Abstract
An asymptotic approximation is applied to study the instability of slow hydromagnetic waves with magnetic diffusion. This approximation extends the method of geometric optics to admit complex valued phase functions. It assumes that the waves are short in some directions other than the azimuthal, and vary slowly in those directions. The approximation embeds the local solution obtained by previous workers in the global asymptotic approximation. It also unifies the derivation of both magnetic field gradient and resistive instabilities.
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