Recent gyrokinetic stability calculations have revealed that the spherical tokamak is susceptible to tearing parity instabilities with length scales of a few ion Larmor radii perpendicular to the magnetic field lines. Here we investigate this 'micro-tearing' mode in greater detail to uncover its key characteristics, and compare it with existing theoretical models of the phenomenon. This has been accomplished using a full numerical solution of the linear gyrokinetic-Maxwell equations. Importantly, the instability is found to be driven by the free energy in the electron temperature gradient as described in the literature. However, our calculations suggest it is not substantially affected by either of the destabilising mechanisms proposed in previous theoretical models. Instead the instability is destabilised by interactions with magnetic drifts, and the electrostatic potential. Further calculations reveal that the mode is not significantly destabilised by the flux surface shaping or the large trapped particle fraction present in the spherical tokamak. Its prevalence in spherical tokamak plasmas is primarily due to the higher value of plasma β, and the enhanced magnetic drifts due to the smaller radius of curvature.

Nonlinear gyrokinetic simulations have been conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E × B shear value for plasma confinement. Local maxima in the momentum fluxes are also observed, allowing for the possibility of bifurcations in the E × B shear. The sensitive dependence of heat flux on temperature gradient is relaxed for large flow shear values, with the critical temperature gradient increasing at lower flow shear values. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.Introduction. Experimental measurements in magnetic confinement fusion devices indicate that sheared mean E × B flows can significantly reduce and sometimes fully suppress turbulent particle, momentum, and heat fluxes [1,2]. Since these turbulent fluxes determine mean plasma density and temperature profiles, their reduction leads to a local increase in the profile gradients. This increase can be dramatic: transport barriers in both the plasma core and edge have been measured with radial extents on the order of only tens of ion Larmor radii [3]. The associated increase in core density and temperature results in increased fusion power. Thus, understanding how shear flow layers develop and what effect they have on turbulent fluxes is both physically interesting and practically useful.This Letter reports a numerical study of the influence of sheared toroidal rotation on turbulent heat and momentum transport in tokamak plasmas. Two main effects of sheared toroidal rotation were identified in previous numerical work [4][5][6][7][8]: suppression of turbulent transport by shear in the perpendicular (to the mean magnetic field) velocity and linear destabilization due to the parallel velocity gradient (PVG). While the former observation indicates that a finite flow shear improves plasma confinement, the latter raises the question of whether more shear is always beneficial. Below we report that the PVG-driven linear instability [9] is stabilized at sufficiently large flow shear values, consistent with fluid theory in slab geometry [10]. Correspondingly, fluxes decrease with increasing flow shear as the linear stabilization point is approached. However, beyond this point, transiently growing modes driven by the PVG give rise to subcritical turbulence. The fluxes associated with this turbulence increase with flow shear. This implies an optimal flow shear for each temperature gradient; the fact that the minimum heat flux value is finite indicates that there is a maximum attainable temperature gradient that can be maintained for a given heat flux. Additionally, the observed presence of maxima in the momentum fluxes admits the possibility of bifurcations in the flow shear (and thus the temperature gr...

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.