Non-linear Diffusive Shock Acceleration of Cosmic Rays -- Quasi-thermal and Non-thermal Particle Distributions

TL;DR

This paper advances the understanding of cosmic ray acceleration by developing a semi-analytical model that incorporates non-linear effects, magnetic instabilities, and realistic particle distributions to produce more accurate non-thermal spectra.

Contribution

It introduces a comprehensive non-linear DSA model that includes electron heating, magnetic instabilities, and realistic quasi-thermal distributions, improving upon previous simplified approaches.

Findings

Produced non-thermal spectra for protons and electrons from quasi-thermal distributions.

Included effects of magnetic field instabilities and electron heating.

Accounted for proton escape flux and electron synchrotron losses.

Abstract

Diffusive shock acceleration (DSA) of particles at collisionless shocks is the major accepted paradigm about the origin of cosmic rays (CRs). As a theory it was developed during the late 1970s in the so-called test-particle case. If one considers the influence of CR particles at shock structure, then we are talking about non-linear DSA. We use semi-analytical Blasi's model of non-linear DSA to obtain non-thermal spectra of both protons and electrons, starting from their quasi-thermal spectra for which we assumed the $\kappa$-distribution, a commonly observed distribution in out-of-equilibrium space plasmas. We treated more carefully than in previous work the jump conditions at the subshock and included electron heating, resonant and, additionally, non-resonant magnetic field instabilities produced by CRs in the precursor. Also, corrections for escaping flux of protons and synchrotron losses of electrons have been made.