The Magnetohydrodynamic-Particle-In-Cell Module in Athena++: Implementation and Code Tests

We present a new magnetohydrodynamic-particle-in-cell (MHD-PIC) code integrated into the Athena++ framework. It treats energetic particles as in conventional PIC codes while the rest of thermal plasmas are treated as background fluid described by MHD, thus primarily targeting at multi-scale astrophysical problems involving the kinetic physics of the cosmic-rays (CRs). The code is optimized toward efficient vectorization in interpolation and particle deposits, with excellent parallel scaling. The code is also compatible with static/adaptive mesh refinement, with dynamic load balancing to further enhance multi-scale simulations. In addition, we have implemented a compressing/expanding box framework which allows adiabatic driving of CR pressure anisotropy, as well as the $\delta f$ method that can dramatically reduce Poisson noise in problems where distribution function $f$ is only expected to slightly deviate from the background. The code performance is demonstrated over a series of benchmark test problems including particle acceleration in non-relativistic parallel shocks. In particular, we reproduce the linear growth of the CR gyro-resonant (streaming and pressure anisotropy) instabilities, under both the periodic and expanding/compressing box setting. We anticipate the code to open up the avenue for a wide range of astrophysical and plasma physics applications.