Weak Langmuir turbulence

Abstract 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.

[1]  B. Sturman,et al.  Collective effects associated with lower hybrid heating of plasma , 1978 .

[2]  A. Wong,et al.  Nonlinear evolution of electron-beam-plasma interactions , 1985 .

[3]  J. Fejer,et al.  Structure in the nonlinear saturation spectrum of parametric instabilities , 1973 .

[4]  T. Johnston,et al.  Instability Cascades, Lotka-Volterra Population Equations, and Hamiltonian Chaos , 1982 .

[5]  H. Chen,et al.  Saturation spectrum of the parametric decay instability in the presence of an external magnetic field. [geomagnetic effect in ionospheric heating , 1975 .

[6]  T. Marshall,et al.  EFFECTS OF PLASMA FLOW ON ELECTROSTATIC DISTURBANCES IN A Q MACHINE. , 1970 .

[7]  M. Wakatani,et al.  Plasma Physics: Basic Theory with Fusion Applications , 1994 .

[8]  D. Ryutov,et al.  Relaxation of Relativistic Electron Beam in a Plasma with Random Density Inhomogeneities , 1976 .

[9]  M. Goldman,et al.  Spectrum and Anomalous Resistivity for the Saturated Parametric Instability , 1972 .

[10]  A. A. Galeev,et al.  Basic plasma physics II , 1983 .

[11]  Rose,et al.  Power spectra of fluctuations in strong Langmuir turbulence. , 1988, Physical review letters.

[12]  M. Rietveld,et al.  Langmuir turbulence and ionospheric modification , 1992 .

[13]  V. Tikhonchuk,et al.  Parametric plasma turbulence , 1986 .

[14]  W. Kruer,et al.  Nonlinear evolution of the decay instability in a plasma with comparable electron and ion temperatures , 1973 .

[15]  Perkins,et al.  Fluid closures which mimic wave-praticle interactions in strong Langmuir turbulence. , 1993, Physical Review Letters.

[16]  V. L’vov.  Wave Turbulence Under Parametric Excitation , 1994 .

[17]  V. Tsytovich,et al.  Theory of Turbulent Plasma , 1977 .

[18]  G. Marchuk.  Methods of Numerical Mathematics , 1982 .

[19]  Rose,et al.  Coexistence of parametric decay cascades and caviton collapse at subcritical densities. , 1991, Physical review letters.

[20]  Gregory Falkovich,et al.  Kolmogorov Spectra of Turbulence I , 1992 .

[21]  E. Valeo,et al.  SATURATION OF THE DECAY INSTABILITY FOR COMPARABLE ELECTRONIC AND ION TEMPERATURES. , 1972 .

[22]  V. Zakharov,et al.  REVIEWS OF TOPICAL PROBLEMS: Spin-wave turbulence beyond the parametric excitation threshold , 1975 .

[23]  A. Rogister,et al.  Theory of parametric heating of plasma in the lower hybrid frequency range , 1976 .

[24]  V. Zakharov,et al.  Statistical description of nonlinear wave fields , 1975 .

[25]  Perkins,et al.  Fluid moment models for Landau damping with application to the ion-temperature-gradient instability. , 1990, Physical review letters.

[26]  J. Dawson,et al.  Anomalous High‐Frequency Resistivity of a Plasma , 1972 .