Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas

Differential rotation is known to suppress linear instabilities in fusion plasmas. However, numerical experiments show that even in the absence of growing eigenmodes, subcritical fluctuations that grow transiently can lead to sustained turbulence, limiting the ability of the velocity shear to suppress anomalous transport. Here transient growth of electrostatic fluctuations driven by the parallel velocity gradient (PVG) and the ion temperature gradient (ITG) in the presence of a perpendicular (E x B) velocity shear is considered. The maximally simplified (but, as numerical simulations suggest, most promising for transport reduction) case of zero magnetic shear is treated in the framework of a local shearing box approximation. In this case there are no linearly growing eigenmodes, so all excitations are transient. In the PVG-dominated regime, the maximum amplification factor is found to be e(N) with N proportional to q/epsilon (safety factor/inverse aspect ratio), the maximally amplified wavenumbers perpendicular and parallel to the magnetic field are related by k(y)rho(i) approximate to (epsilon/q)(1/3)k parallel to upsilon(th i)/S, where rho(i) is the ion Larmor radius, upsilon(thi) the ion thermal speed and S the E x B shear. In the ITG-dominated regime, N is independent of wavenumber and N proportional to upsilon(th i)/(LTS), where L-T is the ion-temperature scale length. Intermediate ITG-PVG regimes are also analysed and N is calculated as a function of q/epsilon, L-T and S. Analytical results are corroborated and supplemented by linear gyrokinetic numerical tests. Regimes with N less than or similar to 1 for all wavenumbers are possible for sufficiently low values of q/epsilon (less than or similar to 7 in our model); ion-scale turbulence is expected to be fully suppressed in such regimes. For cases when it is not suppressed, an elementary heuristic theory of subcritical PVG turbulence leading to a scaling of the associated ion heat flux with q, epsilon, S and L-T is proposed; it is argued that the transport is much less 'stiff' than in the ITG regime.