Grounds for the application of fractional-order diffusion equations in channeling theory using the Langevin approach

Abstract

Transverse-energy distribution densities in the case of ultrarelativistic proton channeling in the (100) planes of diamond-like crystals have been numerically calculated within the framework of the Langevin approach. Based on the self-similarity principle, the subdiffusion character of the motion under consideration has been established, which can be regarded as grounds for using fractional-order diffusion equations to adequately describe channeling and dechanneling processes mathematically.