The influence of an external, transversal, periodic force on the local dynamics of magnetosonic waves is studied. We show that periodic, transversal plasma motions generated by this force lead to a periodical drift of the wavevector of the spatial Fourier harmonics in the local frame and, as a result, their amplitude is governed by Mathieu's equation. Thus, those harmonics with half the frequency of the external force have an exponential growth, and in consequence the energy of transversal oscillations can be transformed into the energy of magnetosonic waves. Some of the many applications of this mechanism to different astrophysical situations are discussed.
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