Linear tearing mode stability equations for a low collisionality toroidal plasma

Tearing mode stability is normally analysed using MHD or two-fluid Braginskii plasma models. However for present, or future, large hot tokamaks like JET or ITER the collisionality is such as to place them in the banana regime. Here we develop a linear stability theory for the resonant layer physics appropriate to such a regime. The outcome is a set of ‘fluid ’ equations whose coefficients encapsulate all neoclassical physics: the neoclassical Ohm’s law, enhanced ion inertia, cross field transport of particles, heat and momentum all play a role. While earlier treatments have also addressed this type of neoclassical physics we differ in incorporating the more physically relevant ‘semi-collisional fluid ’ regime previously considered in cylindrical geometry; semi-collisional effects tend to screen the resonant surface from the perturbed magnetic field, preventing reconnection. Furthermore we also include thermal physics, which may modify the results. While this electron description is of wide relevance and validity, the fluid treatment of the ions requires the ion banana orbit width to be less than the semi-collisional electron layer. This limits the application of the present theory to low magnetic shear – however this is highly relevant to the sawtooth instability- or to colder ions. The outcome of the