Spectrum of Cosmic Rays from a Stationary Point Source in the Non-Classical Diffusion Model

The stationary model of cosmic ray propagation in the Galaxy is widely used to interpret observed cosmic ray spectra. The paper analyzes the applicability of this model for the case of particle diffusion in a highly inhomogeneous interstellar medium. The analytical solution of the non-classical diffusion equation, expressed in terms of stable distributions, is obtained. Also, the impossibility to describe the observed cosmic ray spectrum break is shown in the paper. It is found that when energy increases, the particle concentration decreases faster than for the case with the normal diffusion model. To understand this phenomenon, spectrum modifications for the pulsed source case are analyzed in transition from the non-stationary model to the stationary one. The impact of progressive energy loss by particles on stationary model spectrum shapes is investigated. It is shown that energy losses are negligible at E> 102 GeV. The stationary non-classical diffusion model is concluded to be applicable to describe experimental cosmic ray fluxes observed on Earth.