Axial feedback stabilization of flute mode in a simple mirror reactor

Axial feedback stabilization of the flute mode in a mirror-confined plasma of density n₀ is considered. The instability is described using the usual low frequency slab model. The instability potential phi is sampled at various azimuths around the plasma circumference. The sampled potential is amplified, phase shifted in azimuth, and the resulting feedback voltage e is applied to a conducting endwall split into azimuthal segments. For typical mirror reactor conditions, stabilization is obtained for exactly 90 degrees azimuthal phase shift provided (e/ phi )(n_x/n₀) is greater than 7p²a_i²/R_p², where p is the azimuthal mode number, a_i the ion Larmor radius, and R_p the plasma radius.