Comparison between coasting and bunched beams on optimum stochastic cooling and signal suppression

A comparison has been performed between coasting and bunched particle beams pertaining to the mechanism of stochastic cooling. In the case where particles occupy the entire sinusoidal RF bucket, the optimum cooling rate for the bunched beam is shown to be the same as that predicted from the coasting-beam theory using local particle density. However, in the case where particles occupy only the center of the bucket, the optimum rate decreases in proportion to the ratio of the bunch area to the bucket area. Furthermore, it has been shown for both coasting and bunched beams that particle motion is stable upon signal suppression if the amplitude of the gain is less than twice the optimum value over the entire frequency bandwidth of the cooling system.<>