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

The interchange and ballooning stability of general anisotropic pressure pl asma equilibria in a dipolar magnetic field are investigated. Starting with the Kruskal-Oberman form of the energy principle and using a Schwarz inequ ality, a fluid form of the anisotropic pressure energy principle is derived , which, after appropriate minimization, gives an interchange stability con dition and an integro-differential ballooning equation. These results are a pplied to the case of an anisotropic pressure equilibrium having the perpen dicular pressure equal to the parallel pressure times a constant and, in pa rticular, to a model point dipole equilibrium. It is found that the model e quilibrium is interchange stable for all plasma betas = (plasma pressure/ma gnetic pressure) and ballooning stable for all betas up to some critical va lue. The interesting planetary case of "tied" field lines is also considere d. (C) 2000 American Institute of Physics. [S1070-664X(00)01908-X].