Test particle simulations of cosmic rays
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REVIEW ARTICLE
Test particle simulations of cosmic rays Philipp Mertsch1
Received: 11 October 2019 / Accepted: 4 July 2020 / Published online: 7 August 2020 © The Author(s) 2020
Abstract Modelling of cosmic ray transport and interpretation of cosmic ray data ultimately rely on a solid understanding of the interactions of charged particles with turbulent magnetic fields. The paradigm over the last 50 years has been the so-called quasi-linear theory, despite some wellknown issues. In the absence of a widely accepted extension of quasi-linear theory, wave-particle interactions must also be studied in numerical simulations where the equations of motion are directly solved in a realisation of the turbulent magnetic field. The applications of such test particle simulations of cosmic rays are manifold: testing transport theories, computing parameters like diffusion coefficients or making predictions for phenomena beyond standard diffusion theories, e.g. for cosmic ray small-scale anisotropies. In this review, we seek to give a low-level introduction to test particle simulations of cosmic rays, enabling readers to perform their own test particle simulations. We start with a review of quasi-linear theory, highlighting some of its issues and suggested extensions. Next, we summarise the state-of-theart in test particle simulations and give concrete recipes for generating synthetic turbulence. We present a couple of examples for applications of such simulations and comment on an important conceptual detail in the backtracking of particles. Keywords Cosmic ray theory · Cosmic ray transport · Wave-particle interactions · Magnetic turbulence · Computer simulations This article belongs to the Topical Collection: Plasma, Particles, and Photons: ISM Physics Revisited. Guest Editors: Manami Sasaki, Ralf-Jürgen Dettmar, Julia Tjus.
B P. Mertsch
[email protected]
1
Institute for Theoretical Physics and Cosmology (TTK), RWTH Aachen University, Sommerfeldstr. 16, 52074 Aachen, Germany
1 Introduction Cosmic rays (CRs), that is the population of charged, relativistic particles with non-thermal spectra, are ubiquitous in the Universe. They pervade systems of all sizes, from stellar systems to whole galaxies, from galaxy clusters to the intercluster medium. See Berezinsky et al. (1990), Strong et al. (2007), Grenier et al. (2015), Kotera and Olinto (2011) for reviews on Galactic and extra-galactic cosmic rays. CRs are not only responsible for genuinely non-thermal phenomena: the fluxes of CRs observed at Earth, the non-thermal emission of radio, X-ray and gamma-ray sources or the diffuse Galactic and extragalactic emission; but CRs oftentimes have energy densities comparable or even superior to other components, like the thermal gas, magnetic fields or radiation backgrounds. As such, CRs can contribute to the pressure equilibrium or even drive large-scale outflows (e.g. Everett et al. 2008, Hanasz et al. 2013, Simpson et al. 2016, Recchia et al. 2016). At the largest scales, it has been suggested that CRs (or gamma-rays
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