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A symmetric tandem mirror plugging a long central cell, with plugs stabilized by a hot-component plasma is considered. The system is taken to have a flat pressure profile with a steep edge gradient. The interaction of the precessional mode with Alfvén waves generated in the central cell is then considered. This analysis is noneikonal and is valid when mΔ/r<1 (m is the azimuthal mode number, r the plasma radius, and Δ the radial gradient scale length) for long-wavelength radial modes. Without finite-Larmor-radius (FLR) effects the precessional mode is always destabilized by the excitation of the Alfvén waves for m≥2. For m=1, it is possible to achieve stabilization with conducting walls. A discussion is given of how FLR affects stabilization of the m≥2 long-wavelength modes and of FLR stabilization of modes described in the eikonal approximation.
Berk et al. (1985) studied this question.