The classical instability of a differentially rotating fluid takes place according to Rayleigh's criterion, i.e. when there is a radially outward decrease of angular momentum (per unit mass). In 1978, however, I showed that (i) a tiny radial decrease of angular velocity is sufficient to give instability if a small azimuthal magnetic field is present, and (ii) the fastest-growing modes then amplify very fast indeed, at a rate determined solely by the differential rotation.
This phenomenon - now generally known as the magnetorotational instability - arises when the magnetic energy is small compared with the rotational energy, provided that the electrical conductivity of the fluid or gas is not too weak. Non-axisymmetric waves then grow and propagate around the rotation axis.
Phil. Trans. Roy. Soc. A Vol 289, pp 459-500, 1978
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