Local magnetohydrodynamic instabilities of cylindrical plasma with sheared equilibrium flows

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Abstract
The ideal magnetohydrodynamic stability of cylindrical equilibria with mass flows is investigated analytically and numerically. The flows modify the local (Suydam) criterion for instability at the resonant surfaces where k⋅B=0. Sheared flows below the propagation speed for the slow wave are found to be destabilizing for the Suydam modes. At a critical velocity, where the shear of the flow exactly balances the propagation of the slow wave along the sheared magnetic field, and the k⋅B=0 surface is at the edge of a slow wave continuum, there is instability regardless of the pressure gradient. Above the critical velocity, the k⋅B=0 surface is stable, but an infinite sequence of unstable modes still exists with frequencies accumulating toward the edge of the slow wave continuum at nonzero Doppler shifted frequency. The stability of the infinite sequences becomes a nonlocal problem whenever the accumulation frequency overlaps with a continuum at some other radial location.