Abstract
The stability of periodic MHD shear flows generated by an external transversal periodic force in magnetized plasma is studied. It is shown that the temporal behaviour of magnetosonic wave spatial Fourier harmonics in such flows is governed by Mathieu equation. Consequently the harmonics with the half frequency of the shear flows grow exponentially in time. Therefore the periodic shear motions are unstable to the perturbations of compressible magnetosonic waves. The motions represent the kinetic part of the transversal oscillation in magnetized plasma. Therefore due to the instability of periodic shear motions, the transversal oscillations may quickly be damped, so transferring their energy to compressible magnetosonic perturbations.
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