Effect of Synchrotron Radiation on Particle Motion in the Neighbourhood of Resonance Fixed Points

Radiation damping and quantum excitation of transverse and longitudinal oscillations of particles trapped in betatron resonance islands are studied. An analytical expression for the damping partition numbers on the resonance orbit confirms the strong dependence on chromaticity reported in Ref. 1. It is found that the deviation of the damping partition numbers from the central orbit values can be resonantly enhanced when the synchrotron tune approaches the so-called island tune. The conditions of particle loss due to longitudinal anti-damping are established. In the case of LEP there can be non anti damping owing to a high synchrotron tune, but the escape time from the islands is found to be long enough for a possibility of coupling resonances to develop.