RF gymnastics in the PS - CERN

Fig. 21: Multiple splitting scenario for the nominal bunch distance of 25 ns for the LHCTriple splitting is started as soon as the second batch is received, which provides 18consecutive bunches on h=21. The beam is then accelerated on this harmonic up to the 25 GeV flattop,where each bunch is twice split into two to give 72 consecutive bunches on h=84. This leaves a320 ns gap in the bunch train for the rise-time of the ejection kicker.Triple splitting requires three simultaneous RF harmonics (h=7, h=14 and h=21) which can beprovided by the ferrite cavities divided in three different tuning groups. The relative phases betweenharmonics are such that a stable phase on h=21 and an unstable phase on h=14 coincide with thestable phase on h=7. Starting with h=7 alone, the effect of increasing the voltages on h=14 and h=21is to flatten the bunch (t = 7 ms in Fig. 22). In phase space, two new stable points emerge close to theinitial one, encircled by three buckets. Using numerically determined laws of variation, these threeareas are kept equal throughout the process so that layers of increasing emittance in the initial bunchare progressively peeled off and accumulated evenly into the three new buckets. Provided that the rateof change of the voltages is sufficiently slow, the particles of the initial bunch are gradually capturedin the new buckets whose area grows as the voltage decreases on h=7 and increases on h=21(t = 14 ms). Three equal bunches are finally obtained, each with the same distribution of particledensity as the initial one (t = 25 ms). The low-level RF generates the different harmonics, preciselycontrolling their relative phases. A beam phase loop is active throughout the process, controlling thesum of all harmonics whose relative phase is rigidly fixed. A typical result at the nominal intensity forthe LHC is shown in Fig. 23(a).Fig. 22: Principle of triple splitting12