Modulational processes and limits of weak turbulence theory.

Abstract

Modulational instability of a broad spectrum of Langmuir waves in unmagnetized plasmas is considered. The problem of thresholds of the modulational instability is studied in detail. Applicability limits (which are associated with stochastic properties of turbulent plasma waves) of the theory of weak plasma turbulence are discussed. It is demonstrated that the weak turbulence theory is appropriate for the description of modulational processes developed only for sufficiently wide wave spectra (and/or sufficiently low levels of plasma turbulence). Instability thresholds found on the basis of the theory of weak plasma turbulence are compared with those obtained on the basis of the WKB ansatz, which does not use the random phase approximation. It is demonstrated that for isotropic three-dimensional as well as for one-dimensional Langmuir wave spectra both these approaches result in similar instability conditions and it is shown that for some special spectra of Langmuir waves those are necessary and sufficient (in the mathematical sense) conditions for the development of the modulational instability. Applicability limits of the WKB approximation for the description of the modulational processes are considered in detail and compared with those of the weak turbulence theory.