Test particle simulations of cosmic rays

TL;DR

This paper reviews test particle simulations of cosmic rays, discussing their role in understanding cosmic ray transport, comparing them to quasi-linear theory, and providing practical guidance for conducting such simulations.

Contribution

It offers a comprehensive introduction to test particle simulations, including methods for generating turbulence and applying simulations to cosmic ray transport analysis.

Findings

Test particle simulations help evaluate cosmic ray diffusion coefficients.

Simulations reveal limitations of quasi-linear theory.

Practical recipes for turbulence generation are provided.

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 well-known 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-the-art 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.