The role of thermal conduction in tearing mode theory

The role of anisotropic thermal diffusivity in tearing mode stability is analysed in general toroidal geometry following similar techniques to Glasser et al (1975 Phys. Fluids 18 875), although a stronger ordering of the plasma compressibility is required. Resistive layer equations are obtained for a resistive magnetohydrodynamic (MHD) model with anisotropic transport of pressure. A dispersion relation linking the growth rate to the tearing mode stability parameter, Δ′, characterising the external ideal MHD region, is derived. By using a resistive MHD code modified to include such thermal transport to calculate tearing mode growth rates, this dispersion relation is employed to determine Δ′ in situations with finite plasma pressure that are stabilised by favourable average curvature when using a simple resistive MHD code. We also demonstrate that the same code can be used to obtain the basis-functions (Ham et al 2012 Plasma Phys. Control. Fusion 54 105014) needed for an alternative approach to calculating Δ′.