ABSTRACT
Nonlinear effects in the description of collisionless plasmas are concerned with two basically different types of problems. One is steady state solutions with large amplitudes, the other with dynamic wave phenomena. Some of these are to some extent trivial modifications of phenomena encountered also in fluid models. The fully nonlinear Vlasov equation can be solved at least in one spatial dimension to give a steady state electrostatic equilibrium solution without restrictions on the wave amplitudes. This observation was first made by Bernstein et al., and these solutions are hence termed “Bhatnagar-Gross-Krook-solutions”. For the present one-dimensional model we have no electromagnetic effects, and ignore also steady state magnetic fields generated by possible currents in the plasma. It is found that there are in principle infinitely many possibilities for stationary, fully nonlinear solutions to the coupled one-dimensional Vlasov-Poisson system of equations.
