Diffraction radiation of charged rings moving in a corrugated cylindrical pipe: A model of radiation losses in a electron ring accelerator

The energy loss of a charged ring passing an infinitely long periodic sequence of rf accelerating cavities which has recently received much attention in connection with the collective acceleration of ions in electron rings is calculated by expanding the vector potential into a series of eigenfunctions of the empty waveguide and computing their individual excitation. The frequency spectra obtained are compared to the predictions of simpler analytical models from which a set of formula for the practical design of rf accelerating structures for electron rings can be derived. The energy loss becomes independent of gamma when the electron rings have a highly relativistic speed. (24 refs).