New Theory and Applications with the Regularized Kappa-Distribution

在这个项目中，我们将通过采用最近引入的正则化Kappa分布（RKD）来推进非平衡等离子体理论和相应的具体应用，该分布用于实际处理和解释超热粒子群及其在各种天体物理系统中的含义。该RKD允许人们克服标准Kappa分布（SKD）的一系列关键限制和缺陷，这些限制和缺陷主要由发散速度矩、非广泛熵以及非物理超光速粒子的不期望贡献决定。新的RKD概念促使系统地探索其在动力学和流体理论以及小尺度和大尺度天体物理等离子体系统的相应研究中的影响。因此，拟议项目的主要目标是基于RKD发展新的理论方法，并将其应用于非平衡多尺度等离子体，重点是观测到的最佳天体物理系统，即日球层。这一目标是由两个科学关键问题明确制定的，其中一个是解决动力学理论，另一个是解决流体理论：（Q1）在动力学理论中使用RKD对等离子体波的性质和不稳定性有什么影响？（Q2）如何推导出基于RKD的流体理论并将其应用于非热天体物理系统？第一个问题的答案将澄清，通过分析和数值模拟的手段，使用RKD等离子体波在小，即动力学尺度的后果。对第二个问题的回答将在大尺度（即流体尺度）上建立等离子体动力学的一致定量处理。利用数据进行建模和评估将通过完成以下三项任务来实现：(i)发展RKD的动力学理论并将其应用于太阳风等离子体中的粒子群；（ii）利用RKD的宏观矩和质量、动量和能量的适当源项推导出类似mhd的流体方程及其应用；（iii）利用航天器数据验证动力学和流体结果。通过相应的分析和数值研究，我们不仅将加深对RKD的物理相关性及其对天体物理等离子体系统，特别是太阳风的意义的理解，而且还将首次建立彼此完全一致的非热天体物理等离子体的动力学和流体描述。理论和模型的验证将在各种航天器数据的基础上进行，特别是来自最近发射的NASA任务帕克太阳探测器和即将发射的ESA任务太阳轨道器。

With this project we will advance the non-equilibrium plasma theory and corresponding specific applications by employing the Regularized Kappa Distribution (RKD) that was introduced recently for a realistic treatment and interpretation of suprathermal particle populations and their implications in various astrophysical systems. This RKD allows one to overcome a series of critical limitations and deficiencies of the standard Kappa distribution (SKD) mainly determined by the diverging velocity moments, a non-extensive entropy as well as undesired contributions of unphysical superluminal particles. The new RKD concept motivates systematic explorations of its consequences in kinetic as well as fluid theory and corresponding studies of astrophysical plasma systems on small and large scales. Consequently, the main objective of the proposed project is to develop new theoretical approaches based on the RKD and to apply them to non-equilibrium multi-scale plasmas, with an emphasis on the best observed astrophysical system, i.e., the heliosphere. This objective is explicitly formulated with two scientific key questions, one of which is addressing kinetic theory and the other the fluid theory: (Q1) What are the implications of using the RKD in the kinetic theory for the properties of plasma waves and instabilities? (Q2) How can a fluid theory based on the RKD be derived and applied to nonthermal astrophysical systems? The answer to the first question will clarify, by means of analytical and numerical modelling, the consequences of using the RKD for plasma waves on small, i.e. kinetic scales. That to the second question will establish a consistent quantitative treatment of the plasma dynamics on large, i.e. fluid scales. The modelling and its assessment with data will be realized by the fulfillment of the following three tasks: (i) the development of the kinetic theory for the RKD and its application to particle populations in the solar wind plasma, (ii) the use of macroscopic moments of the RKD and appropriate source terms for mass, momentum and energy to derive MHD-like fluid equations and their application, and (iii) the validation of the kinetic and fluid results with spacecraft data. With the corresponding analytical and numerical studies we will not only deepen the understanding of the physical relevance of the RKD and its significance for astrophysical plasma systems, in particular the solar wind, but also establish, for the first time, a kinetic and a fluid description of nonthermal astrophysical plasmas that are fully consistent with each other. The validation of the theory and the modelling will be made on the basis of various spacecraft data, particularly from the recently launched NASA mission Parker Solar Probe and the forthcoming ESA mission Solar Orbiter.