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Statistical Theory of Plasmas Turbulence

Eun-jin KIM and Johan ANDERSON

Department of Applied Mathematics, University of Sheffield, Sheffield, S3 7RH, U.K.

(Received 31 August 2008 / Accepted 20 April 2009 / Published 23 June 2009)

Abstract

We present a statistical theory of intermittency in plasma turbulence based on short-lived coherent structures (instantons). In general, the probability density functions (PDFs) of the flux R are shown to have an exponential scaling P(R) ∝ exp (-cR^s ) in the tails. In ion-temperature-gradient turbulence, the exponent takes the value s = 3/2 for momentum flux and s = 3 for zonal flow formation. The value of s follows from the order of the highest nonlinear interaction term and the moments for which the PDFs are computed. The constant c depends on the spatial profile of the coherent structure and other physical parameters in the model. Our theory provides a powerful mechanism for ubiquitous exponential scalings of PDFs, often observed in various tokamaks. Implications of the results, in particular, on structure formation are further discussed.

Copyright (c) 2009 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

turbulence, structure, shear flow, confinement, probability density function (PDF)

DOI: 10.1585/pfr.4.030

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This paper may be cited as follows:

Eun-jin KIM and Johan ANDERSON, Plasma Fusion Res. 4, 030 (2009).