Relaxation to the steady state in neutral-beam-injected mirrors

The nonlinear stability of ion velocity distributions in simple beam-injected mirror machines is investigated using a one-dimensional kinetic equation. The steady states and their linear response functions are calculated, and the nonlinear behavior is studied both analytically and numerically. It is shown that when charge exchange effects are negligible, oscillatory instabilities found are suppressed. When unstable steady states are present, the eventual equilibrium of the system is shown to depend not only on the initial density, but on the initial velocity distribution as well