On numerical errors to the fields surrounding a relativistically moving particle in PIC codes
On numerical errors to the fields surrounding a relativistically moving particle in PIC codes
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DOI：
10.1016/j.jcp.2020.109451
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
Xinlu Xu;Fei Li;F. Tsung;T. Dalichaouch;W. An;H. Wen;V. Decyk;R. Fonseca;M. Hogan;W. Mori
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文献类型：
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作者：
Xinlu Xu;Fei Li;F. Tsung;T. Dalichaouch;W. An;H. Wen;V. Decyk;R. Fonseca;M. Hogan;W. Mori
粒子网格（PIC）方法被广泛用于模拟离散粒子与电磁场之间的自洽相互作用。它已成功地应用于等离子体物理的问题，包括等离子体加速，惯性约束聚变，磁约束聚变，空间物理，天体物理，高能量密度等离子体。在许多情况下，物理学涉及相对论性粒子（具有高相对论性γ因子的粒子）如何产生并与等离子体相互作用。然而，当相对论粒子流穿过网格时，无论是在“真空”还是在等离子体中，都可能出现许多数值问题，这些问题可能导致非物理结果。我们提出了一个详细的分析，如何离散麦克斯韦求解器中使用的PIC代码可以导致数值误差的领域，围绕粒子的相对论速度跨越网格移动。给出了轴向电场的积分表达式，揭示了两种误差。第一个是由于被积函数分子的错误，导致非物理场关于粒子反对称。第二个问题是由于被积函数的分母存在误差，导致真空中的类切伦科夫辐射。这些场不是反对称的，在粒子后面延伸，并导致粒子加速或减速，具体取决于解算器和参数。非物理领域的两个代表性的求解器-Yee求解器和基于FFT的求解器进行了详细研究。虽然切伦科夫场不存在，空间电荷场仍然存在于基于FFT的求解器的基本布里渊区中。此外，切伦科夫场存在于基于FFT的求解器的高阶区域中。给出了解析解与PIC模拟结果的比较。本文还提出了一种通过在轴向修正k算子来消除这些非物理场的方法。使用定制的有限差分求解器，该解决方案已成功实施到OSIRIS [1]中。还介绍了自定义求解器的结果。这个解对于所有粒子都以小的角发散沿一个方向运动的粒子束将是有用的。
The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles (those with high relativisticγfactors) are generated and interact with plasmas. However, when relativistic particles stream across the grid, both in “vacuum” and in plasma, many numerical issues may arise which can lead to unphysical results. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals inkspace are presented that reveal two types of errors. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. The second arises from errors to the denominator of the integrand and lead to Cherenkov like radiation in “vacuum”. These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. Although the Cherenkov fields are absent, the space charge fields are still present in the fundamental Brillouin zone for the FFT based solvers. In addition, the Cherenkov fields are present in higher order zones for the FFT based solvers. Comparison between the analytical solutions and PIC simulation results are presented. A solution for eliminating these unphysical fields by modifying thekoperator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS [1]. Results from the customized solver are also presented. This solution will be useful for a beam of particles that all move in one direction with a small angular divergence.