Anisotropic pressure stability of a plasma confined in a dipole magnetic field

The interchange and ballooning stability of general anisotropic pressure plasma equilibria in a dipolar magnetic field are investigated. Starting with the Kruskal–Oberman form of the energy principle and using a Schwarz inequality, a fluid form of the anisotropic pressure energy principle is derived, which, after appropriate minimization, gives an interchange stability condition and an integro-differential ballooning equation. These results are applied to the case of an anisotropic pressure equilibrium having the perpendicular pressure equal to the parallel pressure times a constant and, in particular, to a model point dipole equilibrium. It is found that the model equilibrium is interchange stable for all plasma betas = (plasma pressure/magnetic pressure) and ballooning stable for all betas up to some critical value. The interesting planetary case of “tied” field lines is also considered.