Turbulence and Energetic Particles in Interplanetary and Interstellar Spaces

空间和天体物理学中的两个基本问题是对湍流和高能粒子(如宇宙射线)的理解。这两个问题是相互关联的，因为粒子受到湍流磁场的强烈影响。这里描述的问题可以在各种各样的场景中找到，从星际空间到我们自己和外部星系的星际介质。此外，在实验聚变反应堆中也可以发现类似的问题，如热核实验堆。湍流是一种复杂的非线性动力学现象，因此，没有简单的方法来描述它。人们必须依靠分析工作、计算机模拟以及通常通过旅行者1号等太空探测器上的磁力计进行的观测。人们发现，在太阳风和非常局部的星际介质中，湍流在大多数情况下几乎是不可压缩的。此外，还可以观察到冯-卡曼-科尔莫戈洛夫叶栅的所有范围。太阳高能粒子和宇宙射线的运动受到上述级联的所有范围的影响，包括能量范围、惯性范围和耗散范围。高能粒子的运动和湍流一样，也是一种复杂的非线性现象，微扰理论等简单工具在一般情况下是失效的。解决这个问题的一种方法是开发计算机模拟。在这种纯数值方法中，湍流是在随机数发生器的帮助下产生的。然后数值求解粒子系综的牛顿-洛伦兹方程。如果对数千个粒子这样做，就可以得到高能粒子的统计数据。尽管这样的模拟确实很强大，但对输运的纯粹数字描述是不完整的。首先，人们无法对粒子散射的机制有一个详细的了解。此外，粒子扩散系数的解析式在许多应用中也有应用。因此，除了上述数值工具外，我们还发展了先进的非线性理论来描述高能粒子的运动。提案中概述的研究涉及非线性理论的发展和改进，通过模拟进行检验，推导不同扩散参数的简单解析形式，以及应用。拟议的工作包括调查行星际冲击和超新星冲击的扩散冲击加速等主题。这一机制负责产生宇宙射线。通过拟议的工作获得的结果对空间气象和太阳调制研究等其他调查也将是重要的。此外，我们将基于几乎不可压缩的磁流体动力学来探索湍流及其输运。这项拟议工作的主要目标是提高我们对湍流、高能粒子运动和扩散激波加速的理解。

Two fundamental problems in space and astrophysics are the understanding of turbulence and energetic particles such as cosmic rays. Both problems are linked to each other because the particles are strongly influenced by turbulent magnetic fields. The problems described here can be found in a variety of scenarios ranging from the interplanetary space to the interstellar media of our own and external galaxies. Furthermore, similar problems can be found in experimental fusion reactors such as ITER. Turbulence is a complex non-linear dynamical phenomenon and, therefore, there is no simple way of describing it. One has to rely on a combination of analytical work, computer simulations, as well as observations usually performed via magnetometers onboard space probes such as Voyager 1. It was found that in the solar wind and the very local interstellar medium, turbulence is nearly incompressible in most cases. Furthermore, all ranges of the von-Karman-Kolmogorov cascade can be observed. The motion of solar energetic particles as well as cosmic rays is influenced by all ranges of the aforementioned cascade including energy, inertial, and dissipation range. The motion of energetic particles is, like turbulence, also a complicated non-linear phenomenon and simple tools such as perturbation theory fail in the general case. One way to tackle this problem is the development of computer simulations. Within such a pure numerical approach, the turbulence is created with the help of random number generators. Then one solves the Newton-Lorentz equation for an ensemble of particles numerically. If this is done for thousands of particles, one can obtain the statistics of the energetic particles. Although such simulations are indeed powerful, a pure numerical description of the transport is incomplete. First, one cannot obtain a detailed insight into the mechanisms of particle scattering. Furthermore, there is a variety of applications where one desires analytical forms of particle diffusion coefficients. Therefore, in addition to the numerical tools described above, we develop advanced non-linear theories to describe the motion of energetic particles. The research outlined in the proposal deals with the development and improvement of non-linear theories, their test via simulations, the derivation of simple analytical forms for the different diffusion parameters, and applications. The proposed work includes topics such as investigating diffusive shock acceleration at interplanetary and supernova shocks. This mechanism is responsible for the creation of cosmic rays. The results obtained via the proposed work will also be important for other investigations such as space weather and solar modulation studies. Furthermore, we shall explore turbulence and its transport based on nearly incompressible magnetohydrodynamics. The main goal of the proposed work is to improve our understanding of turbulence, the motion of energetic particles, and diffusive shock acceleration.