用混合有限差分-FFT Maxwell解算器和局部电荷守恒电流沉积减轻数值Cerenkov辐射和不稳定性
Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit
摘要：
描述了一种完全相对论和电磁（EM）粒子单元（PIC）代码的混合麦克斯韦求解器。在该求解器中，通过在一个方向上执行FFT，同时在其他方向上使用有限差分算子，在$k$空间中求解EM场。该求解器消除了在优选方向上移动的粒子的数值切伦科夫辐射。此外，数值切伦科夫不稳定性（NCI）引起的相对论漂移等离子体和光束可以消除使用这种混合求解器通过应用策略，是最近开发的纯FFT求解器类似。电流校正应用于电荷守恒电流沉积，以正确地解释混合Yee-FFT求解器中的EM计算。对该混合求解器在真空和漂移等离子体中的色散特性进行了理论分析，并与粒子模拟结果进行了比较，两者吻合较好。这种混合求解器适用于二维和三维笛卡尔和准三维（其中的字段和电流被分解成方位角谐波）的几何形状。激光尾流场加速器模拟在洛伦兹助推框架中使用的混合求解器在二维笛卡尔几何的说明性结果，并从2D UPIC-EMMA模拟，使用纯频谱麦克斯韦求解器，从OSIRIS 2D实验室框架模拟使用标准的Yee求解器的结果进行比较。非常好的协议，这表明使用混合求解器的相对论漂移等离子体的高保真度模拟的可行性，没有证据的数值切伦科夫不稳定性。
英文摘要：
A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to correctly account for the EM calculation in hybrid Yee-FFT solver. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.
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