  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.
