一种用于高$\eta$等离子体模拟的全隐式电磁能量与电荷守恒PIC模型

中文摘要 AI 辅助

本文提出了一种三维等离子体数值模型，在该模型中，具有全局能量和局部电荷精确守恒特性的全隐式PIC方法被推广到电磁情形。这为模拟在开放磁阱中形成的具有高（乃至极端）等离子体压力与磁场压力比值的等离子体平衡态提供了可能性。本研究的主要目标是探究全隐式模型（其在求解耦合的Vlasov-Maxwell系统时通常需要进行大量非线性迭代）能否在性能上与半隐式模型竞争，后者以每个时间步仅需一次粒子推进为代价即可实现相同的守恒特性。结果表明，在三维几何中，由于半隐式方法中质量矩阵评估的计算成本不断增长，这种竞争是相当可行的。所提出数值模型的软件实现采用C++编写，集成于并行的\ exttt{xpic}代码中。在Weibel不稳定性发展和极端压力等离子体形成等问题的测试中，半隐式方法与全隐式方法表现出良好的一致性，并确定了它们的相对速度。

英文摘要

The paper presents a 3D numerical model of plasma in which a fully implicit PIC method with exact conservation of global energy and local charge is generalized to the electromagnetic case. This opens the possibility of simulating plasma equilibria with a high (up to an extreme) ratio of plasma pressure to magnetic field pressure, which are formed in open magnetic traps. The main goal of this work is to find out whether a fully implicit model, which usually performs numerous nonlinear iterations when solving the coupled Vlasov--Maxwell system, can compete in performance with semi-implicit models that achieve the same conservative properties at the cost of only a single particle push per time step. It turns out that in 3D geometry such competition is quite possible due to the growing computational cost of evaluating the mass matrices in the semi-implicit approach. The software implementation of the proposed numerical model is written in C++ within the parallel \texttt{xpic} code. Testing the code on problems of the development of the Weibel instability and the formation of plasma with extreme pressure showed good agreement between the semi-implicit and fully implicit approaches and made it possible to establish their relative speed.

发表机构

• Novosibirsk State University（新西伯利亚国立大学）
• Budker Institute of Nuclear Physics SB RAS（布杜克尔核物理研究所（俄罗斯科学院西伯利亚分院））

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