Dissipative trapped particle modes in tandem mirrors

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Abstract
Dissipative trapped particle modes are studied in tandem mirrors by including electron collisions and ion Landau damping. A variational approach is used to obtain a collisional response in terms of the collisionless result plus a collisional term. The collisional term is then self‐consistently solved in all collision frequency regimes. When ν/ω≪1 (ν≡electron collision frequency) and the dissipationless mode is stable through a positive (negative) charge uncovering mechanism, there are two stable waves with phase velocities in the ion (electron) diamagnetic direction. The higher frequency wave with ω∼ω*i(ω*e) is destabilized by ion (electron) dissipation while the lower frequency wave is destabilized by electron (ion) dissipation. At high collision frequency (ν>ω*e), the only unstable trapped particle wave has ω∼ω*e, with electron collisions being destabilizing.