Beam loading analysis of a transformer-coupled rf cavity

Coherent dipole longitudinal instabilities have been observed in the Electron-Positron Accumulation Ring (EPA), which is part of the LEP injector chain. These instabilities turn into a strong limitation upon the maximum beam current, depending on RF cavity voltage and tuning angle. Although the nominal performances of the machine are not affected, as far as the operation of the LEP injector chain is concerned, a study of beam loading effects seems worthwhile, because: it might be necessary to accumulate up to 4 times the nominal intensity for LEP injection, it was foreseen to reduce the cavity voltage for optimum injection to the PS, owing to the rather unconventional design of the RF cavity, one might expect the intensity limits to be different from those predicted by classical Robinson's criterion. In this paper a transformer-coupled resonator model for the EPA RF cavity is presented, and a detailed analysis of its beam loading stability is performed. The results are compared both with Robinson's criterion and with some measurements taken during EPA running-in