Nonlinear Resonance of Two-dimensional Ion Layers

Résumé du livre

A nonlinear theory of wave resonances in a two-dimensional ion layer confined under the surface of liquid helium is presented. The ion layer is modelled as a two-dimensional cold plasma fluid. In addition to the usual nonlinearities present in the continuity equation and the equation of motion, the theory considers a nonlinear dependence of the mass of a plasma particle on its velocity, as suggested by indirect experimental evidence. Secular perturbation theory is used to find the plasma response when the damped, nonlinear system is driven externally. For typical experimental parameters, the mass nonlinearity is found to be the dominant nonlinear effect, giving rise to a backbending of the resonance curve. In the present work, the simpler Cartesian model is emphasized for clarity of exposition, but the corresponding results for the cylindrical case are also described. Previous work on the nonlinear waves in Cartesian two-dimensional plasmas makes idealized assumptions on the equilibrium density profile and uses boundary conditions (satisfied by the wave potential) which are not well justified; furthermore, only the ponderomotive nonlinearity is considered. The goal of the present work is to present a rigorous treatment, including exact equilibrium profiles and correct boundary conditions, of the nonlinearities present in the continuity equation and the equation of motion as well as the mass nonlinearity.