Orders of Fermi- and Plasma-Accelerations of Cosmic Rays

TL;DR

This paper explores the theoretical framework of cosmic ray acceleration, integrating Fermi mechanisms with plasma interactions, and analyzes how acceleration orders depend on relativistic conditions and plasma parameters.

Contribution

It extends the generic acceleration model to include plasma field interactions and clarifies the conditions under which different orders of Fermi acceleration occur.

Findings

Fermi acceleration orders vary with relativistic conditions.

Plasma field interactions influence acceleration coefficients.

Acceleration mechanisms depend on initial and final velocities.

Abstract

The generic acceleration model for ultra high energy cosmic rays, which has been introduced in {\tt 1006.5708 [astro-ph.HE]}, 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 first- and second-order of $\beta$, the ratio of particle's velocity relative to the velocity of the stellar magnetic cloud, in the plasma field sector, $\beta$ does not play any role, i.e. zero-order. In the relativistic limit, the orders 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 $\beta$ are functions of the initial and final velocities and the characteristic Larmor radius.