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Abstract:
Cosmic ray (CR) protons are an important component in many astrophysical systems. Processes
like CR injection, cooling, adiabatic changes as well as active CR transport through the
medium strongly modify the CR momentum distribution and have to be taken into account
in hydrodynamical simulations. We present an efficient novel numerical scheme to accurately
compute the evolution of the particle distribution function by solving the Fokker–Planck
equation with a low number of spectral bins (10–20), which is required to include a full
spectrum for every computational fluid element. The distribution function is represented
by piecewise power laws and is not forced to be continuous, which enables an optimal
representation of the spectrum. The Fokker–Planck equation is solved with a two-moment
approach evolving the CR number and energy density. The low numerical diffusion of the
scheme reduces the numerical errors by orders of magnitude in comparison to classical
schemes with piecewise constant spectral representations. With this method not only the
spectral evolution of CRs can be computed accurately in magnetohydrodynamic simulations
but also their dynamical impact as well as CR ionization. This allows for more accurate
models for astrophysical plasmas, like the interstellar medium, and direct comparisons with
observations.
