LHC Baseline = BCMS 25ns S. Hancock

Background For given LHC optics and energy, luminosity scales roughly as the product of the beam brightness in collision and the total current in each beam. However, this does not mean that the empirical fact of constant beam brightness at the exit of the PS Booster implies that luminosity can only be increased by raising the intensity.

Batch Compression versus Splitting The pivotal harmonic of h=21 prior to acceleration in the PS is achieved by additive steps (batch compression) and not just by multiplicative ones (splitting). Double-batch injection into h=9 makes maximum use of Booster rings. The trick of bunch merging reduces the effective splitting factor by two, so that the BCMS 25ns beam has the same splitting factor as the nominal 50ns one. Issues of limited longitudinal acceptance (rather than of high transverse brightness) mean that this merging step must be made at higher energy – hence the introduction of an intermediate plateau at 2.5GeV (kinetic). Pure h=21  100ns h=7→ 7+14+21 → 21, 18b “Nominal” 𝑆 𝐶𝑃𝑆 (25𝑛𝑠) = 12 h=9→ 10 → 20 → 21, 16b “BCS” 𝑆 𝐶𝑃𝑆 (25𝑛𝑠) = 8 h=9→10→11→12→13→14→7→21, 12b “BCMS” 𝑆 𝐶𝑃𝑆 (25𝑛𝑠) = 6 1.4GeV 2.5GeV

Cavity Tuning Groups The 10MHz coarse tuning has been reconfigured during LS1 specifically to increase the number of cavities available on a given harmonic during rf gymnastics. The previous 6-2-2 grouping has been modified to 4-3-3, which permits three triplets of cavities to operate where before three pairs were used. CT1: C56, C66, C76, C81 CT2: C36, C46, C51 CT3: C86, C91, C96 CT4: C11, Test Cavity CT1: C51, C56, C66, C76, C81, C91 CT2: C36, C46 CT3: C86, C96 CT4: C11, Test Cavity

Cavity Voltage Groups Pre-LS1 “H84” matrix pattern The downside of the new tuning groups is that the voltage groups of the 10MHz matrix must follow suit, which in turn means rebuilding all timing trees that are multi-harmonic and reprogramming their associated functions for all users for which those trees are active. Consequently, the only pre-LS1 users that are safe to reload in the machine are single-harmonic ones. C11 C36 C46 C51 C56 C66 C76 C81 C86 C91 C96 Pre-LS1 “H84” matrix pattern Post-LS1 “H84” matrix pattern

Cavity Group Programmes During batch compression from h=9 to h=14, two groups are active at any one time on harmonics h and h+1, with the third group tuning to h+2. During merging, two groups are active on h=14 and h=7, with the third group tuning to h=21. Although the h=14 component is reduced to zero, the corresponding group remains tuned at this harmonic for the final step. During triple splitting, all three groups are active on h=7, 14 and 21. The voltage programmes shown are correct for the measured waterfall plot, but after LS1 each cavity group will deliver up to 60kV providing more acceptance throughout the process. This is important at the critical stage when the merged “super bunches” are triple split into h=21 buckets. New TREEH21BCMS will pilot all this.

Special Case: BCMS Intermediate The merging step means not only that the minimum number of Booster bunches injected into a BCMS cycle is two, but also that the phases of all triple splitting components must be inverted for such an intermediate beam. Otherwise each populated bucket gets merged with an empty one.

Nota Bene 25ns is less demanding for the PS than 50ns, not least because all 25ns schemes in Run 2 will be limited to a maximum intensity per bunch of some 1.3×1011 by the rf power available in the SPS. The radial and phase loops of the low-level beam control remain closed throughout, but they do not need to be switched to follow every single harmonic number change as the cavity return is simulated by an MHS. The harmonic sequence for the loops is h=9, 11, 13, 7, 21. The roles of the controlled blow-ups are essentially unchanged: the first is before any acceleration, the second is after triple splitting and the third is after transition. However, the parameters of BU2 get adapted for 2.5GeV (the synchrotron frequency is reduced by a factor of 2 with respect to that at 1.4GeV). Apart from minor modifications to the 10MHz part due to the change in cavity matrix pattern, a revised TREEH84 pilots almost identical functions for the 10MHz voltage descent and subsequent 20 and 40MHz splitting and 40+80MHz bunch rotation. It has been proposed to establish a common extraction timing at C2850 (or C1650 for a 2bp cycle) for all LHC-type proton beams and to incorporate a 2.5GeV intermediate plateau irrespective of whether the beam delivered is single- or multi-bunch (including nominal). This would make all extraction settings identical and mean only two magnetic cycles need to be maintained – which is a principle previously established for protons but is only still the case for lead ions. The deadtime at 2.5GeV for non-BCMS beams would lead to negligible beam degradation and would make little extra demand on the main power supply.

Booster Specs. The upper intensity limit of 1.3×1011 ppb at LHC injection corresponds to 0.9×1012 p/Ring at transfer from the Booster. Although this is significantly less than already achieved, the risetime of the kickers in the transfer line limits the length of the bunches to 150ns when they are recombined for injection into h=9 PS buckets, which is less than the well-established 180ns of the nominal scheme. Consequently, to mitigate the penalty of shorter bunches, it is proposed to transfer them with the maximum possible momentum spread as this increases their physical size and hence reduces their space charge footprint in the downstream PS. Using 8+8kV of C02+C04 voltage in bunch shortening mode will produce 150ns bunches with an emittance of 1.5eVs – i.e., much more than the 0.9eVs for 8kV of pure h=1 (and more even than the 1.3eVs empirical limit of the old nominal scheme). But this is new and must be tested. 0.9eVs: h=1 @ 8kV → h=9 @ 25kV 1.5eVs: h=1+2 @ 8+8kV → h=9 @ 65kV

Reserve Slide Measurements (end 2012) Nominal 50ns BCMS 50ns 1.4GeV NPSB [1012/Ring] 1.2 0.6 1.6 0.8 450GeV1) Nb [1011] 1.7 1.63) 1.1 βγε<H+V> [µm] 2.6 1.3 Brightness [1011/µm] 1.0 1.5 0.42 0.85 Rel. Brightness (Potential) 1.54) (2.0) 2.0 (2.0) Equivalent L/M [arb. units] 1.4 0.27 0.55 1) Measurements were made early on the LHC injection plateau. It was not always possible to make wirescans at SPS extraction, but agreement between the two machines at transfer is known to be good. 2) Operational experience with nominal 25ns beams was scant. These results are derived from fills 3425 and 3429; the latter saw 804 bunches at 4TeV. 3) 1.9×1011 ppb could have been delivered but this was considered inexpedient. 4) The minimum emittance from the Booster is set at ~1.0µm by Linac2. For the BCMS 50ns beam to reach its full potential, it would first have to be shaved down to well below this value.