The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response to a non-evolving laser or particle beam is calculated using Maxwell's equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. At the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r-z and a gridless description in $\phi$. We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations are derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code, a full 3D quasi-static code, and the new quasi-static PIC code with azimuthal decomposition are also presented.

中文翻译：

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基于方位角傅立叶分解的准静态粒子内粒子算法，用于高效模拟基于等离子体的加速度：QPAD

3D 准静态细胞内粒子 (PIC) 算法是一种非常有效的方法，用于模拟短脉冲激光或相对论带电粒子束 - 等离子体相互作用。在该算法中，等离子体对非演化激光或粒子束的响应是使用麦克斯韦方程组基于排除辐射的准静态近似方程计算的。然后使用等离子体场以大的时间步长向前推进激光或光束。该算法比 3D 完全显式相对论电磁 PIC 算法快许多数量级。它已被证明能够在各种情况下准确地模拟激光和粒子束的演变。同时，一种算法，其中的领域，电流和麦克斯韦方程被分解为方位角谐波已被证明可以在扩展被截断时将 3D 显式 PIC 算法的复杂性降低到 2D 算法的复杂性，同时保持接近方位对称性问题的准确性。这种混合算法使用 rz 中的 PIC 描述和 $\phi$ 中的无网格描述。我们描述了一种结合准静态和混合 PIC 方法的新方法。该算法将场、电荷和电流密度扩展为方位角谐波。为每个谐波导出一组准静态场方程。然后使用有限差分方法求解场的复振幅。使用总场在笛卡尔坐标系中推进光束和等离子体粒子。详细介绍了如何使用与现有准静态代码 QuickPIC 类似的工作流程来实现该算法。新代码称为 QPAD for QuickPIC with Azimuthal Decomposition。还介绍了完全 3D 显式 PIC 代码、完全 3D 准静态代码和具有方位角分解的新准静态 PIC 代码之间的基准和比较。