Interaction of the precessional wave with free-boundary Alfven surface waves in tandem mirrors

We consider a symmetric tandem mirror plugging a long central cell, with plugs stabilized by a hot component plasma. The system is taken to have a flat pressure profile with a steep edge gradient. We then consider the interaction of the precessional mode with Alfven waves generated in the central cell. This analysis is non-eikonal 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. We find that without FLR effects the precessional mode is always destabilized by the excitation of the Alfven waves for m greater than or equal to 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 greater than or equal to 2 long-wavelength modes and of finite-Larmor-radius stabilization of modes described in the eikonal approximation