Numerical Studies of Structure Formation of Plasmas in Non-equilibrium Open System through Modeling of Inter-hierarchy Interaction

本研究的目的是开发一种大规模的数值模拟方法，利用一种新的模型来处理多尺度的时空域，并将其应用于等离子体中结构瞬变现象的动力学研究。研究结果如下：1.建立了基于非线性可压缩Hall-MHD方程的双流体模型，对自组织过程进行了分析。与传统的MHD模型相比，证实了跨场等离子体流的形成，这是双Beltrami(DB)平衡的性质，并证实了过程的约束。环流中结构的形成研究了高β环流中的松弛机理。对于基于修正的Grad-Shafrov方程的数值平衡、场反转过程中极向流的自发形成和反磁旋转的情况，分析了压力驱动的不稳定性。阐明了由于流动而导致的选择性稳定。大型螺旋装置(LHD)等离子体中压力驱动不稳定性的发展显示了自发环状流和可压缩性的抑制作用。将上述模型应用于球形托卡马克中的边缘局域模式。榆树上花丝的形成重现得很好。通过反磁效应验证了该模型的可靠性。用自适应网格加密(AMR)方法形成多层结构一种采用高分辨率紧致差分方法的数值代码已被修改，以包括AMR方法。验证了该程序对MHD模拟的有效性。

This study aims at developing a large-scale numerical simulation method by using a new modeling which can treat self-consistently a multi-scaled spatio-temporal domain, and applying it to the dynamics of structural transient phenomena in plasma. The results are as follows :1. Analysis of self-organization process by means of two-fluid modelA two-fluid model based on nonlinear compressible Hall-MHD equations has been developed. In contrast to conventional MHD models, the formation of cross-field plasma flows which is a nature of double-Beltrami (DB) equilibria, and constraint of the process is confirmed.2. Structure formation in tori with flowsRelaxation mechanisms in a high-beta tori with flows are studied. For the cases of numerical equilibria based on the modified Grad-Shafranov equation, the spontaneous formation of poloidal flows in a translation process of a field-reversed configuration, and a diamagnetic rotation, the pressure-driven instabilities are analyzed. Selective stabilization due to flows are clarified. The development of pressure-driven instabilities in the large helical device (LHD) plasma has shown the suppression effect due to the spontaneous toroidal flows and the compressibility.3. Edge-localized mode (ELM) in spherical tokamak (ST)Abovementioned models are applied to ELM in ST. The formation of filaments on ELMs are well reproduced. The soundness of the model is confirmed against the diamagnetic effect.4. Formation of multi-layered structure by means of adaptive mesh refinement (AMR) methodA numerical code with a high-resolution compact difference method has been modified to include the AMR method. The effectiveness of the code towards the MHD simulations is confirmed.