Particle-In-Cell Simulations of Two-Dimensional Bernstein-Greene-Kruskal Modes using Exact Analytic Distributions as Initial Conditions

We will report 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)] 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. Our previous runs used local Maxwellian approximation of the analytic electron distribution functions by matching the first three moments of density, flow velocity and temperature at each spatial location. Now, we present runs using the exact analytic distributions as initial conditions. We found that the modes are significantly steadier in time for cases with large background magnetic fields, but exhibit unique wave patterns apparently from kinetic instability for cases with weak background magnetic fields, as compared to the local Maxwellian runs. Such wave patterns begin as co-rotating azimuthal electrostatic perturbations, and evolve into spiral shapes later in the instability.