Finite Larmor Radius Equations with Nonuniform Electric Fields and Velocities

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.