Abstract
The bounce-kinetic model is developed and applied to driven nonlinear Langmuir waves. The waves are described in terms of an eikonal with slow envelope variation. It is assumed that the bounce frequency of trapped electrons is large. A kinetic equation involving only slowly varying quantities is derived and it is shown that the characteristic equations form a Hamiltonian system. Conservation of particles, momentum, and energy are shown to depend on first-order corrections to this kinetic equation. The low order correction moments are derived exactly from these conservation laws, eliminating the need for a complicated boundary layer treatment of the separatrix. Previous results for nonlinear Langmuir waves are reproduced by a simplified version of this theory which neglects variations of the amplitude envelope and phase velocity. A particle-in-cell method is proposed for solution of the nonlinear kinetic problem. Extensions of this method required to correctly describe small amplitude waves are suggested. Such an extended model may be useful for the modeling of laser-plasma interaction in the trapping regime.
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