The wire compensation is one of the possible LHC upgrade plans to overcome the beam-beam limit. We present weak-strong simulation results for the effect of long-range beam-beam interaction (LR-BBI) in LHC. In particular, we discuss the effectiveness of compensation, the difference between nominal and PACMAN bunches for the LHC, and wire tolerances

Dorda, U

Zimmermann, F

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Long-Range Beam-Beam Compensation with WiresU. Dorda, F. Zimmermann, CERN, Geneva, SwitzerlandAbstractThe wire compensation is one of the possible LHC up-grade plans to overcome the beam-beam limit. We presentweak-strong simulation results for the effect of long-rangebeam-beam interaction (LR-BBI) in LHC. In particular, wediscuss the effectiveness of compensation, the differencebetween nominal and PACMAN bunches for the LHC, andwire tolerances.INTRODUCTIONThe short bunch spacing in the LHC of 25ns causes 15LRBBI to occur at each side of each IP. The design cross-ing angle θ = 300µrad was chosen as trade off betweenbeam-losses due to long range beam beam interaction andgeometric luminosity losses and triplet aperture. Still thenonlinear forces will cause beam blow up and beam loss.As this distortion is proportional to the bunch population,the bunch spacing and the crossing angle, any upgrade sce-nario, aiming to tightem one of these parameters, will makethe situation even worse.The nonlinear field due to an opposing bunch (e.g: roundGaussian beam shape: ∆x′ ∝ 1/r(1 − e−r22σ2 )) is - withinlimits - comparable to the one of a current carrying wire(∆x′ ∝ 1/r). Therefore we studied the idea of installingwires into the beam pipes at both sides of the IP at loca-tions where the two beams are already separated (Fig:1).In the nominal case a current of 81A for a 1m long wireFigure 1: Principle of the LRBB compensationat a distance of 9.5σ from the beam-center would be ideal.The wire current can be adapted to compensate for a higherbunch population or a higher number of bunches.The compensation will not be perfect for a number ofreasons: there remains a small discrepancy in the fieldshapes, there is a finite phase advance between the LR-IPsand the wire (on average 2.6 ◦), there is a variation of thebeam-beam spacing between the different long range beambeam encounters (LR-IPs, min: 7σ, max: 13σ), and theactual beam might deviate from a perfect Gaussian shape.Furthermore there it might be nescessary to offset the wirefrom its optimal position (the wire must be positioned inthe shadow of the collimators instead of at the optimal dis-tance (9.5σ)).Weak strong simulations were performed using BBTrack[1]. In order to find the dynamical aperture (DA) particledistributions (off-momentum by δp = 2.7 ∗ 10−4) weretracked for 300.000 turns and the stability evaluated usingthe criterion of nonzero Lyapunov exponent. In addition tothe beam-beam interactions triplet errors and their correc-tors were included in the simulation model.NOMINALBunches in the center of a bunch train are affected by allLRBBI at both sides of the IP and are referred to as nominalones. The significant tune spread can be seen in Figure 2.The DA is found at 6.2σ(a) Tune footprint (b) Stability, the coloring encodingindicates the turnnumber of the on-set of chaosFigure 2: LRBBI affecting a nominal bunchOptimal compensationThe tune shift due to a wire alone is in the opposite di-rection and is depicted in Figure 3 a. The optimal compen-sation is given for 81A at 9.5 sigma from the beam center.This improves the DA by 1σ and eliminates the tune spreaddue to the LRBBI almost completely (fig: 3 b).(a) Footprint of a wire (b) Compensated footprintFigure 3: The optimal wire compensationLHC-LUMI-06 PROCEEDINGS71Larger Wire SeparationIn the introduction it was mentioned that it might notbe possible to position the wire compensator at 9.5σ but itmight have to be positioned further out. The difference indistance might be partially compensated for by increasingthe wire current, but the mismatch in field pattern reducesthe effectiveness slightly. Figure 4 shows the compensationof a nominal LHC bunch by wires at 11σ. The border ofstability is found at 6.7 σ, still improving by 0.5 σ com-pared to the uncompensated case.Figure 4: Footprint of a nominal LHC bunch with compen-sation at 11σULTIMATEThe most straightforward upgrade scenario, increasingthe bunch population, was chosen as an example, to studythe benefit of the wire compensator for an LHC lumi-nosity upgrade. The wire current is adapted to fit thenew requirements. An increase from 1.15E11/bunch to1.725E11/bunch would reduce the DA to 4.5σ. In this casethe wire compensation could recover 2 σ. The dynamical(a) uncompensated (b) compensatedFigure 5: 1.715E11 protons/bunchapertures for the different cases are summarized in table 1PACMAN BUNCHESPacman bunches are bunches at the start and end of abunch train which will experience a reduced number ofLRBBI. In the following we show simulation results forthe very last ones (the extreme Pacman bunches), whichprotons/bunch DA uncompensated DA compensated1.15E11 6.2 7.21.725E11 4.5 6.52.3E11 3.8 5.5Table 1: Comparison between the uncompensated and theoptimal (9.5σ) compensated caseencounter no LRBBI at one side of the IP. The nominalcompensation will overcompensate these bunches. The un-compensated DA is found at 6.7 σ. The nominal compen-sation reduces this slightly to 6.4σ.(a) no wire compensation (b) nominal wire compensationFigure 6: Tune footprints of the uncompensated and nomi-nally compensated Pacman bunchesAdapted compensationIt would be of interest to adapt the wire current to thespecific bunches. In a first approach one can try to finda trade off in performance of a DC wire between nomi-nal and Pacman bunches (Fig:8). Individually adapting thewire current poses severe technological problems as thiswould require switching times of the order of 400ns on ainductive load. Furthermore any turn-to-turn jitter wouldcause emittance blow up. From figure 7b) one can find thata turn to turn jitter of 4mA (=0.02ns assuming for a linearramp) results in a 10 % emittance increase within 20 h.(a) Current adapted for Pacmanbunches(b) Simulated emittance growth asa function of the jitter amplitudeFigure 7: A pulsed compensation scheme compensates alsothe Pacman bunches perfectly but poses severe technologi-cal challengesLHC-LUMI-06 PROCEEDINGS72Figure 8: DA of a DC-compensation for Pacman bunchesand nominal bunches as a function of the wire currentSUMMARY & OUTLOOKIn simulation the wire compensation proves to an ef-fective remedy for the LRBBI of nominal and Pacmanbunches. A pulsed device is a desirable upgrade option,promising even better performance, but faces significanttechnological problems. In the future, it will be studiedwhether the transverse feedback can be used to relax therequirements.REFERENCES[1] U. Dorda, “BBTrack, a tracking program for study-ing long-range beam-beam interaction”, http://ab-abp-bbtrack.web.cern.ch/ab-abp-bbtrack/.LHC-LUMI-06 PROCEEDINGS73

Long-range beam-beam compensation with wires

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