Nonlinear Landau damping of resonantly excited fields in nonuniform plasmas

In this study the resonant excitation of a nonuniform plasma by two electromagnetic waves at closely spaced frequencies ω1, ω2 with ω1>ω2 is considered. Each of the pump waves excites a Langmuir wave at the point in the density profile, where plasma resonance is achieved. For profiles having scale lengths L large compared to the characteristic Airy scale length (i.e., kAL much-gt 1) the linear Landau damping of the Langmuir waves is quite small close to their cutoff, hence the beat interaction with slow electrons plays an important role. The problem is formulated in terms of differential equations in configuration space for the waves at ω1, ω2, which are coupled to the idler field at ω1-ω2. The idler is described kinetically by a differential equation in Fourier space. The interaction is governed by the parameter ω3=(1-ω2/ω1)kAL and the scaled pump strength. For ω3 much-lt 1 the ponderomotive nonlinearity is recovered and a dissipative contribution is obtained. For ω3>1 plasmon transfer from ω1 to ω2 causes strong depletion of the high-frequency wave before significant ponderomotive profile changes set in. The fractional power absorbed through the idler is smaller than the power transferred to ω2 by a factor of (1-ω2/ω1)