Radiation damping in focusing-dominated systems

A quasi-classical method is developed to calculate the radiation damping of a relativistic particle in a straight, continuous focusing system. In one limiting case where the pitch angle of the particle θ_p is much larger than the radiation opening angle 1/γ, the radiation power spectrum is similar to synchrotron radiation and the relative damping rate of the transverse action is proportional to the relative energy loss rate. In the other limiting case where θ_p≪1/γ, the radiation is dipole in nature and the relative damping rate of the transverse action is energy-independent and is much faster than the relative energy rate. Quantum excitation to the transverse action is absent in this focusing channel. These results can be extended to bent systems provided that the focusing field dominates over the bending field