Stochastic Cooling with a Double RF System

Stochastic cooling for a bunched beam of hadrons stored in an accelerator with a double rf system of two different frequencies has been investigated. The double rf system broadens the spread in synchrotron-oscillation frequency of the particles when they mostly oscillate near the center of the rf bucket. Compared with the case of a single rf system, the cooling rate is significantly increased. When the rf voltage is raised, the reduction rate of the emittance, instead of decreasing linearly, now is independent of the ration of the bunch area to the bucket area. With the double rf system, the spread in synchrotron-oscillation frequency is small for particles with synchrotron-oscillation amplitudes comparable to the dimension of the rf bucket. consdquently, stochastic cooling becomes less effective when the bunch area is close to the bucket area.