Weak Langmuir turbulence

Sam L. Musher, Alexander M. Rubenchik, Vladimir E. Zakharov

Research output: Contribution to journalReview articlepeer-review

91 Scopus citations


Weak turbulence theory presents a regular method for a statistical description 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 electron temperatures, both magnetized and unmagnetized. In this practically important situation ion-sound motions are heavily damped, which simplifies the physics of nonlinear phenomena. We will demonstrate that the turbulence spectra are highly anisotropic and take the form of "jets" in k-space, and that the onset of a steady state is nontrivial and sometimes does not occur at all. On the base of the jet-like spectra 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 pure weak turbulence is valid is pretty narrow. The jet-like spectra structure stimulates a modulation instability and after that wave self-focusing and collapse. Then, weak and strong turbulence coexist. The final part of the review deals with the turbulence of nonisothermal plasmas when additional degrees of freedom are excited. We demonstrate that the ideas, models and methods, presented in this review, give us a chance to advance greatly in the understanding of turbulence patterns.

Original languageEnglish (US)
Pages (from-to)177-274
Number of pages98
JournalPhysics Reports
Issue number4
StatePublished - Feb 1995

ASJC Scopus subject areas

  • General Physics and Astronomy


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