On the Classical Approach to Describing the Diffusion of Cosmic Rays in a Turbulent Medium

The inhomogeneous structure of the interstellar medium (ISM) is characterized by large-scale fluctuations that significantly affect the cosmic ray propagation process. Accounting for this influence can only lead to adjustments in the diffusion process parameters but even to pass from differential operators to integral ones. The most crucial characteristics of a turbulent medium is its power spectrum. Including appropriate approximations of this spectrum allows considering this problem in the framework of the traditional diffusion approach [ 1 , 2 ]. This article explores the analytical representations of this spectrum applied in the cosmic ray transfer theory, including the four-parameter Uchaikin–Zolotarev approximation, derived from the generalized Ornstein–Zernike equation. Testing of the latter revealed that, with carefully chosen parameters, it accurately replicates numerical modeling results both in the inertial interval and beyond. Therefore, it can be effectively employed in addressing cosmic ray transfer issues within a turbulent interstellar medium.