  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.
