Space charge compensation with pulsed electron lenses for intense ion beams in synchrotrons

For booster synchrotrons, like the SIS at GSI, space charge is one of the main intensity limitations. At injection energy the space charge induced tune shifts in booster synchrotrons are large, reaching up to 0.5 and the ramping times are typically short. We study the effect of localized electron lenses distributed symmetrically around the circumference in order to compensate for the distributed transverse space charge force. The lenses compensate part of the space charge induced tune spread, but meanwhile perturb the optical functions and introduce stopbands that reduce the available space for a working point in the tune diagram. The undesired effects increase as the number of lenses is decreased. We estimate the minimum number of lenses needed. In addition we show that matching the transverse distribution of the electron lenses to the ion beam introduces additional, nonlinear resonances. Instead, we propose the use of a homogeneous electron lens distribution, which when pulsed serves to compensate the tune spread along the longitudinal bunch distribution.