Nonlinear gyrokinetic turbulence simulations of E×B shear quenching of transport

The effects of $E\times B$ velocity shear have been investigated in nonliner gyrokinetic turbulence simulations with and without kinetic electrons. The impact of $E\times B$ shear stabilization in electrostatic flux-tube simulations is well modeled by a simple quench rule with the turbulent diffusivity scaling like $1-{\alpha }_E{\gamma }_E∕{\gamma }_{\max }$ , where ${\gamma }_E$ is the $E\times B$ shear rate, ${\gamma }_{\max }$ is maximum linear growth rate without $E\times B$ shear, and ${\alpha }_E$ is a multiplier. The quench rule was originally deduced from adiabatic electron ion temperature gradient (ITG) simulations where it was found that ${\alpha }_E\approx 1$ . The results presented in this paper show that the quench rule also applies in the presence of kinetic electrons for long-wavelength transport down to the ion gyroradius scale. Without parallel velocity shear, the electron and ion transport is quenched near ${\gamma }_E∕{\gamma }_{\max }\approx 2$ $({\alpha }_E\approx 1∕2)$ . When the destabilizing effect of parallel velocity shear is included in the simulations, consistent with purely toroidal rotation, the transport may not be completely quenched by any level of $E\times B$ shear because the Kelvin–Helmholtz drive increases ${\gamma }_{\max }$ faster than ${\gamma }_E$ increases. Both ITG turbulence with added trapped electron drive and electron-directed and curvature-driven trapped electron mode turbulence are considered.