Electron beam depolarization in a damping ring

Depolarization of a polarized electron beam injected into a damping ring is analyzed by extending calculations conventionally applied to proton synchrotrons. Synchrotron radiation in an electron ring gives rise to both polarizing and depolarizing effects. In a damping ring, the beam is stored for a time much less than the time for self polarization. Spin flip radiation may therefore be neglected. Synchrotron radiation without spin flips, however, must be considered as the resonance strength depends on the vertical betatron oscillation amplitude which changes as the electron beam is radiation damped. An expression for the beam polarization at extraction is derived which takes into account radiation damping. The results are applied to the electron ring at the Stanford Linear Collider and are compared with numerical matrix formalisms