The problem of superluminal diffusion of relativistic particles and its phenomenological solution

Abstract

We discuss the problem of superluminal propagation in diffusion of ultra-high energy (UHE) protons with energy losses taken into account. The phenomenological solution of this problem is found with the help of the generalized Jüttner propagator, originally proposed for the relativization of the Maxwellian gas distribution. It is demonstrated that the generalized Jüttner propagator gives correct expressions in limits of diffusive and rectilinear propagation of the charged particles in magnetic fields, together with the intermediate regime, in all cases without superluminal velocities. This solution, very general for the diffusion, is considered for two particular cases: the diffusion inside stationary objects, such as, e.g., galaxies, clusters of galaxies, etc., and for the expanding universe. The comparison with previously obtained solutions for the propagation of UHE protons in magnetic fields is performed. © 2009. The American Astronomical Society. All rights reserved.