It is shown that parallel ion viscosity and thermal conduction can drive instabilities in a plasma with a sheared parallel flow delta (U.B0)/ delta r; the thresholds are generally well below that of the ideal Kelvin-Helmholtz instability; the relationship between mode number and frequency is compatible with that of the Toi mode (Toi et al., 1989, Phys. Rev. Lett, 62, 430). A quasi-linear calculation shows that the variation of the total, i.e. laminar and turbulent, parallel momentum and energy inside a thin annular volume, localized in the vicinity of the plasma edge, are matched by the differences of anomalous momentum and energy fluxes carried by turbulence autocorrelations through the boundaries: this corresponds to total momentum and energy conservation. If the rotation velocity is close to threshold, two instabilities are found to be self-stabilizing when the theory is particularized to self-similar solutions; they indeed slow down the rotation. As for the other two, the turbulence at first destabilizes the plasma further while spinning up the rotation.
Effect of sheared flow on drift and Kelvin - Helmholtz instabilities in a tandem mirror