Nonlinear stability theorem for high-intensity charged particle beams

Global conservation constraints based on the nonlinear Vlasov-Maxwell equations are used to derive a three-dimensional kinetic stability theorem for an intense non-neutral ion beam (or charge bunch) propagating with average axial velocity upsilon(b) = const. It is shown that a sufficient condition for linear and nonlinear stability for perturbations with arbitrary polarization is that the equilibrium distribution be a monotonically decreasing function of the single-particle energy H' in the beam frame, i.e., partial derivative f(eq)(H')/partial derivative H' less than or equal to 0.