Measurements of Stacking Efficiency in the CERN Intersecting Storage Rings (ISR)

The efficiency of the stacking process, in which protons are accumulated into longitudinal phase space by means of a radio frequency (RF) voltage, was measured as function of different parameters such as energy, RF voltage, number of stacking cycles and ¿ = sin ¿s, ¿s is the relative phase of protons in synchronism with the RF voltage. The efficiency was found to depend predominantly on ¿ and the number n of stacking cycles. Efficiencies higher than 70% were measured for values of ¿ ¿ 0.5 and n ¿ 30 for both the repetitive and the nonrepetitive stacking scheme. The agreement between theoretical predicted efficiencies, obtained from a computer simulation of the stacking process, and the measured efficiencies is very good for higher values of n. From both the theoretical calculations and the measurements a rule of thumb could be derived which gives a good approximation of the stacking efficiency far above transition energy as function of ¿ and n.