Low beta rigid mode stability criterion for an arbitrary Larmor radius plasma

The low beta flute axisymmetric dispersion relation for rigid displacement perturbation of plasma equilibria with arbitrary Larmor radius particles and field line radius of curvature large compared to the plasma radius is derived. The equilibrium particle orbits are characterized by two constants of motion, energy and angular momentum, and a third adiabatic invariant derived from the rapid radial motion. The Vlasov equation is integrated, assuming that the mode frequency, axial ''bounce'' frequency, and particle drift frequency are small compared to the cyclotron frequency, and it is demonstrated that the plasma response to a rigid perturbation has a universal character independent of Larmor radius. As a result the interchange instability is the same as that predicted from conventional MHD theory. However, a new prediction, more optimistic than earlier work, is found for the low density threshold of systems like Migma, which are disc-shaped, that is, the axial extent Δz is less than the radial extent r0. For Δz/r0 << 1, the stability criterion is determined by the total particle number. Whereas the older theory (Δz/r0 >> 1) predicted instability at about the densities achieved in actual Migma experiments, the present theory (Δz/r0 << 1) indicates that the experimental results are for plasmas with particle number below the interchange threshold. (orig./AH)