A nonuniform one-dimensional magnetohydrodynamic cavity is driven by a prescribed random motion which has a broadband frequency spectrum. The time dependent behaviour of the system is calculated numerically, and two criteria are identified for the efficient excitation of an Alfven resonance: (1) the fast, or global, eigenfrequencies of the cavity must lie within the spectrum of the driving motions. (2) The fast eigenfrequencies must lie within the Alfven continuum. When these conditions are met, are broadband driving motion will excite Alfven resonances at frequencies corresponding to the fast eigenfrequencies-even though these frequencies may not be particularly favored in the driving spectrum. Our results confirm the importance of the fast global modes noted by previous studies which employed steady harmonic driving. Our principal result is that resonant excitation of Alfven waves can still occur when a cavity is driven by a nonmonochromatic source, and it gives confidence that resonant coupling may indeed play a key role in heating the solar corona and establishing geomagnetic pulsations- situations in which nature does not provide a monochromatic driving motion.
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Wright et al. (1995) studied this question.