Differential-geometric structures of ideal magnetohydrodynamics and plasma instabilities

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Abstract

The differential-geometric structures of ideal magnetohydrodynamics are studied by calculating sectional curvatures of a semidirect product of the volume-preserving diffeomorphism group and the vector field on it. Some propositions on the negativeness and positiveness of the sectional curvatures are derived. In particular, the curvature of the section corresponding to the sausage instability of plasma is shown to be negative.

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