Abstract
The axisymmetric linear stability of the Taylor-Couette flow with an azimuthal magnetic field is considered. It is shown that a flow with the combination of a linearly unstable rotation and a linearly unstable azimuthal magnetic field can be linearly stable. The flow stabilization takes place for both ideal and dissipative flows. For dissipative flow the stabilization exists only for a combination of counter-rotating cylinders and a counterdirecting azimuthal magnetic field on cylinders. The effect can be important for the problem of a plasma confinement by the magnetic field.
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