Adiabatically reduced magnetohydrodynamic equations for a cylindrical plasma with an anisotropic pressure
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MA DYNAMICS
Adiabatically Reduced Magnetohydrodynamic Equations for a Cylindrical Plasma with an Anisotropic Pressure V. A. Nebogatov and V. P. Pastukhov National Research Centre Kurchatov Institute, pl. Akademika Kurchatova 1, Moscow, 123182 Russia email: [email protected] Received October 18, 2012; in final form, January 10, 2013
Abstract—A closed set of reduced equations describing lowfrequency nonlinear flute magnetohydrody namic (MHD) convection and the resulting nondiffusive processes of particle and energy transport in a weakly collisional cylindrical plasma with an anisotropic pressure is derived. The Chew–Goldberger–Low anisotropic magnetohydrodynamics is used as the basic dynamic model, because this model is applicable to describing flute convection in a cylindrical plasma column even in the lowfrequency limit. The reduced set of equations was derived using the method of adiabatic separation of fast and slow motions. It is shown that the structure of the adiabatic transformation and the corresponding velocity field are identical to those obtained earlier in the isotropic MHD model. However, the derived heat transfer equations differ drastically from the isotropic pressure model. In particular, they indicate a tendency toward maintaining different radial profiles of the longitudinal and transverse pressures. DOI: 10.1134/S1063780X1306007X
1. INTRODUCTION Studies of anomalous particle and energy transport occupy one of the central positions in controlled fusion research. Many authors associate anomalous transport with plasma fluctuations induced by differ ent types of smallscale drift instabilities and discuss it in the terms of a diffusion model with local transport coefficients (see, e.g., [1, 2]). At the same time, the results obtained in the past few years indicate that low frequency (LF) turbulence and the resulting anoma lous transport observed in different magnetic confine ment systems, including tokamaks [3–5], stellarators [6, 7], and tandem mirror traps [8, 9], demonstrate a number of phenomena that cannot be adequately described in terms of a diffusion model with local transport coefficients. Among these phenomena, it is worth mentioning the processes of selforganization (including the formation of selfconsistent pressure profiles), L–H transitions, and fast nonlocal response of transport fluxes to variations in the heating condi tions and other external actions. One of promising methods for investigating LF turbulence and the resulting nonlocal and nondiffusive transport in mag netized plasma (especially in transient conditions) is direct computer simulation of selfconsistent nonlin ear plasma dynamics. In the past few years, different gyrokinetic models [10–12] allowing one to obtain detailed information on the nonlinear plasma dynam ics have been developed. However, gyrokinetic calcu lations require a large CPU time even with the use of highpower supercomputers, which makes them very expensive and substantially limits their application for
simulations on macroscopic time sca
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