Minimizing the Energy Spread within a Single Bunch by Shaping Its Charge Distribution

When electrons or positrons in a bunch pass through the periodic structure of a linear accelerator, they leave behind them energy in the form of longitudinal wake fields. The wakefields thus induced by early particles in a bunch offset the energy of later particles. For a linear collider, the energy spread introduced within the bunches by this beam loading effect must be minimized because it limits the degree to which the particles can be focused to a small spot due to chromatic effects in the final focus system. For example, for the SLC, the maximum allowable energy spread is + or - 0.5%. It has been known for some time that partial compensation of the longitudinal wake field effects can be obtained for any bunch by placing it ahead of the accelerating crest (in space), thereby letting the positive rising sinusoidal field offset the negative beam loading field. The work presented in this paper shows that it is possible to obtain complete compensation, i.e., to reduce the energy spread essentially to zero by properly shaping the longitudinal charge distribution of the bunch and by placing it at the correct position on the wave.