Local Stability Analysis of Three-dimensional Magnetically Confined Plasmas

Abstract

Local stability analysis of three-dimensional magnetically confined plasmas is presented using the energy principle. Fluid displacements with long parallel wavelengths by short perpendicular are retained. To lowest order in the mode fluteness the total energy density variation depends on the local magnetic shear, normal and geodesic magnetic curvatures, parallel current density, and magnetic field strength. The perpendicular fluid displacement is written in terms of a slowly-varying amplitude and a phase angle which varies rapidly in (or across) the magnetic surface. Assuming that the fluid displacement is quasi-incompressible, the solution for the phase angle is found in two limiting cases. Local stability analysis of stellarators with low or strong global magnetic shear is discussed.