VSHPIC: a particle-in-cell algorithm based on vector spherical harmonics expansion

The particle-in-cell (PIC) method has been widely used for studying plasma physics. However, fully three-dimensional PIC simulations always require huge computational resources. For problems with near azimuthal symmetry, recent work (Lifschitz et al 2009 J. Comput. Phys.228 1803–14, Davidson et al 2015 J. Comput. Phys.281 1063–77, Li et al 2021 Comput. Phys. Commun.261 107784, Li et al 2022 J. Comput. Phys.470 111599) has shown that expanding all the quantities defined on the grid in azimuthal harmonics and truncating the expansion can improve the code efficiency. In this paper, we describe a novel parallel algorithm for efficiently simulating three-dimensional near-spherical symmetry problems. Our approach expands all physical quantities in the and directions in spherical coordinates using vector spherical harmonics. The code is capable of simulating three-dimensional asymmetric scenarios by accurately tracking the evolution of distinct individual modes while preserving the charge conservation law. The fundamental dispersion relation of EM waves in the plasma has been obtained using VSHPIC simulation results. The code also shows a well strong scalability up to more than 1000 cores.