On the validity of the weak turbulence approximation

The weak Langmuir turbulence approach to explain the artificial plasma line in ionospheric radio modification experiments, is examined. The mathematical model is a version of the one dimensional Zakharov equations, including damping and a nonlinear ac driving. Numerical full wave solutions to this set of equations are compared with the saturation spectrum determined by a wave kinetic equation derived from the same set of equations. It was found that a distance below the O-mode reflection level, omega - omega(sub p) is much greater than (m/M)omega(sub p) (omega is the applied frequency; omega(sub p) is the plasma frequency; m,M is the electron and ion masses), the full wave solution is in good qualitative agreement with the cascade theory. The number of cascades seen in the full wave solution is generally smaller than that of the saturation spectrum of the wave kinetic equation. On the other hand, in the reflection region omega - omega(sub p) is less than (m/M)omega(sub p), a qualitatively different process takes place, describable as many localized cycles of nucleation, (one dimensional driven) collapse, and burnout, similar to the results of Doolen et. al. These findings are discussed with respect the experiments performed in Arecibo and Tromso.