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

We will report 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 latest 3D simulations to compare with our previous 2D runs to show how the stability changes with dimensionality.