Complete fluid equations for low-n singular modes in axisymmetric toroidal plasmas

A system of equations governing the singular region of magnetohydrodynamic (MHD) instabilities in a collisional, axisymmetric toroidal plasma with magnetic shear has been derived from Braginskii’s fluid equations. This is an extension of earlier work, incorporating anisotropic resistivity, anisotropic ion viscosity, anisotropic ion and electron thermal conductivity, and diamagnetic and E×B drifts. The equations describe the narrow layer in the neighborhood of a singular surface for tearing and interchange instabilities with low toroidal mode number n. Ordering assumptions allow for the maximum range of physical effects while retaining the principal terms in the earlier work and ensuring the validity of the fluid equations. The equations are complete in the sense that all terms, and only those terms, consistent with this carefully constructed ordering are included.