  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.
