dHybridR: A Hybrid Particle-in-cell Code Including Relativistic Ion Dynamics

Abstract

We present the first plasma simulations obtained with the code dHybridR , a hybrid particle-in-cell code with fluid electrons and both thermal and energetic ions that retain relativistic dynamics. dHybridR is constructed to study astrophysical and space-physics problems where a few energetic nonthermal particles (i.e., cosmic rays, CRs) affect the overall dynamics of a nonrelativistic plasma, such as CR-driven instabilities, collisionless shocks, magnetic reconnection, turbulence, etc. In this method paper we provide some applications to linear (resonant/nonresonant CR streaming instability) and strongly nonlinear (parallel shocks) problems that show the capabilities of the code. In particular, we provide the first self-consistent hybrid runs that show the acceleration of relativistic ions at nonrelativistic shocks; CRs develop a power law in momentum, which translates into a broken power law in energy that exhibits a steepening around the ion rest mass, as predicted by the theory of diffusive shock acceleration. We present examples of 2D dHybridR runs relevant for fast shocks in radio supernovae, whose evolution can be followed in real time, and 3D runs of low-Mach-number heliospheric shocks, which can be compared with in situ spacecraft observations.