I . Radiation Damping in Focusing-dominated

A qumi-classicalmethod is developed to calculate the radiation damping of a relativisticparticle in a straight, continuous focusing system. In one limiting case where the pitch angle of the particle OPis much larger than the radiation opening angle l/y, the radiation power spectrum is similar to synchrotron radiation and the relative damping rate of the transverseaction is proportional to the relativeenergy 10SS rate. In the other limiting cme where 6P<<117, the radiation is dipole in nature and the relative damping rate of the transverseaction is energy-independentand is much fwter than the relative energy rate. Quantum excitation to the transverseaction is absent in this focusing channel. These results can be extended to bent systems provided that the focusing field dominates over the bending field.