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A. C. Birch (Stanford U.), A. G. Kosovichev (W.W. Hansen Experimental Physics Lab, Stanford U.), E. A. Spiegel, L. Tao (Columbia U.)
We apply linear stability analysis to a stratified plane parallel perfectly conducting atmosphere with a vertical magnetic field and Newton's law of cooling. For the case of a polytropically stratified atmosphere we find that there are overstable modes. The instability is due to the background temperature gradient combined with the cooling. We show perturbation results for the case of the cooling time much longer or much shorter than the oscillation period. Numerical calculations of the dispersion relations are shown for the weak and strong magnetic field cases, for long and short cooling times, and for polytrope and isothermal atmospheres. Generically the k-\omega diagrams show a complicated pattern of avoided crossings. The damping or growth rates in general show features where branches undergo avoided crossings. The results, in particular the existence of overstable modes in the polytrope atmosphere, may be significant to the investigation of MHD phenomena in solar and stellar atmospheres, for example solar spicules.
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