A "Galactic Disk"-Model for Three-Dimensional Bernstein-Greene-Kruskal Modes in a Finite Magnetic Field

TL;DR

This paper introduces a novel galactic disk-inspired model for three-dimensional BGK plasma modes with finite magnetic fields, providing analytical and numerical solutions for localized nonlinear plasma structures.

Contribution

It presents the first galactic disk-inspired model for 3D BGK modes in finite magnetic fields, with analytical existence proofs and an iterative numerical solution method.

Findings

Analytical proof of BGK mode existence in small perturbation limit.

Numerical solutions for moderate field perturbations.

Localized 3D plasma structures satisfying Poisson and Ampere laws.

Abstract

A new model, inspired by the structure of galactic disks, for three-dimensional Bernstein-Greene-Kruskal (BGK) modes in a plasma with a uniform finite background magnetic field is presented. These modes are exact nonlinear solutions of the steady-state Vlasov equation, with an electric potential and a magnetic potential perturbation localized in all three spatial dimensions that satisfies the Poisson equation, and the Ampere Law, self-consistently. The existence of solutions is shown analytically in the limit of small electric and magnetic field perturbations associated with the disk species, and numerically using an iterative method that converges up to moderately strong field perturbations.