Low beta Rigid Mode Stability Criterion for an Arbitrary Larmor Radius Plasma

摘要

The low beta flute interchange dispersion relation for rigid displacement perturbation of axisymmetric plasma equilibria with arbitrary Larmor radius particles and field line 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 delta z is less than the radial extent r sub 0 . For delta z/sub r sub 0 / much less than 1, the stability criterion is determined by the total particle number. Whereas the older theory ( delta z/sub r sub 0 / much greater than 1) predicted instability at about the densities achieved in actual Migma experiments, the present theory ( delta z/sub r sub 0 / much less than 1) indicates that the experimental results were for plasmas with particle number below the interchange threshold. (ERA citation 12:038334)