Microtearing turbulence saturation via electron temperature flattening at low-order rational surfaces

Microtearing instability is one of the major sources of turbulent transport in high-$\beta$ tokamaks. These modes lead to very localized transport at low-order rational magnetic field lines, and we show that they can saturate by flattening the local temperature gradient. This saturation process depends crucially on the density of rational surfaces, and thus the system-size, and gives rise to a worse-than-gyro-Bohm transport scaling for system-sizes typical of existing tokamaks and simulations.