A SECOND-ORDER DIVERGENCE-CONSTRAINED MULTIDIMENSIONAL NUMERICAL SCHEME FOR RELATIVISTIC TWO-FLUID ELECTRODYNAMICS

A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.

[1]  O. Skjaeraasen,et al.  The Sigma Problem of the Crab Pulsar Wind , 2003, astro-ph/0309573.

[2]  C. Kennel,et al.  Confinement of the Crab pulsar's wind by its supernova remnant , 1984 .

[3]  S. Komissarov,et al.  A Godunov-type scheme for relativistic magnetohydrodynamics , 1999 .

[4]  Alexander Kurganov,et al.  Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations , 2001, SIAM J. Sci. Comput..

[5]  TWO-FLUID MAGNETOHYDRODYNAMIC SIMULATIONS OF RELATIVISTIC MAGNETIC RECONNECTION , 2009 .

[6]  D. Balsara,et al.  A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations , 1999 .

[7]  Takanobu Amano,et al.  A robust method for handling low density regions in hybrid simulations for collisionless plasmas , 2014, J. Comput. Phys..

[8]  General relativistic magnetohydrodynamic simulations of the jet formation and large-scale propagation from black hole accretion systems , 2006, astro-ph/0603045.

[9]  Michael Hesse,et al.  Two-Fluid MHD Simulations of Relativistic Magnetic Reconnection , 2008 .

[10]  S. Komissarov,et al.  Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources , 2008, 0811.1467.

[11]  K. Toma,et al.  Electromotive force in the Blandford–Znajek process , 2014, 1405.7437.

[12]  J. Gunn,et al.  The Origin of the Magnetic Field and Relativistic Particles in the Crab Nebula , 1974 .

[13]  S. Komissarov,et al.  Relativistic tearing and drift-kink instabilities in two-fluid simulations , 2016, 1602.02848.

[14]  Hiroyuki R. Takahashi,et al.  SCALING LAW OF RELATIVISTIC SWEET–PARKER-TYPE MAGNETIC RECONNECTION , 2011, 1108.3891.

[15]  James M. Stone,et al.  A SECOND-ORDER GODUNOV METHOD FOR MULTI-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMICS , 2011, 1101.3573.

[16]  T. Esirkepov,et al.  Exact charge conservation scheme for Particle-in-Cell simulation with an arbitrary form-factor , 2001 .

[17]  Dinshaw Balsara,et al.  Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction , 2003, astro-ph/0308249.

[18]  F. Curtis Michel,et al.  MAGNETIC STRUCTURE OF PULSAR WINDS , 1994 .

[19]  Dinshaw S. Balsara.  Multidimensional HLLE Riemann solver: Application to Euler and magnetohydrodynamic flows , 2010, J. Comput. Phys..

[20]  Kazunari Shibata,et al.  Relativistic Jet Formation from Black Hole Magnetized Accretion Disks: Method, Tests, and Applications of a General RelativisticMagnetohydrodynamic Numerical Code , 1999 .

[21]  Francesco Miniati,et al.  A Divergence-free Upwind Code for Multidimensional Magnetohydrodynamic Flows , 1998 .

[22]  Dinshaw Balsara,et al.  Divergence-free adaptive mesh refinement for Magnetohydrodynamics , 2001 .

[23]  Y. Lyubarsky,et al.  Reconnection in a Striped Pulsar Wind , 2000, astro-ph/0009270.

[24]  Harish Kumar,et al.  Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations , 2011, J. Sci. Comput..

[25]  J. Kirk,et al.  THE ROLE OF SUPERLUMINAL ELECTROMAGNETIC WAVES IN PULSAR WIND TERMINATION SHOCKS , 2013, 1303.2702.

[26]  H. C. Spruit,et al.  Efficient acceleration and radiation in Poynting flux powered GRB outflows , 2002, astro-ph/0202387.

[27]  Cosmology,et al.  EFFICIENCY OF MAGNETIC TO KINETIC ENERGY CONVERSION IN A MONOPOLE MAGNETOSPHERE , 2009, 0901.4776.

[28]  Uri Shumlak,et al.  Analytical and computational study of the ideal full two-fluid plasma model and asymptotic approximations for Hall-magnetohydrodynamics , 2011 .

[29]  P. Londrillo,et al.  An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. Magnetohydrodynamics , 2002 .

[30]  Uri Shumlak,et al.  A high resolution wave propagation scheme for ideal Two-Fluid plasma equations , 2006, J. Comput. Phys..

[31]  Takanobu Amano,et al.  Divergence-free approximate Riemann solver for the quasi-neutral two-fluid plasma model , 2015, J. Comput. Phys..

[32]  C. Kennel,et al.  Relativistic nonlinear plasma waves in a magnetic field , 1975, Journal of Plasma Physics.

[33]  Michael Hesse,et al.  RESISTIVE MAGNETOHYDRODYNAMIC SIMULATIONS OF RELATIVISTIC MAGNETIC RECONNECTION , 2010, 1005.4485.

[34]  A. Klimas,et al.  RELATIVISTIC TWO-FLUID SIMULATIONS OF GUIDE FIELD MAGNETIC RECONNECTION , 2009, 0909.1955.

[35]  P. Londrillo,et al.  On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method , 2004 .

[36]  C. Thompson.  A Model of gamma-ray bursts , 1994 .

[37]  Paul R. Woodward,et al.  A Simple Finite Difference Scheme for Multidimensional Magnetohydrodynamical Equations , 1998 .

[38]  M. Lyutikov,et al.  Tearing instability in relativistic magnetically dominated plasmas , 2007 .

[39]  Shigenobu Hirose,et al.  DEPENDENCE OF THE SATURATION LEVEL OF MAGNETOROTATIONAL INSTABILITY ON GAS PRESSURE AND MAGNETIC PRANDTL NUMBER , 2015, 1506.03524.

[40]  P. Londrillo,et al.  High-Order Upwind Schemes for Multidimensional Magnetohydrodynamics , 1999, astro-ph/9910086.

[41]  S. Komissarov,et al.  A multidimensional numerical scheme for two-fluid relativistic magnetohydrodynamics , 2013, 1309.5221.

[42]  T. Yokoyama,et al.  Two-dimensional Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection , 2006, astro-ph/0607285.

[43]  Michael Hesse,et al.  Geospace Environmental Modeling (GEM) magnetic reconnection challenge , 2001 .

[44]  G. Fishman,et al.  A General Relativistic Magnetohydrodynamic Simulation of Jet Formation , 2004, astro-ph/0403032.

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

[46]  Dinshaw S. Balsara,et al.  A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism , 2016, J. Comput. Phys..

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

[48]  M. Takamoto.  EVOLUTION OF RELATIVISTIC PLASMOID CHAINS IN A POYNTING-DOMINATED PLASMA , 2013, 1307.5677.

[49]  Dinshaw S. Balsara.  Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics , 2009, J. Comput. Phys..

[50]  O. Zanotti,et al.  ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics , 2007, 0704.3206.

[51]  S. Komissarov,et al.  Multi-dimensional Numerical Scheme for Resistive Relativistic MHD , 2007, 0708.0323.

[52]  General Relativistic Magnetohydrodynamic Simulations of Collapsars , 2004, astro-ph/0404152.

[53]  F. Coroniti.  Magnetically Striped Relativistic Magnetohydrodynamic Winds: The Crab Nebula Revisited , 1990 .

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