  In the limit of sufficiently fast rotation, rotating mirror traps are known
to be stable against the loss-cone modes associated with conventional
(non-rotating) mirrors. This paper calculates how quickly a mirror
configuration must rotate in order for several of these modes to be stabilized
(in particular, the high-frequency convective loss cone, drift cyclotron loss
cone, and Dory-Guest-Harris modes). Commonalities in the stabilization
conditions for these modes then motivate a modified formulation of the Gardner
free energy and diffusively accessible free energy to be used for systems in
which the important modes have wave vectors that are orthogonal or nearly
orthogonal to the magnetic field, as well as a modification to include the
effects of a loss region in phase space.
