An accurate treatment of scattering and diffusion in piecewise power-law models for cosmic ray and radiation/neutrino transport

Understand

A popular numerical method to model the dynamics of a 'full spectrum' of cosmic rays (CRs), also applicable to radiation/neutrino hydrodynamics (RHD), is to discretize the spectrum at each location/cell as a piecewise power law in 'bins' of momentum (or frequency) space.

• This gives rise to a pair of conserved quantities (e.g.
• CR number and energy) which are exchanged between cells or bins, that in turn give the update to the normalization and slope of the spectrum in each bin.
• While these methods can be evolved exactly in momentum-space (considering injection, absorption, continuous losses/gains), numerical challenges arise dealing with spatial fluxes, if the scattering rates depend on momentum.