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Two-dimensional gyrokinetic turbulence

Published online by Cambridge University Press:  19 October 2010

Department of Physics and IREAP, University of Maryland, College Park, MD 20742, USA Department of Physics, University of California, Los Angeles, CA 90095, USA Wolfgang Pauli Institute, University of Vienna, A-1090 Vienna, Austria
EURATOM/CCFE Association, Culham Science Center, Abington OX1 3DB, UK Plasma Physics, Blackett Laboratory, Imperial College, London SW7 2AZ, UK
Plasma Physics, Blackett Laboratory, Imperial College, London SW7 2AZ, UK Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK Institut Henri Poincaré, Université Pierre et Marie Curie, 75231 Paris CEDEX 5, France
Department of Physics and IREAP, University of Maryland, College Park, MD 20742, USA
Email address for correspondence:


Two-dimensional gyrokinetics is a simple paradigm for the study of kinetic magnetised plasma turbulence. In this paper, we present a comprehensive theoretical framework for this turbulence. We study both the inverse and direct cascades (the ‘dual cascade’), driven by a homogeneous and isotropic random forcing. The key characteristic length of gyrokinetics, the Larmor radius, divides scales into two physically distinct ranges. For scales larger than the Larmor radius, we derive the familiar Charney–Hasegawa–Mima equation from the gyrokinetic system, and explain its relationship to gyrokinetics. At scales smaller than the Larmor radius, a dual cascade occurs in phase space (two dimensions in position space plus one dimension in velocity space) via a nonlinear phase-mixing process. We show that at these sub-Larmor scales, the turbulence is self-similar and exhibits power-law spectra in position and velocity space. We propose a Hankel-transform formalism to characterise velocity-space spectra. We derive the exact relations for third-order structure functions, analogous to Kolmogorov's four-fifths and Yaglom's four-thirds laws and valid at both long and short wavelengths. We show how the general gyrokinetic invariants are related to the particular invariants that control the dual cascade in the long- and short-wavelength limits. We describe the full range of cascades from the fluid to the fully kinetic range.

Copyright © Cambridge University Press 2010

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