The impact of E × B shear on microtearing based transport in spherical tokamaks

Electromagnetic microtearing modes (MTMs) have been observed in many different spherical tokamak (ST) regimes. Understanding how these and other electromagnetic modes nonlinearly saturate is likely critical in understanding the confinement of a high beta ST. Equilibrium E x B sheared flows have sometimes been found to significantly suppress low beta ion scale transport in both gyrokinetic simulations and in experiment. This work aims to understand the conditions under which E x B sheared flow impacts on the saturation of MTM simulations, as there have been examples where it does (Guttenfelder et al 2012 Phys. Plasmas 19 056119) and does not (Doerk et al 2012 Phys. Plasmas 19 055907) have a considerable effect. Two experimental regimes are examined from MAST and NSTX, on surfaces that have unstable MTMs. The MTM driven transport on a local flux surface in MAST is shown to be more resilient to suppression via E x B shear, compared to the case from NSTX where the MTM transport is found to be significantly suppressed. This difference in the response to flow shear is explained through the impact of magnetic shear, s<^>, on the MTM linear growth rate dependence on ballooning angle, theta 0. At low s<^>, the growth rate depends weakly on theta 0, but at higher s<^>, the MTM growth rate peaks at theta 0 = 0, with regions of stability at higher theta 0. Equilibrium E x B sheared flows act to advect the theta 0 of a mode in time, providing a mechanism to reduce the linear drive and suppress the transport from modes where the growth rate is strongly peaked in theta 0 (Roach et al 2009 Plasma Phys. Control. Fusion 51 124020). Bicoherence analysis demonstrates that with the inclusion of E x B shear there is a more effective coupling between the linearly driven drift-waves responsible for transport and zonal modes, which enhances damping. The dependence of gamma MTM on theta 0 is in qualitative agreement with a recent theory (Hardman et al Plasma Phys. Control. Fusion 65 045011) at low beta when q similar to 1, but the agreement worsens at higher q where the theory breaks down. At higher s<^>, MTMs drive more stochastic transport due a stronger overlap of magnetic islands centred on neighbouring rational surfaces, but equilibrium E x B shear acts to mitigate this. This is especially critical towards the plasma edge where s<^> can be larger and where the total stored energy in the plasma is more sensitive to the local gradients. This work highlights the important role of the safety factor profile in determining the impact of equilibrium E x B shear on the saturation level of MTM turbulence.