Abstract
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.
Highlights
The main feature of such a trapping is the constancy of the shape of the RF voltage V(t) regardless of the injected beam conditions, i.e. V(t) is the sane for any XL 5 (CEL)max.l Space-charge effects were estimated by mean.5 of a multiparticle computation.’
When the collective space-charge field c($,t) is rigorously self-consistent and the bunch area, defined by the contour C(t), does not have an invariant form with respect to the total longitudinal focusing field, E($,t) has necessarily an oscillatory time-dependence which is in precise synchronism with twice the rotation frequency of C(t) in the phase p:ane
RF trapping with improved bunch shapes matching to the subsequent acceleration can be obtained by deviating from the iso-adiabatic voltage rise
Summary
Tie RF trapping in the PSB was designed to work with an iso-adiabatic voltage rise’ and a relatively large injected beam energy spread (hEi z +15@ keV). 2 The iso-adiabatic voltage rise was expected to be optimal for injected beams with widely differing energy sp;e;ds, intensities, and charge den-. When the collective space-charge field c($,t) is rigorously self-consistent and the bunch area, defined by the contour C(t), does not have an invariant (stationary) form with respect to the total longitudinal focusing field, E($,t) has necessarily an oscillatory time-dependence which is in precise synchronism with twice the rotation frequency of C(t) in the phase p:ane. Filamentation, which may lead to a stationary bunch envelope C with a reduced phase plane charge density, needs a Longer time than that available during RF trapping. The main effect of a weak resonance consists in producing two bulges in the contour C(t) and reducing the maximal longitudinal charge density, or in other words, converting single-peaked bunches into double-peaked ones (Fig. 2).
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