WEAK LANGMUIR TURBULENCE

Weak turbulence theory presents a regular method for a statistical des cription of nonlinear wave interactions. The present review deals with an application of weak turbulence theory to Langmuir wave turbulence. Our main attention is devoted to a plasma with comparable ion and ele ctron temperatures, both magnetized and unmagnetized. In this practica lly important situation ion-sound motions are heavily damped, which si mplifies the physics of nonlinear phenomena. We will demonstrate that the turbulence spectra are highly anisotropic and take the form of ''j ets'' in k-space, and that the onset of a steady state is nontrivial a nd sometimes does not occur at all. On the base of the jet-like spectr a approach it is possible to find the turbulence spectra, to evaluate the anomalous absorption rate and to determine the comparable role of the different absorption mechanisms for a number of practical problems : the excitation of waves by powerful electromagnetic radiation or by electron and ion beams. We demonstrate also that the range in which pu re weak turbulence is valid is pretty narrow. The jet-like spectra str ucture stimulates a modulation instability and after that wave self-fo cusing and collapse. Then, weak and strong turbulence coexist. The fin al part of the review deals with the turbulence of nonisothermal plasm as when additional degrees of freedom are excited. We demonstrate that the ideas, models and methods, presented in this review, give us a ch ance to advance greatly in the understanding of turbulence patterns.