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Squire's theorem for the magnetohydrodynamic sheet pinch

The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfven velocity) are raised from small values, two-dimensional perturbations become unstable first.