Stabilization of MHD Turbulence by Applied Steady and Oscillating Velocity Shear

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Some aspects of velocity shear stabilization of magnetized plasma instabilities are considered. In the first part, steady externally forced flow shears are considered. In the second part, resonantly excited oscillating flow shears are considered.

The stabilizing effect of steady forced velocity shear on the ideal interchange instability is studied in linear and nonlinear regimes, with a 2D dissipative magnetohydrodynamic (MHD) code.  With increasing flow shear <italic>V'</italic>, the linearly unstable band in wavenumber-space shrinks so that the peak growth results for modes that correspond to intermediate wavenumbers. In the nonlinear turbulent state, the convection cells are roughly circular on the scale of the density gradient.   Unstable modes are almost completely stabilized, with the density profile reverting to laminar, when <italic>V'</italic> is a few times the classic interchange growth rate. The simulations are compared with measurements of magnetic fluctuations from the Maryland Centrifugal Experiment.   The spectral data, taken in the plasma edge, are in general agreement with data obtained in higher viscosity simulations.   Finally, concomitant Kelvin-Helmholtz instabilities in the system are also examined.   

Geodesic acoustic modes (GAMs) are axisymmetric electrostatic poloidal oscillations of plasma in tokamaks. It has been proposed to drive GAMs resonantly by external drivers, thus setting up velocity shears to suppress turbulence.  Here, we study enhanced damping of GAMs from (1) phase mixing of oscillations and (2) nonlinear detuning of the resonance.   It is well-known that phase mixing of Alfven waves propagating in inhomogeneous media results in enhanced damping.  The enhancement goes as the 1/3 power of the dissipation.   We study this phenomenon for GAMs in tokamaks with temperature profiles.   Our analysis is verified by numerical simulation.  In addition, the system of nonlinear GAM equations is shown to resemble the Duffing oscillator. Resonant amplification is shown to be suppressed nonlinearly. The results are applied to the proposed GAM excitation experiment on the DIII-D tokamak.