Abstract
We suggest that the periodic shaking of coronal magnetic field lines due to photospheric periodic motions may induce the parametric excitation of slow magnetoacoustic waves in short coronal magnetic structures (with length <50-70$ Mm). Considering the periodic shaking of field lines as an external transversal periodic action on the coronal plasma we show that the temporal behaviour of slow wave spatial Fourier harmonics in the low plasma β limit is governed by the Mathieu equation. Consequently, harmonics of slow magnetoacoustic waves with half the frequency of the photospheric driver have an exponential growth in time. The growth rate of slow waves is proportional to the amplitude of photospheric motions and to the value of the plasma β in the corona. The mechanism may explain the existence of slow magnetoacoustic waves at least in short coronal loop systems (Nightingale et al. [CITE], Sol. Phys., 190, 249).
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