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Nonlinear diffusive shock acceleration of cosmic rays: quasi-thermal and non-thermal particle distributions

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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 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 \(\kappa \)-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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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.]

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Funding

The author acknowledges the funding provided through the contract No. 451-03-47/2023-01/200104 by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia, and through the joint project of the Serbian Academy of Sciences and Arts and Bulgarian Academy of Sciences on the detection of Galactic and extragalactic SNRs and HII regions.

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  1. Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, Belgrade, 11000, Serbia

    Bojan Arbutina

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Arbutina, B. Nonlinear diffusive shock acceleration of cosmic rays: quasi-thermal and non-thermal particle distributions. Eur. Phys. J. Plus 138, 863 (2023). https://doi.org/10.1140/epjp/s13360-023-04500-5

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