The Influence of RF Noise on the Lifetime of Bunched Proton Beams

RF system considerations for a large hadron collider

“…However, because of the nonlinearity present in a stationary bucket generated by a sinusoidal rf voltage, there will always be a finite spread in synchrotron frequency for a finite bunch width. B(<a) = ja>/(a>| -o> 2 ) can be related to the dispersion integral for the bunch, (24) figure 5.4, with Il/B(ja>)l ~ S the spread in OD S (see Appendix A). One still has KB » 1 and by increasing the gain K(a> s ) the contribution of the VCO noise & rf can be suppressed relative to the other noise sources.…”

“…In the SPS j5p system there are only a total of six bunches (3p and 3p) so that individual loop filters for each bunch with multiplexed output from the phase detector and a multiplexed input stage for the phase shifter are feasible. (24) However, in a large hadron collider there will be many thousands of bunches per ring (> 17,000 in the SSC conceptual design) and one must consider some form of compromise if the above scheme is to be maintained. For the SSC design there will be fifteen separate groups of bunches each occupying somewhat less than 1/15 the circumference.…”