Abstract
We investigate the propagation of Alfvén waves in a simple medium consisting of three uniform layers; each layer is characterized by a different value for the Alfvén speed, υ A. We show how the central layer can act as a resonant cavity under quite general conditions. If the cavity is driven externally, by an incident wave in one of the outer layers, there result resonant transmission peaks, which allow large energy fluxes to enter the cavity from outside. The transmission peaks result from the destructive interference between a wave which leaks out of the cavity, and a directly reflected wave. We show that there are two types of resonances. The first type occurs when the cavity has the largest (or smallest) of the three Alfvén speeds; this situation occurs on coronal loops. The second type occurs when the cavity Alfvén speed is intermediate between the other two values of υ A; this situation may occur on solar spicules. Significant heating of the cavity can occur if the waves are damped. We show that if the energy lost to heat greatly exceeds the energy lost by leakage out of the cavity, then the cavity heating can be independent of the damping rate. This conclusion is shown to apply to coronal resonances and to the spicule resonances. This conclusion agrees with a point made by Ionson (1982) in connection with the coronal resonances. Except for a numerical factor of order unity, we recover Ionson's expression for the coronal heating rate. However, Ionson's qualities are much too large. For solar parameters, the maximum quality is of the order of 100, but the heating is independent of the damping rate only when dissipation reduces the quality to less than about 10.
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Hollweg, J.V. Alfvénic resonant cavities in the solar atmosphere: Simple aspects. Sol Phys 91, 269–288 (1984). https://doi.org/10.1007/BF00146299
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DOI: https://doi.org/10.1007/BF00146299