Beam Amplitude Behavior upon Crossing a Linear Coupling Resonance with Damping in One Dimension*

A small coupling perturbation in a synchrotron can cause instability of the particle motionslas a beam is being accelerated through a resonance. Such a resonance may occur whenever nlv 1 + n2v2 = n3, where “1, n2 and n3 are integers and vl and v2 are the ratios of the frequencies of horizontal and vertical betatron oscillations to the frequency of revolution. Recently, large growth of beam dimensions in the horizontal direction relative to the vertical direction has been observed2 in the ZGS for some acceleration routes in which several resonances were crossed. The experimental observation suggests that the damper used for the vertical beam instability may be responsible for this effect.