Finite Larmor Radius Equations with Nonuniform Electric Fields and Velocities

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Abstract
A low‐β collisionless plasma cylinder confined in a uniform magnetic field is considered. The well‐known flute instabilities occur due to plasma rotation or radial gravity which simulates field line curvature. The effects of finite Larmor radius and nonuniform rotation are included deriving a proper set of hydromagnetic equations and variational principles for determining stability. In most cases these are merely sufficient but in a variety of cases may be both necessary and sufficient for stability.

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