Abstract
Tandem-mirror trapped-particle modes are studied in a model system consisting of two connected square wells representing the solenoid and the end cells. Collisions are described by a Lorentz operator. A dispersion relation that is valid for arbitrary ν/ω (ω=wave frequency, ν=collision frequency) is derived. Four limits are investigated. When ε≡νRam/ω ≪1+pi/pe, where Ram is the mirror ratio separating electrons trapped in the anchor from those passing to the solenoid and pe and pi are the fractions of passing electrons and ions, collisions destabilize a trapped-particle mode that is stable in the collisionless limit; the growth rate is proportional to ε1/2 for ε≪1 and ε/ln ε for 1+pi/pe ≫ε≫1. When ε ≫1+pi/pe, the trapped-particle mode becomes a weakly growing drift wave with growth rate proportional to ε−1 ln ε for ν/ω≪1 and ν−1 for ν/ω≫1; additionally identified are two flute modes, one of which is unstable for some parameters, and a strongly damped high-frequency mode.
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