MHD stability in 3D anisotropic pressure plasmas

Auxiliary heating methods and nonuniform losses of energetic particles can cause significant pressure anisotropies in magnetic confinement systems. We have formulated the global and local 3D linear MHD stability variationally in the limit of a fully interacting anisotropic pressure fluid from the universal term of the Kruskal-Oberman energy principle. We have adopted for this purpose the Boozer magnetic coordinate system, appropriately modified for anisotropic plasmas. The 3D MHD equilibrium state is constrained to have nested magnetic flux surfaces. The effective parallel current density is identified as an important source of free energy for MHD instabilities due to its singular nature on rational magnetic surfaces in 3D systems. The energy principle is Fourier decomposed in the periodic angular variables and finite elements are applied for the radial discretisation to reduce the global MHD stability problem to a special block pentadiagonal matrix eigenvalue equation that can be solved with an inverse vector iteration method. The local MHD stability is investigated through the formulation of the 3D ballooning equation in Boozer coordinates. In these coordinates, the geodesic magnetic curvature is demonstrated to be related to the effective parallel current density. This allows the asymptotic analysis of the ballooning equation to yield a closed form for the Mercier criterion. (author) 15 refs