Nonlinear Gyrokinetic Equations
Authors: D.H.E. Dubin, J.A. Krommes, C. Oberman and W.W. Lee
Abstract: Nonlinear gyrokinetic equaions are derived from a systematic Hamiltonian theory. The derivation emplos Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asympotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straightforward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and barious of its limitts are considered. The weak turbulene theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokineticc effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory several new nonlinear terms absent from conventional theories appear and are discussed. The resulting theory is very similar in content to the recent work of Lee. However, the systematic nature of our derivation provides considerable insight into the structure and interpretation of the equations.
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Submitted to: PPPL Reports
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Download PPPL-1969 (pdf KB 41 pp)
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