Analytic forms of the cosmic ray perpendicular diffusion coefficient with implicit contribution of slab modes

Abstract

The analytical description of the diffusion of cosmic rays is an important topic in space and astrophysics. Recently an extension of non-linear diffusion theory for the perpendicular transport of energetic particles interacting with magnetic turbulence was developed. This theory can be used to compute the perpendicular diffusion coefficient for two-component turbulence in which the turbulent magnetic field is a superposition of slab and two-dimensional modes. It was demonstrated earlier that there is no explicit contribution from the slab modes but the new extended theory takes into account their implicit contribution leading to a reduction of the perpendicular diffusion coefficient. The latter effect is in particular important for high energy cosmic rays. In the current paper we derive simple analytical forms for this case to understand for which parameter regime the new effect is important. The new formulas will be important for different astrophysical applications such as diffusive shock acceleration at perpendicular interstellar shock waves.