Stability of Two-Dimensional Bernstein-Greene-Kruskal Modes: Latest Two-Dimensional Particle-In-Cell Simulations

We will report 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)] in a magnetized plasma with a finite background uniform magnetic field. The simulations were performed using the Plasma Simulation Code (PSC) [Germaschewski et al., J. Comp. Phys., 318, 305 (2016)]. These modes are exact nonlinear solutions of the steady-state Vlasov equation with an electric potential localized in both spatial dimensions perpendicular to the axial magnetic field that satisfies the Poisson equation self-consistently. These solutions have cylindrical symmetry and are invariant along the axial direction, with distribution functions depending on the particle energy, the axial component of the canonical angular momentum, and the axial component of the canonical momentum. Cases with different strength of the background magnetic field will be presented to show the changes in the stability. We will present simulations using higher resolutions to compare with our previous runs. We will also present simulations using ions of realistic mass ratio and with an initial Boltzmann distribution, to contrast with simulations using a background of uniform ion density.