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.
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