Quantum lifetime in electron storage rings

One of the mechanisms which contribute to beam lifetime in electron storage rings is the quantum emission of energetic photons causing particles to be lost from the rf bucket. This quantum lifetime is among other things important in defining the required aperture in a storage ring. An approximate expression of quantum lifetime, predicted by a one-dimensional model which takes into account only the betatron motion, has been used in most storage ring designs. If the beam is aperture-limited at a position with nonzero dispersion, both the betatron and synchrotron motions have to be included and a two-dimensional model must be used. An exact expression of quantum lifetime for the one-dimensional case and an approximate expression for the two-dimensional case are given