Discontinuous distributions in thermal plasmas

We develop a new method for describing the dynamics of 3-dimensional thermal plasmas. Using a piecewise constant 1-particle distribution, we reduce the Vlasov equation to a generalized Lorentz force equation for a family of vector fields encoding the discontinuity. By applying this equation to longitudinal electrostatic plasma oscillations, and coupling it to Maxwell's equations, we obtain a limit on the magnitude of the electric field in relativistic thermal plasma oscillations. We derive an upper bound on the limit and discuss its applicability in a background magnetic field.