New linear stability parameter to describe low- electromagnetic microinstabilities driven by passing electrons in axisymmetric toroidal geometry

In magnetic confinement fusion devices, the ratio of the plasma pressure to the magnetic field energy, beta, can become sufficiently large that electromagnetic microinstabilities become unstable, driving turbulence that distorts or reconnects the equilibrium magnetic field. In this paper, a theory is proposed for electromagnetic, electron-driven linear instabilities that have current layers localised to mode-rational surfaces and binormal wavelengths comparable to the ion gyroradius. The model retains axisymmetric toroidal geometry with arbitrary shaping, and consists of orbit-averaged equations for the mode-rational surface layer, with a ballooning space kinetic matching condition for passing electrons. The matching condition connects the current layer to the large scale electromagnetic fluctuations, and is derived in the limit that beta is comparable to the square root of the electron-to-ion-mass ratio. Electromagnetic fluctuations only enter through the matching condition, allowing for the identification of an effective beta that includes the effects of equilibrium flux surface shaping. The scaling predictions made by the asymptotic theory are tested with comparisons to results from linear simulations of micro-tearing and electrostatic microinstabilities in MAST discharge #6252, showing excellent agreement. In particular, it is demonstrated that the effective beta can explain the dependence of the local micro-tearing mode (MTM) growth rate on the ballooning parameter theta (0)-possibly providing a route to optimise local flux surfaces for reduced MTM-driven transport.