用于圆柱形等离子体源的方位角模态分解粒子网格算法
Azimuthal mode decomposition Particle in Cell algorithm for cylindrical plasma sources
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中文总结 AI 辅助
本文提出一种方位角模态分解粒子网格算法，利用圆柱几何的傅里叶分解，将二维问题简化为一维耦合问题，实现谱精度并节省一个数量级计算时间，用于低温等离子体模拟。
中文摘要 AI 辅助
本文提出了一种高效的粒子网格数值方法，用于对低温等离子体进行全维动力学模拟。利用大多数等离子体源的圆柱几何特性，在方位角（$\ heta$）方向上对场进行傅里叶模态分解，直至选定的最大模态数 $N_m$。宏粒子在所有 $D$ 维中推进，并为每个模态 $m$ 加权到 $(D-1)$ 维网格上。每个模态的电场计算是独立的，归结为求解 $(N_m+1)$ 个 $(D-1)$ 维泊松问题。该方法在方位角方向上具有谱精度，而计算成本与 $(D-1)$ 维模拟相当。我们针对基于潘宁放电的平面测试案例验证了该方法，该案例在低温等离子体社区中广泛用于基准测试和验证。我们的方法能够将二维问题简化为一系列耦合的一维问题，并自然地执行不同方位角模态的谱分析，恢复每个模态对径向输运的贡献，与最先进的二维粒子网格代码相比，计算时间节省了一个数量级。
英文摘要
An efficient Particle-in-Cell numerical approach to perform full-dimensional kinetic simulations of low temperature plasmas is presented. Taking advantage of the cylindrical geometry of most plasma sources, a Fourier mode decomposition of the fields is carried out in the azimuthal ($θ$) direction up to a chosen maximum number of modes $N_m$. Macroparticles are pushed in all $D$ dimensions and weighed, for each mode $m$, onto a $(D-1)$ dimensional grid. The computation of the electric field for each mode is independent and reduces to solving $(N_m+1)$ $(D-1)$ dimensional Poisson problems. The approach brings spectral accuracy in the azimuthal direction, while the computational cost is comparable to that of a simulation with $(D-1)$ dimensions. We verify this approach against a planar test case based on a Penning discharge, widely used for benchmarking and validation purposes in the low-temperature plasma community. Our approach allows us to reduce the 2D problem into a collection of coupled 1D problems and to naturally perform spectral analysis of the different azimuthal modes, recovering the contribution of each mode to radial transport, with a computational time saving of one order of magnitude with respect to state of the art 2D particle-in-cell codes.
发表机构
- Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
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