Dynamics of high-beta tokamaks with anisotropic pressure

On the basis of a high-beta 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 nonlinear MHD equations. To lowest order, the perpendicular component of pressure is not necessarily constant on the flux surfaces. 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 (1963) energy principle shows that the CGL principle never overestimates stability. For an effective pressure (equal to half the sum of the parallel and perpendicular pressure components) that is constant on flux surfaces, the MHD linear stability of an anisotropic tokamak to long-wavelength modes is identical (within the ordering) to 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).