005)
[56] Johansen, A.; Youdin, A.; Klahr, H., Zonal flows and long-lived axisymmetric pressure bumps in magnetorotational turbulence, Astrophys. J., 697, 1269-1289, (June 2009)
[57] Gressel, O.; Ziegler, U., Shearingbox-implementation for the central-upwind, constraint-transport MHD-code NIRVANA, Comput. Phys. Commun., 176, 652-659, (June 2007)
[58] Matthews, A. P., Current advance method and cyclic leapfrog for 2D multispecies hybrid plasma simulations, J. Comput. Phys., 112, 102-116, (May 1994)
[59] Karimabadi, H.; Krauss-Varban, D.; Huba, J. D.; Vu, H. X., On magnetic reconnection regimes and associated three-dimensional asymmetries: hybrid, Hall-less hybrid, and Hall-MHD simulations, J. Geophys. Res., 109, 9205, (September 2004)
[60] M.W. Kunz, G. Lesur, Magnetic self-organisation in Hall-dominated magnetorotational turbulence. ArXiv e-prints, June 2013.
[61] Gear, C. W., Numerical initial value problems in ordinary differential equations, (1971), Prentice-Hall Englewood Cliffs · Zbl 1145.65316
[62] Teukolsky, S. A., Stability of the iterated Crank-Nicholson method in numerical relativity, Phys. Rev. D, Part. Fields, 61, 8, 087501, (April 2000)
[63] Braginskii, S. I., Transport processes in a plasma, Rev. Plasma Phys., 1, 205, (1965)
[64] Kennel, C. F.; Sagdeev, R. Z., Collisionless shock waves in high β plasmas: 1, J. Geophys. Res., 72, 3303-3326, (July 1967)
[65] Davidson, R. C.; Völk, H. J., Macroscopic quasilinear theory of the garden-hose instability, Phys. Fluids, 11, 2259-2264, (October 1968)
[66] Shapiro, V. D.; Shevchenko, V. I., Quasilinear theory of instability of a plasma with an anisotropic ion velocity distribution, Sov. Phys. JETP, 18, 1109, (April 1964)
[67] Schekochihin, A. A.; Cowley, S. C.; Kulsrud, R. M.; Rosin, M. S.; Heinemann, T., Nonlinear growth of firehose and mirror fluctuations in astrophysical plasmas, Phys. Rev. Lett., 100, 8, 081301, (February 2008)
[68] Yoon, P. H.; Wu, C. S.; de Assis, A. S., Effect of finite ion gyroradius on the fire-hose instability in a high beta plasma, Phys. Fluids, B Plasma Phys., 5, 1971-1979, (July 1993)
[69] Hellinger, P.; Matsumoto, H., New kinetic instability: oblique Alfvén fire hose, J. Geophys. Res., 105, 10519-10526, (May 2000)
[70] Winske, D., Hybrid simulation codes with application to shocks and upstream waves, Space Sci. Rev., 42, 53-66, (October 1985)
[71] Quest, K. B., Theory and simulation of collisionless parallel shocks, J. Geophys. Res., 93, 9649-9680, (September 1988)
[72] Giacalone, J., Large-scale hybrid simulations of particle acceleration at a parallel shock, Astrophys. J., 609, 452-458, (July 2004)
[73] Hellinger, P.; Trávníček, P.; Lembège, B.; Savoini, P., Emission of nonlinear Whistler waves at the front of perpendicular supercritical shocks: hybrid versus full particle simulations, Geophys. Res. Lett., 34, 14109, (July 2007)
[74] Gargaté, L.; Spitkovsky, A., Ion acceleration in non-relativistic astrophysical shocks, Astrophys. J., 744, 67, (January 2012)
[75] Caprioli, D.; Spitkovsky, A., Cosmic-ray-induced filamentation instability in collisionless shocks, Astrophys. J. Lett., 765, L20, (March 2013)
[76] Guo, F.; Giacalone, J., The acceleration of thermal protons at parallel collisionless shocks: three-dimensional hybrid simulations, Astrophys. J., 773, 158, (August 2013)
[77] Matsumoto, M.; Kajimura, Y.; Usui, H.; Funaki, I.; Shinohara, I., Application of a total variation diminishing scheme to electromagnetic hybrid particle-in-cell plasma simulation, Comput. Phys. Commun., 183, 2027-2034, (October 2012)
[78] Quataert, E.; Dorland, W.; Hammett, G. W., The magnetorotational instability in a collisionless plasma, Astrophys. J., 577, 524-533, (September 2002)
[79] Riquelme, M. A.; Quataert, E.; Sharma, P.; Spitkovsky, A., Local two-dimensional particle-in-cell simulations of the collisionless magnetorotational instability, Astrophys. J., 755, 50, (August 2012)
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