Cosmic Ray Transport

Governing equations

The cosmic ray module solves the two moment equations for cosmic ray transport including both diffusion and streaming as described by Jiang & Oh (2018, ApJ, 854, 5). Anisotropic diffusion with respect to the direction of magnetic field is also allowed.

Configuration

• use -cr to turn on the cosmic ray transport module

Input File

All the parameters for the cosmic ray module are set in the <cr> block. The reduced speed of light, which is the maximum speed cosmic rays are allowed to travel needs to be set.

<cr>
vmax            = 1000      # maximum speed of cosmic rays in the same unit as flow velocity

User-defined Opacity

To set the streaming and diffusion coefficients, users can enroll a function using EnrollOpacityFunction provided by the cosmic ray class. pcr->sigma_diff(0,k,j,i) is always the diffusion coefficient parallel to the magnetic field direction while pcr->sigma_diff(1,k,j,i) and pcr->sigma_diff(2,k,j,i) are diffusion coefficients perpendicular to the magnetic field.

Cosmic-ray diffusion module

Athena++ now has another cosmic-ray solver using diffusion approximation and a fully-implicit time integrator with Multigrid. This is more crude approximation of CR transport but is computationally more efficient when the hydrodynamic timescale is much longer than the CR transport timescale. Please refer to Cosmic‐ray diffusion with Multigrid.