Numerical test of the weak turbulence approximation to ionospheric Langmuir turbulence

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Abstract
The standard weak Langmuir turbulence approach to explain the artificial plasma line in ionospheric radio modification experiments is examined. We compare solutions of a weak turbulence approximation (WTA) derived from a version of the one‐dimensional driven and damped Zakharov system of equations (ZSE) with solutions to the same full ZSE. The electromagnetic pump field is modeled as a long‐wavelength parametric driving term. We found that from a certain distance below the O mode reflection level the wave number saturation spectra computed from the WTA agree qualitatively with those from the ZSE for weak driving strengths, in the sense that the number of cascade lines increases with increasing pump strength. However, in general, the number of cascades apparent in the WTA solutions is larger than that predicted from the full ZSE. At higher intensities of the driver the saturation spectra from the ZSE differ from the WTA cascade spectra, in that a truncation of the cascade sets in, with a subsequent filling in of the bands between the cascades. This truncation takes place far before the ZSE cascade spectra reach the so‐called “Langmuir condensate,”; contrary to earlier conjectures based mainly on dimensional analysis arguments. In the reflection region a qualitatively different process takes place: temporal cycles of large ensembles of localized events; nucleation of cavitons, collapse, and burnout constitute the basic elements of the turbulence in this region of space. No WTA exists for this region. Our findings are discussed with respect to the experiments performed at Arecibo and Tromsø, the conclusion being that the ZSE yields results closer to observations than does the WTA, in all regions of space.