High-Resolution Three-Dimensional Particle-In-Cell Simulations of Two-Dimensional Bernstein-Greene-Kruskal Modes

We will report the latest three-dimensional (3D) Particle-In-Cell (PIC) simulations to study the stability of two-dimensional (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. We will present simulation results using higher resolutions to study whether solutions stable in 2D simulations can remain stable as the box size along the axial direction increases. We have also utilized the exact form of the solution for the initial conditions of the simulations. We will present our most recent results using this new method of initialization to study kinetic instabilities as seen in our latest 2D simulations.