Reduced description of strong Langmuir turbulence from kinetic theory

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Abstract
A reduced description of strong Langmuir turbulence is derived from the Vlasov–Poisson equations by using an oscillation center transformation that decomposes the distribution function into envelope components which vary slowly on the plasma frequency time scale. The familiar high-frequency response is identified in the context of a basic ordering of small quantities. A generalization of the ion acoustic wave equation to the regime of equal electron and ion temperatures which is valid in this ordering is derived using a three-pole approximant for the collisionless ion susceptibility. The resulting extended Zakharov model is solved numerically in two dimensions for parameters relevant to radio-frequency heating of the ionosphere, producing energy and power spectra of fluctuations that are qualitatively similar to experimental observations. A new local quasilinear equation for the spatial and temporal evolution of the slowly varying part of the oscillation center distribution function is proposed.