We present a study of the standard plasma physics test, Landau damping, using the Particle-In-Cell (PIC) algorithm. The Landau damping phenomenon consists of the damping of small oscillations in plasmas without collisions. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic and/or gravitational fields, and a distribution of delta functions to represent the particle field. Approximations to the dispersion relation are found to be inadequate in accurately calculating values for the electric field frequency and damping rate when parameters of the physical system, such as the plasma frequency or thermal velocity, are varied. We present a full derivation and numerical solution for the dispersion relation, and verify the PETSC-PIC numerical solutions to the Vlasov-Poisson for a large range of wave numbers and charge densities.

翻译：我们利用粒子网格（PIC）算法对标准等离子体物理测试问题——朗道阻尼进行了研究。朗道阻尼现象是指无碰撞等离子体中微小振荡的衰减过程。在PIC方法中，通过构建混合离散化方案，采用具有有限支撑基函数的网格表示电场、磁场和/或引力场，并利用δ函数分布表示粒子场。研究发现，当物理系统参数（如等离子体频率或热速度）变化时，通过色散关系近似值计算的电场频率和阻尼率存在精度不足的问题。本文给出了色散关系完整的推导过程及其数值解，并验证了PETSc-PIC在宽波数范围和电荷密度条件下对弗拉索夫-泊松方程组的数值解。