Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics

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 @df 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.

[1]  David J. Larson,et al.  A Coulomb collision model for PIC plasma simulation , 2003 .

[2]  D. Winske,et al.  HYBRID SIMULATION CODES WITH APPLICATION TO SHOCKS AND UPSTREAM WAVES , 1985 .

[3]  Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results , 2004, astro-ph/0404020.

[4]  Homa Karimabadi,et al.  HYPERS: A unidimensional asynchronous framework for multiscale hybrid simulations , 2012, J. Comput. Phys..

[5]  Thermostatted {delta}f , 1999 .

[6]  A. Spitkovsky,et al.  ION ACCELERATION IN NON-RELATIVISTIC ASTROPHYSICAL SHOCKS , 2011, 1107.0762.

[7]  William B. Thompson Transport Processes in the Plasma , 1960 .

[8]  Charles F. Gammie,et al.  Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks , 2001, astro-ph/0101501.

[9]  G. Lesur,et al.  On the relevance of subcritical hydrodynamic turbulence to accretion disk transport , 2005 .

[10]  Douglas S. Harned,et al.  Quasineutral hybrid simulation of macroscopic plasma phenomena , 1982 .

[11]  Don S. Lemons,et al.  A Grid-Based Coulomb Collision Model for PIC Codes , 1996 .

[12]  J. Stone,et al.  IMPLEMENTATION OF THE SHEARING BOX APPROXIMATION IN ATHENA , 2010, 1006.0139.

[13]  J. Stone,et al.  PARTICLE–GAS DYNAMICS WITH ATHENA: METHOD AND CONVERGENCE , 2010, 1005.4980.

[14]  Hybrid Simulations of the Effects of Energetic Particles on Low-Frequency MHD Waves , 1997 .

[15]  Ricardo A. Fonseca,et al.  dHybrid: A massively parallel code for hybrid simulations of space plasmas , 2007, Comput. Phys. Commun..

[16]  B. Lembège,et al.  Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: Hybrid versus full particle simulations , 2007 .

[17]  Mark Sherlock,et al.  A Monte-Carlo method for coulomb collisions in hybrid plasma models , 2008, J. Comput. Phys..

[18]  M. Norman,et al.  ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I - The hydrodynamic algorithms and tests. II - The magnetohydrodynamic algorithms and tests , 1992 .

[19]  P. Teuben,et al.  Athena: A New Code for Astrophysical MHD , 2008, 0804.0402.

[20]  K. Yee Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[21]  Michael R. Combi,et al.  A Coulomb collision algorithm for weighted particle simulations , 1994 .

[22]  G. Hu,et al.  The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox , 1994 .

[23]  Cohen,et al.  Collision operators for partially linearized particle simulation codes. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  F. Masset,et al.  FARGO: A fast eulerian transport algorithm for differentially rotating disks , 2000 .

[25]  F. Guo,et al.  THE ACCELERATION OF THERMAL PROTONS AT PARALLEL COLLISIONLESS SHOCKS: THREE-DIMENSIONAL HYBRID SIMULATIONS , 2013, 1303.5174.

[26]  D. Lynden-Bell,et al.  II. Spiral Arms as Sheared Gravitational Instabilities , 1965 .

[27]  L. Yin,et al.  Hybrid Simulation Codes: Past, Present and Future—A Tutorial , 2003 .

[28]  Masaharu Matsumoto,et al.  Application of a total variation diminishing scheme to electromagnetic hybrid particle-in-cell plasma simulation , 2012, Comput. Phys. Commun..

[29]  J. Brackbill,et al.  The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations☆ , 1980 .

[30]  E. Quataert,et al.  THE HEATING OF TEST PARTICLES IN NUMERICAL SIMULATIONS OF ALFVÉNIC TURBULENCE , 2009, 0908.4078.

[31]  R. Sagdeev,et al.  Collisionless shock waves in high β plasmas: 1 , 1967 .

[32]  R. Kulsrud,et al.  Nonlinear growth of firehose and mirror fluctuations in astrophysical plasmas. , 2007, Physical review letters.

[33]  C. Gammie,et al.  Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows , 2008, 0804.4699.

[34]  G. Hu,et al.  Generalized weighting scheme for δf particle‐simulation method , 1994 .

[35]  J. Stone,et al.  BUOYANCY INSTABILITIES IN A WEAKLY COLLISIONAL INTRACLUSTER MEDIUM , 2012, 1202.3442.

[36]  Richard E. Denton,et al.  {delta}f Algorithm , 1993 .

[37]  Elena Belova,et al.  Numerical study of tilt stability of prolate field-reversed configurations , 2000 .

[38]  J. M. Watt Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[39]  H. Matsumoto,et al.  New kinetic instability: Oblique Alfvén fire hose , 2000 .

[40]  Daniel W. Swift,et al.  Use of a Hybrid Code for Global-Scale Plasma Simulation , 1996 .

[41]  S. Parker,et al.  A fully nonlinear characteristic method for gyrokinetic simulation , 1993 .

[42]  J. D. Huba,et al.  On magnetic reconnection regimes and associated three‐dimensional asymmetries: Hybrid, Hall‐less hybrid, and Hall‐MHD simulations , 2004 .

[43]  M. Norman,et al.  ZEUS-2D : a radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II : The magnetohydrodynamic algorithms and tests , 1992 .

[44]  James M. Stone,et al.  An unsplit Godunov method for ideal MHD via constrained transport in three dimensions , 2007, J. Comput. Phys..

[45]  T. Takizuka,et al.  A binary collision model for plasma simulation with a particle code , 1977 .

[46]  J. Giacalone Large-Scale Hybrid Simulations of Particle Acceleration at a Parallel Shock , 2004 .

[47]  J. Hawley,et al.  Simulation of magnetohydrodynamic flows: A Constrained transport method , 1988 .

[48]  Matthew W. Kunz,et al.  Magnetic self-organization in Hall-dominated magnetorotational turbulence , 2013, 1306.5887.

[49]  J. Stone,et al.  An unsplit Godunov method for ideal MHD via constrained transport , 2005, astro-ph/0501557.

[50]  Wallace M. Manheimer,et al.  Langevin Representation of Coulomb Collisions in PIC Simulations , 1997 .

[51]  Saul A. Teukolsky Stability of the iterated Crank-Nicholson method in numerical relativity , 2000 .

[52]  Petr Hellinger,et al.  A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma , 2007, J. Comput. Phys..

[53]  K. Quest,et al.  Theory and simulation of collisionless parallel shocks , 1988 .

[54]  J. Krommes Thermostatted δf , 1999 .

[55]  Gavin J. Pringle,et al.  A.I.K.E.F.: Adaptive hybrid model for space plasma simulations , 2011, Comput. Phys. Commun..

[56]  Bruce I. Cohen,et al.  Hybrid simulations of quasineutral phenomena in magnetized plasma , 1978 .

[57]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[58]  Charles F. Gammie,et al.  Local Three-dimensional Magnetohydrodynamic Simulations of Accretion Disks , 1995 .

[59]  J. D. Ramshaw A method for enforcing the solenoidal condition on magnetic field in numerical calculations , 1983 .

[60]  Yang Chen,et al.  A second-order semi-implicit δfδf method for hybrid simulation , 2013, J. Comput. Phys..

[61]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[62]  Eric J. Horowitz,et al.  QN3D: A three-dimensional quasi-neutral hybrid particle-in-cell code with applications to the tilt mode instability in field reversed configurations , 1989 .

[63]  Richard E. Denton,et al.  δf Algorithm , 1995 .

[64]  Leiden University,et al.  ZONAL FLOWS AND LONG-LIVED AXISYMMETRIC PRESSURE BUMPS IN MAGNETOROTATIONAL TURBULENCE , 2008, 0811.3937.

[65]  A. Schekochihin,et al.  A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma , 2010, 1002.4017.

[66]  V. Shevchenko,et al.  QUASILINEAR THEORY OF INSTABILITY OF A PLASMA WITH AN ANISOTROPIC ION VELOCITY DISTRIBUTION , 1963 .

[67]  C. W. Nielson,et al.  A multidimensional quasineutral plasma simulation model , 1978 .

[68]  Scott E. Parker,et al.  Coarse-graining phase space in δf particle-in-cell simulations , 2007 .

[69]  A. Matthews,et al.  Current Advance Method and Cyclic Leapfrog for 2D Multispecies Hybrid Plasma Simulations , 1994 .

[70]  D. Winske,et al.  Hybrid codes: Methods and applications , 1991 .

[71]  Alexander S. Lipatov,et al.  The Hybrid Multiscale Simulation Technology: An Introduction with Application to Astrophysical and Laboratory Plasmas , 2010 .

[72]  A. Spitkovsky,et al.  COSMIC-RAY-INDUCED FILAMENTATION INSTABILITY IN COLLISIONLESS SHOCKS , 2012, 1211.6765.

[73]  Don S. Lemons,et al.  Small-angle Coulomb collision model for particle-in-cell simulations , 2009, J. Comput. Phys..

[74]  E. Quataert,et al.  LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY , 2012 .

[75]  R. Davidson,et al.  Macroscopic Quasilinear Theory of the Garden‐Hose Instability , 1968 .

[76]  Prateek Sharma,et al.  Shearing Box Simulations of the MRI in a Collisionless Plasma , 2005, astro-ph/0508502.

[77]  U. Ziegler,et al.  Shearingbox-implementation for the central-upwind, constraint-transport MHD-code NIRVANA , 2007, Comput. Phys. Commun..

[78]  C. Wu,et al.  Effect of finite ion gyroradius on the fire‐hose instability in a high beta plasma , 1993 .

[79]  Alexander S. Lipatov,et al.  The Hybrid Multiscale Simulation Technology: An Introduction with Application to Space and Plasma Physics , 2001 .

[80]  A. Spitkovsky Simulations of relativistic collisionless shocks: shock structure and particle acceleration , 2005, astro-ph/0603211.

[81]  Petr Hellinger,et al.  Langevin representation of Coulomb collisions for bi-Maxwellian plasmas , 2010, J. Comput. Phys..