Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space-time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to resolve Debye lengths spatially. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas.

中文翻译：

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能量守恒粒子内细胞算法中的有限空间网格效应

有限网格（或混叠）不稳定性在粒子内粒子 (PIC) 等离子体模拟算法中普遍存在，并迫使建模者解决问题中的最小 (Debye) 长度尺度，而不管动态相关性如何。这些不稳定性源于网格量和粒子（它们存在于时空连续体中）之间的插值误差的混叠。最近，已经开发出严格节能的 PIC (EC-PIC) 算法，该算法有望增强对混叠不稳定性的鲁棒性。在这项研究中，我们通过分析确认 EC-PIC 对静止等离子体的混叠不稳定性是稳定的。对于漂移等离子体，我们通过分析和数值实验证明，虽然 EC-PIC 算法原则上不能摆脱这些不稳定性，它们具有有限温度等离子体的良性稳定性阈值，使它们在实践中可用于解决一大类问题（具有双极性和现实的离子电子质量比），而无需在空间上解决德拜长度。我们还证明，流行的动量守恒 PIC 算法不存在此阈值，因此对于漂移和静止等离子体都不稳定。