A sufficient condition for the ideal instability of shear flow with parallel magnetic field

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Abstract
A simple sufficient condition is given for the linear ideal instability of plane parallel equilibria with antisymmetric shear flow and symmetric or antisymmetric magnetic field. Application of this condition shows that plane Couette flow, which is stable in the absence of a magnetic field, can be driven unstable by a symmetric magnetic field. Also, although strong magnetic shear can stabilize shear flow with a hyperbolic tangent profile, there exists a range of magnetic shear that causes destabilization.