DYNAMICS OF HIGH-BETA TOKAMAKS WITH ANISOTROPIC PRESSURE

On the basis of a high-Β, long-wavelength ordering, the Chew-Goldberger-Low (CGL) equations are used to discuss the dynamics and linear stability of a general anisotropic, plasma-vacuum tokamak. The multiple time-scale method is used to derive a reduced set of non-linear MHD equations. To lowest order, the perpendicular component of pressure, p⊥ (is not necessarily constant on the flux surfaces, ψ. A simple example of such an equilibrium is given; a heuristic treatment of the Fokker-Planck equation shows that equilibria of this type can only be established by near-perpendicular injection. For practical distribution functions representative of a beam-injected plasma, comparison with the Andreoletti energy principle shows that the CGL principle never overestimates stability. For q –=(1/2)′ (p + p⊥ constant on flux surfaces, the MHD linear stability of an anisotropic tokamak to long-wavelength modes is identical (within the ordering) with that for the equivalent scalar-pressure tokamak. A similar result has recently been obtained in the limit of short-wavelengths for fixed-boundary modes (ballooning). © 1979 IOP Publishing Ltd.