Bunch Shape Oscillation Control in RF Trapping

The bunch formation produces generally an oscillatory time-behaviour of the longitudinal charge density, which is reproduced synchronously in the coherent self-field. The resulting beam behaviour, caused by the space-charge feedback, tends to convert single-peaked bunches into double-peaked ones (as seen on a sum pick-up electrode). It is analysed with the energy spread of the unbunched beam, the beam intensity, and the particle distribution as parameters. For given values of these parameters a theoretical shape of the RF voltage rise V(t) is then obtained by successive approximation, which minimizes bunch shape oscillations without reducing the high trapping efficiency (> 90%). This V(t) (one to five per cent of Vmax for t = 0) imposes operation under very heavy beam-loading conditions. Experimental results, obtained after the corresponding improvement of the systems performance, are presented and compared with the bunch shapes obtained, for equal trapping efficiencies, with an iso-adiabatic voltage rise.