Single Bunch Beam Loading on the SLAC Three-Kilometer Accelerator

Abstract

Since the report on single bunch beam loading experiments at SLAC at the 1975 Particle Accelerator Conference, it has been possible to obtain a much better understanding and agreement of theoretical and experimental results related to this problem. These improvements have been made possible by two developments: the generation of a "wake-field" function for the SLAC 3-km slow-wave structure and the use of this function to calculate single bunch energy spectra. The wake-field function which gives the time decay of the fields generated by the passage of a deltafunction beam has been derived by summing all the TM cylindrically symmetrical modes of an equivalent accelerator cavity. By multiplying this wake-field function by a measured bunch density function and integrating along the bunch, it is possible to calculate the energy of each electron in the bunch. This in turn enables one to predict the energy spectrum for any given phase angle of the bunch with respect to the crest of the RF accelerating wave. Agreement between these calculations and experimental measurements is very good. The paper presents these results and discusses the possible sources of some of the remaining discrepancies.