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.

中文翻译：

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宇宙射线的测试粒子模拟

宇宙射线传输建模和宇宙射线数据解释最终依赖于对带电粒子与湍流磁场相互作用的深入理解。尽管存在一些众所周知的问题，但过去 50 年的范式一直是所谓的拟线性理论。在没有广泛接受的拟线性理论扩展的情况下，还必须在数值模拟中研究波粒相互作用，其中在湍流磁场的实现中直接求解运动方程。这种宇宙射线测试粒子模拟的应用是多方面的：测试传输理论、计算扩散系数等参数或预测超出标准扩散理论的现象，例如宇宙射线小尺度各向异性。在这次审查中，我们试图对宇宙射线的测试粒子模拟进行低层次的介绍，使读者能够执行自己的测试粒子模拟。我们从对拟线性理论的回顾开始，重点介绍其一些问题和建议的扩展。接下来，我们总结了测试粒子模拟的最新技术，并给出了生成合成湍流的具体方法。我们提供了一些此类模拟的应用示例，并对粒子回溯中的一个重要概念细节进行了评论。我们总结了测试粒子模拟的最新技术，并给出了产生合成湍流的具体方法。我们提供了一些此类模拟的应用示例，并对粒子回溯中的一个重要概念细节进行了评论。我们总结了测试粒子模拟的最新技术，并给出了产生合成湍流的具体方法。我们提供了一些此类模拟的应用示例，并对粒子回溯中的一个重要概念细节进行了评论。