Particle-In-Cell Simulations to Study the Stability of Two-Dimensional Bernstein-Greene-Kruskal Modes

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 is studied using the Plasma Simulation Code (PSC) [Germaschewski et al., J. Comp. Phys., 318, 305 (2016)], a Particle-In-Cell (PIC) code. These solutions 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 the distribution functionion or electrondepending on the particle energy and the axial components of the canonical linear and angular momenta. We investigate 2-d stability of both electron-only BGK modes with a uniform ion background as well as full two-species solutions. An extension to high-resolution PIC simulations in 3-d is planned.