Abstract
A solution is obtained for the problem of onset of oscillatory convection in a horizontal layer of fully ionized plasma located in constant vertical gravitational and magnetic fields. In case of significant anisotropy in the thermal conductivity with isotropic viscosity (only the electrons are magnetized) the onset of convection at large Hartmann numbers is accompanied by oscillations if the ''magnetic Prandtl number'' is much larger than unity. The results obtained here are a natural generalization of the well-known Chandrashekar's criteria and can be used in the theory of MHD wave generation in a strongly magnetized plasma.
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