Structure of MHD turbulence in large-Prandtl-number plasmas

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  • 14 March 2002
Abstract
We study the intermittency and field-line structure of the MHD turbulence in plasmas with very large magnetic Prandtl numbers where magnetic fluctuations can be excited at scales below the viscous cutoff. The salient structural feature of the resulting small-scale magnetic turbulence is the folded structure of the fields. It is characterised by very rapid transverse variation of the field at scales ultimately bounded from below only by the resistive length, while the field lines remain largely unbent up to the scale of the flow. Quantitatively, the fluctuation level and the field-line geometry can be studied in terms of the PDFs of the field strength and of the field-line curvature. In the kinematic limit, the distribution of the field strength is an expanding lognormal, while that of the field-line curvature K is stationary and has a power tail ~ K^{-13/7}. The field strength and the curvature are anticorrelated, i.e. the growing fields are mostly flat, while the sharply bent fields remain relatively weak. Thus, the field settles into a reduced-tension state. In the nonlinear regime, the total magnetic energy is approximately equal to the total kinetic energy. The level of intermittency is lower than in the kinematic case, the field-strength distribution developing an exponential tail. The folding structure of the field is unchanged from the kinematic case: the anticorrelation between the field strength and the curvature persists and the distribution of the latter retains the same power tail. For the kinematic case, an exactly solvable model is available. The nonlinear case is treated qualitatively based on the folding picture and the resulting conclusions are supported by numerical simulations.

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