Diffusion rate for the emittance growth due to periodic crossings of nonlinear coupled resonances

Abstract

Assuming that many betatron oscillations occur between crossings so that the betatron phase is uncorrelated from one crossing to the next, we estimate the diffusion rate for the emittance growth due to periodic crossing of coupled nonlinear resonances. It was shown that the diffusion rate is more or less independent of the frequency, but it is inversely proportional to the modulation amplitude