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arXiv 1407.5253physics.plasm-phphysics.comp-ph
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电磁粒子网格程序的数值弥散:有限网格不稳定性

On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability

M. D. Meyers, C. -K. Huang, Y. Zeng, S. A. Yi, B. J. Albright

摘要:

粒子模拟方法(PIC)广泛应用于相对论粒子束和激光等离子体的模拟。然而,PIC方法表现出数值不稳定性,可以使非物理模拟结果,甚至破坏模拟。对于电磁相对论束流和等离子体模拟,最相关的数值不稳定性是有限网格不稳定性和数值切伦科夫不稳定性。我们回顾了电磁PIC算法的数值色散关系,分析了这些不稳定性的来源。我们严格推导了PIC算法的忠实的三维数值色散,然后专注于Yee FDTD方案。特别是,我们占PIC算法更新和采样的字段和分布函数的方式。时间和空间的相位因子求解麦克斯韦方程组的Yee网格与蛙跳计划也明确占。数值解的类静电模式的一维色散关系的冷漂移等离子体的参数的利益。在随后的分析中,我们调查如何有限网格不稳定性产生的相互作用的数值一维模式承认在系统和他们的别名。最重要的相互作用是由于关键的色散关系中的运营商的正确表示。我们得到一个简单的解析表达式的峰值增长率由于这种相互作用。

英文摘要:

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the electromagnetic PIC algorithm to analyze the origin of these instabilities. We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm, and then specialize to the Yee FDTD scheme. In particular, we account for the manner in which the PIC algorithm updates and samples the fields and distribution function. Temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme are also explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical 1D modes admitted in the system and their aliases. The most significant interaction is due critically to the correct represenation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction.

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