RF gymnastics in the PS - CERN

frequency difference. Therefore the separation between the two sets of bunches decreases until theyare superimposed in azimuth. If the RF is then suddenly switched to the average frequency (f 1 + f 2 )/2on both groups and the voltage increased by a large enough factor, pairs of bunches can berecombined in the corresponding large buckets.+Δfh 0 f REV−Δf2 n bunches separatedin energy and azimuthAzimuthal slipFig. 2: Slip stackingCapture on h 0of 2 bunches/bucketFigure 3 shows a mountain range display of a typical result with a total injected intensity of10 13 p/p. Feedforward beam loading compensation was essential for a correct RF operation at such ahigh intensity. However, this process also suffered from excessive beam loss, probably due to thepresence of a large proportion of particles with very large emittances after filamentation and to limitedacceptances at low energy.Fig. 3: Mountain range display of longitudinal recombination by slip stacking at 800 MeVHence a similar but much more sophisticated process was successfully implemented at25 GeV and used until 1989. Again two RF groups are necessary. Combining four cavities operatingat the same peak voltage , with two cavities on h=20, one on h=19 and one on h=21, each of thesegroups generates a 100% amplitude modulation at the revolution frequency ⁄ 2 of a carrier onh=20. Indeed: cos19 2 cos20 cos21 2 cos20 1cos↑Carrier onh=20↑Peak amplitude modulationat the revolution frequencyWith a proper phasing of the different harmonics with respect to the beam, the maximumamplitude of a group can be centred onto a set of five bunches. Starting with two sets of bunchesdiametrically opposite in the PS, each set ‘sees’ a maximum voltage from its RF group and aminimum from the other one. This situation is illustrated in Fig. 4. Separate beam controls can hencehandle both sets separately, giving them a difference in energy, and ‘slip stacking’ begins.3