Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. IV

Sanae Itoh, Kimitaka Itoh

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A Fokker-Planck equation for the probability distribution function of the magnitude of turbulence is deduced. In the statistical description, both the contributions of thermal excitation and turbulence are kept. From the Fokker-Planck equation, the transition probability between the thermal fluctuation and turbulent fluctuation is derived. With respect to the turbulent fluctuations, the coherent part to a certain test mode is renormalized as the drag to the test mode, and the rest, the incoherent part, is considered to be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. The equilibrium distribution function describes the thermal fluctuation, self-sustained turbulence and the hysteresis between them as a function of the plasma gradient. The plasma inhomogeneity is the controlling parameter that governs the turbulence. The formula of transition probability recovers the Arrhenius law in the thermodynamical equilibrium limit. In the presence of self-noise, the transition probability deviates form the exponential law and provides a power law. Application is made to the submarginal interchange mode turbulence, being induced by the turbulent current-diffusivity, in inhomogeneous plasmas. The power law dependence of the transition probability is obtained on the distance between the pressure gradient and the critical gradient for linear instability. Thus a new type of critical exponent is explicitly deduced in the phenomena of subcritical excitation of turbulence. The method provides an extension of the nonequilibrium statistical physics to the far-nonequilibrium states.

Original languageEnglish
Pages (from-to)427-440
Number of pages14
Journaljournal of the physical society of japan
Volume69
Issue number2
DOIs
Publication statusPublished - Jan 1 2000

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turbulence
transition probabilities
Fokker-Planck equation
inhomogeneity
nonequilibrium plasmas
gradients
probability distribution functions
destabilization
random noise
pressure gradients
drag
excitation
diffusivity
distribution functions
hysteresis
exponents
operators
physics

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. IV. / Itoh, Sanae; Itoh, Kimitaka.

In: journal of the physical society of japan, Vol. 69, No. 2, 01.01.2000, p. 427-440.

Research output: Contribution to journalArticle

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