Orders of Magnitude of the Fermi and Plasma Accelerations of Cosmic Rays

Abstract

The generic acceleration model for ultra high energy cosmic rays, which has been introduced in Ref [?], suggests various types of electromagnetic interactions between cosmic charged particles and the different types of the plasma fields, which are assumed to have general configurations, spatially and temporally. The well-known Fermi acceleration mechanisms are also included in the model. Meanwhile Fermi mechanisms in non-relativistic limit adhere firstand second-order of magnitude of β , the ratio of particle’s velocity relative to the velocity of the stellar magnetic cloud, in the plasma field sector, β does not play any role, i.e. zero-order. In the relativistic limit, the orders of magnitude of Fermi acceleration are only possible, when applying the corresponding conditions, either elastic scatterings or shock waves. Furthermore, it is found that the coefficients of β are functions of the initial and final velocities and the characteristic Larmor radius.