Local Kinetic Analysis for the Instability Observed in Particle-In-Cell Simulations of Two-Dimensional Bernstein-Greene-Kruskal Modes

In the latest two-dimensional (2D) Particle-In-Cell (PIC) simulations to study the stability of 2D Bernstein-Greene-Kruskal (BGK) modes [Ng, Phys. Plasmas, 27, 022301 (2020)] using the Plasma Simulation Code (PSC) [Germaschewski et al., J. Comp. Phys., 318, 305 (2016)], an instability was observed in runs with weak background magnetic fields which exhibits a unique wave pattern, apparently from a kinetic instability. Such wave patterns begin as co-rotating azimuthal electrostatic perturbations, and evolve into spiral shapes later in the instability. We will present local analysis along the azimuthal direction based on kinetic theory to try to understand the simulation results. Growth rates and phase velocities of different azimuthal mode numbers will be compared with results from the PIC simulations.