A two-dimensional nonideal magnetohydrodynamic eigenmode equation for the most dangerous perturbation (k ʈ ϭ0) is derived for a high-␤ plasma by making use of the generalized Ohm's law and becomes identical to the equation describing the two-dimensional hydrodynamic stability. When the pressure is nonuniform, the density is uniform, and there is no unperturbed electric field or gravity, a Kelvin-Helmholtz instability, which is driven by the shear in the ion diamagnetic drift velocity, is found.

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... When the unperturbed ion pressure is proportional to the unperturbed total pressure, a necessary condition for the instability is that d 3 B 0 /dx 3 must change sign at least once between xϭx 1 and xϭx 2 , where x is the direction of the nonuniformity perpendicular to the unperturbed magnetic field B 0 (x) and xϭx 1 and x 2 are points where the x component of the velocity perturbation vanishes. An unstable B 0 (x) profile and the dispersion relation are obtained for a polygonal ion diamagnetic drift velocity profile.