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A new model, inspired by the structure of galactic disks, forthree-dimensional Bernstein-Greene-Kruskal (BGK) modes in a plasma with auniform finite background magnetic field is presented. These modes are exactnonlinear solutions of the steady-state Vlasov equation, with an electricpotential and a magnetic potential perturbation localized in all three spatialdimensions that satisfies the Poisson equation, and the Ampere Law,self-consistently. The existence of solutions is shown analytically in thelimit of small electric and magnetic field perturbations associated with thedisk species, and numerically using an iterative method that converges up tomoderately strong field perturbations.

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