On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:413

Article

Xu, Xinlu^1,2  Li, Fei¹  Tsung, Frank S.³  Dalichaouch, Thamine N.³  An, Weiming⁴  Wen, Han¹  Decyk, Viktor K.³  Fonseca, Ricardo A.^5,6  Hogan, Mark J.²  Mori, Warren B.^1,3 

[1] Univ Calif Los Angeles, Dept Elect Engn, Los Angeles, CA 90095 USA

[2] SLAC Natl Accelerator Lab, Menlo Pk, CA 94025 USA

[3] Univ Calif Los Angeles, Dept Phys & Astron, Los Angeles, CA 90095 USA

[4] Beijing Normal Univ, Dept Astron, Beijing 100875, Peoples R China

[5] Univ Lisbon, Inst Super Tecn, Inst Plasma & Fusao Nucl, GOLP, Lisbon, Portugal

[6] ISCTE Inst Univ Lisboa, P-1649026 Lisbon, Portugal

关键词: Relativistic drifting particles;    Numerical Cherenkov radiation;    Numerical space charge like field;    Particle-in-cell method;   

DOI  :  10.1016/j.jcp.2020.109451

来源: Elsevier

【 摘 要 】

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 relativistic gamma factors) 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 in k space 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 antisymmetric, 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 the k operator 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free