Optimum gain and phase for stochastic cooling systems

A detailed analysis of optimum gain and phase adjustment in stochastic cooling systems reveals that the result is strongly influenced by the beam feedback effect and that for optimum performance the system phase should change appreciably across each Schottky band. It is shown that the performance is not greatly diminished if a constant phase is adopted instead. On the other hand, the effect of mixing between pick- up and kicker (which produces a phase change similar to the optimum one) is shown to be less perturbing than is usually assumed, provided that the absolute value of the gain is not too far from the optimum value. (3 refs).