Nonlinear plasma waves excited near resonance

The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δnl between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δnl and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations.