Stability of high‐energy particle plasmas to magnetohydrodynamic‐like modes

The stability of symmetric mirror systems, such as tandem mirrors and multiple mirrors (or equivalently, bumpy tori of large aspect ratio), is investigated when stabilization is attempted with high‐energy particles. The analysis is derived from a zero Larmor radius variational form, and the stability criteria for eikonal and long wavelength layer modes are obtained. For eikonal modes it is shown that line bending can stabilize the low l‐number modes and together with finite Larmor radius effects discussed elsewhere, complete stabilization is possible. For disk‐shaped plasma pressure profiles it is shown that currents induced by conducting walls can stabilize the l=1 layer mode, while the higher‐l layer modes require finite Larmor radius effects for stabilization. For thin, ring‐like pressure profiles, wall stabilization of the l=1 mode cannot be achieved, although the line bending term reduces the core beta limit and the growth rate of low l‐number layer modes. The coupling of the precessional mode of a plasma ring to the surface Alfvén wave in a multiple mirror plasma is also discussed.