Description of the anomalous diffusion of fast electrons by a kinetic equation with a fractional spatial derivative

It is proposed to use fractional spatial derivatives to describe the effect of anomalous diffusion of fast electrons in a stochastic magnetic field on the shape of the distribution function. A self-similar kinetic equation is considered. The use of self-similar variables makes it possible to determine the velocity range in which the distribution function is distorted to the greatest extent. Calculations show that the quantities associated with the stochasticity of the magnetic field lines can be estimated from the experimentally measured characteristic energies of suprathermal electrons in the energy range in which the behavior of the distribution function changes substantially.