https://doi.org/10.1140/epjp/s13360-023-04500-5
Regular Article
Nonlinear diffusive shock acceleration of cosmic rays: quasi-thermal and non-thermal particle distributions
Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia
a
bojan.arbutina@matf.bg.ac.rs
Received:
15
March
2023
Accepted:
15
September
2023
Published online:
28
September
2023
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 nonlinear DSA. We use semi-analytical Blasi’s model of nonlinear DSA to obtain non-thermal spectra of both protons and electrons, starting from their quasi-thermal spectra for which we assumed the 
-distribution, a commonly observed distribution in out-of-equilibrium space plasmas. We treated more carefully than in the 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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
