Scientists have explored how energetic particles such as solar energetic particles and cosmic rays move through a magnetized plasma such as the interplanetary and interstellar medium since more than five decades. From a theoretical point of view, this topic is difficult because the particles experience complicated interactions with turbulent magnetic fields. Besides turbulent fields, there are also large scale or mean magnetic fields breaking the symmetry in such systems and one has to distinguish between transport of particles parallel and perpendicular with respect to such mean fields. In standard descriptions of transport phenomena, one often assumes that the transport in both directions is normal diffusive but non-diffusive transport was found in more recent work. This is in particular true for early and intermediate times where the diffusive regime is not yet reached. In recent years researchers employed advanced numerical tools in order to simulate the motion of those particles through the aforementioned systems. Nevertheless, the analytical description of the problem discussed here is of utmost importance since analytical forms of particle transport parameters need to be known in several applications such as solar modulation studies or investigations of shock acceleration. The latter process is directly linked to the question of what the sources of high energy cosmic rays are, a problem which is considered to be one of the most important problems of the sciences of the 21st century. The present review article discusses analytical theories developed for describing particle transport across a large scale magnetic field as well as field line random walk. A heuristic approach explaining the basic physics of perpendicular transport is also presented. Simple analytical forms for the perpendicular diffusion coefficient are proposed which can easily be incorporated in numerical codes for solar modulation or shock acceleration studies. Test-particle simulations are also discussed together with a comparison with analytical results. Several applications such as cosmic ray propagation and diffusive shock acceleration are also part of this review.

中文翻译：

---

磁湍流中高能粒子的垂直输运

五十多年来，科学家们一直在探索高能粒子（如太阳高能粒子和宇宙射线）如何穿过磁化等离子体（如行星际和星际介质）。从理论的角度来看，这个话题很困难，因为粒子会与湍流磁场发生复杂的相互作用。除了湍流场，在这种系统中也有破坏对称性的大尺度或平均磁场，人们必须区分与这种平均场平行和垂直的粒子传输。在传输现象的标准描述中，人们通常假设双向传输是正常扩散的，但在最近的工作中发现了非扩散传输。对于尚未达到扩散状态的早期和中期尤其如此。近年来，研究人员采用先进的数值工具来模拟这些粒子通过上述系统的运动。然而，这里讨论的问题的分析描述是最重要的，因为在太阳调制研究或冲击加速度研究等几个应用中需要知道粒子传输参数的分析形式。后一个过程与高能宇宙射线的来源问题直接相关，这个问题被认为是 21 世纪科学最重要的问题之一。本评论文章讨论了为描述跨越大规模磁场的粒子传输以及场线随机游走而开发的分析理论。还介绍了一种解释垂直传输基本物理学的启发式方法。提出了垂直扩散系数的简单分析形式，可以很容易地将其合并到用于太阳能调制或冲击加速度研究的数值代码中。还讨论了测试粒子模拟以及与分析结果的比较。一些应用，如宇宙射线传播和扩散冲击加速，也是本次审查的一部分。提出了垂直扩散系数的简单分析形式，可以很容易地将其合并到用于太阳能调制或冲击加速度研究的数值代码中。还讨论了测试粒子模拟以及与分析结果的比较。宇宙射线传播和扩散冲击加速等几个应用也是本次审查的一部分。提出了垂直扩散系数的简单分析形式，可以很容易地将其合并到用于太阳能调制或冲击加速度研究的数值代码中。还讨论了测试粒子模拟以及与分析结果的比较。宇宙射线传播和扩散冲击加速等几个应用也是本次审查的一部分。