In the base line configuration, the tunnel of the ILC will follow the earth curvature. The emittance growth in a curved main linac has been studied including static and dynamic imperfections. These include effects due to current ripples in the power supplies of the steering coils and the impact of the beam position monitors scale errors

Eliasson, P

Latina, A

Poirier, F

Schulte, Daniel

Walker, N

Eliasson, P.

Latina, A.

Schulte, D.

Poirier, Freddy

Walker, Nicholas John

DESY

Study of an ILC main linac that follows the earth curvature

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STUDY OF AN ILC MAIN LINAC THAT FOLLOWS THE EARTHCURVATURE P. Eliasson, A. Latina, D. Schulte, CERN, Geneva, SwitzerlandF. Poirier, N. Walker, DESY, Hamburg, GermanyAbstractIn the base line configuration, the tunnel of the ILCwill follow the earth curvature. The emittance growth ina curved main linac has been studied including static anddynamic imperfections. These include effects due to cur-rent ripples in the power supplies of the steering coils andthe impact of the beam position monitors scale errors.INTRODUCTIONRecently, the ILC-GDE [1] has been formed to promotethe work on the international linear collider (ILC). The firstgoal is to evaluate the cost of the project before the end ofthis year. One of the critical issues that can have signifi-cant impact on the cost is the question of the tunnel layout.A specific question is whether the tunnel can follow theearth gravitational potential or whether it needs to be laserstraight. A discussion of this question can be found in [2]; itconcluded that for the cryogenic system it is advantageousto follow the gravitational potential, to allow for a simplerdesign of the helium distribution system. For the cost ofthe civil engineering, the conclusion is very site dependent.Emittance preservation finally is easiest in the laser straightmachine. However, no unsurmountable obstacle had beenfound that prevented one or the other solution so the recom-mendation has been to realise the cheapest option, which inmany potential sites is likely to be the curved linac.In this paper we will show details of the beam dynamicsstudies that are relevant to demonstrate that the emittancepreservation appears feasible in the curved linac. First theperfect machine will be analysed then the performance ofthe beam-based alignment and tuning procedures. Finallythe beam jitter due to the corrector coils is considered.LATTICE DESIGNWe focus on a lattice design in which each cryomodulecontains eight accelerating cavities and each third modulealso contains a quadrupoles in the centre. The basic con-clusion on the feasibility of the curved linac should also bevalid for somewhat longer quadrupole spacing.The main linac lattice is the same in case of a laserstraight or a curved linac. We assume that the cryo mod-ules are straight and that a small angle is introduced be-tween each pair of modules to follow the earth curvature.The beam will be steered to follow the beam line using This work is supported by the Commission of the European Com-munities under the 6th Framework Programme “Structuring the EuropeanResearch Area”, contract number RIDS-011899.the corrector coils that are integrated into each quadrupole.This will generate dispersion in the linac, which can im-pact the emittance preservation. We add dispersion to thebeam before and remove it after the main linac. The valuesare adjusted as to minimise the final projected emittance atthe end of the linac. For a perfect linac it is indeed foundthat the difference in emittance growth between the laser-straight and curved tunnel is negligible.BEAM-BASED ALIGNMENTPROCEDUREIn order to ensure emittance preservation beam-basedalignment is required in the main linac. We chose disper-sion steering as the alignment method. The beam line issplit into a number of overlapping bins each of which con-tains 40 quadrupoles. Each bin starts 20 quadrupoles afterthe first quadrupole of the previous bin. The bins are cor-rected one after the other starting at the beginning of thelinac using the nominal beam and a test beam. The testbeam has an energy different from the nominal one. Incase of a laser straight machine one aims to minimise thefollowing figure of merit               (1)Here,   are the offsets of the nominal beam in the BPMsand  are the offsets of the probe beam. The first termlimits the trajectory of the nominal beam while the secondminimises dispersion by making the trajectories at differentenergies equal. Typically one uses      .In case of a curved linac, the different beams will not fol-low the same trajectory even for perfect alignment. Hencewe modify the figure of merit to account for the target dif-ference of the trajectories  due to dispersion:                (2)The emittance preservation can be improved by apply-ing tuning bumps after the beam based alignment. Thesebumps are based on an emittance measurement after theend of the main linac. The dispersion added before and af-ter the main linac is varied in order to optimise the finalemittance.The simulations in the following are performed withPLACET [3], assuming completely static machines. Thesame alignment errors as for the laser straight machines areconsidered, see table 1.Table 1: Alignment errors assumed in the simulations. Thefirst four are with respect to the cryo module, the last twowith respect to the ideal machine.Error Symbol ValueBPM position Quadrupole position 		Cavity position 	Cavity angle  	Module position Module angle Errors in the BPM calibration can affect the performanceof the dispersion steering, since the measured dispersiondiffers from the actual one in each BPM. In case of a laser-straight linac the impact of such errors can be removed byiterating the correction procedure. One aims to make thedispersion zero so only the small residual value will be in-correctly measured. In case of a curved tunnel one aims toachieve a non-zero target dispersion and hence will be leftwith a larger error.In the following we assume that the BPM reading  islinear to the actual offset  of the beam from it’s centre,but that the slope  is only known with limited accuracy     It is assumed that the scale factors have a Gaussian distri-bution with a width around 1 and that these factors donot change with time. Without in-situ calibration the scaleerror could be as large as  [6].RESULTSFirst we consider the case with a BPM resolution of  . The test beam has at any point 80% ofthe energy of the nominal beam. We iterate the alignmentprocedure of each bin three times in order to ensure that themethod converged. Figure 1 shows the emittance growth asa function of for this case. A scale error of 5% leadsto a small additional emittance growth; even a scale errorof 10% seems to be acceptable.In the case of a better BPM resolution of   ,the relative impact of the scale error is much larger, seeFig. 2. One can conclude that a 10% BPM scale error ren-ders a BPM resolution of better than   uselessfor the static alignment. The main remaining advantage ofthe better BPM resolution is that it allows to reduce the en-ergy difference between test and nominal beam.In order to reduce the scale error induced emittancegrowth one can try to use in-situ calibration to reduce thesize of the error. If the BPMs where mounted on moversthis calibration could be easily performed; this is howevernot the case in ILC. One can also calibrate the BPMs if thecorrector coils are well calibrated and the beam energy iswell known along the linac. In this case the expected beammotion can be compared to the measured one. It is also pos-sible to induce betatron oscillations and deduce the scale 0 5 10 15 20 1  10  100  1000  10000  100000  1e+06Δεy [nm]w1σscale=0.0σscale=0.05σscale=0.1σscale=0.2Figure 1: Emittance growth as a function of the weight (   ) for different calibration errors . The test beamhas a beam energy 20% below the nominal and the BPMresolution is . 0 5 10 15 20 1  10  100  1000  10000  100000  1e+06Δεy [nm]w1σscale=0.0σscale=0.05σscale=0.1σscale=0.2Figure 2: Emittance growth as a function of the weight for different calibration errors . The BPM resolution is.from them, provided that the lattice is know well enough.However, another solution is to reduce the growth by addi-tional tuning, as is shown in the next section.IMPACT OF EMITTANCE TUNINGBUMPSEmittance tuning bumps can significantly reduce theemittance growth in ILC [5] and is likely required alreadyin the laser-straight linac. We investigate the impact of onedispersion bump before and one after the main linac. Adetailed description of the method can be found in [5].The dispersion tuning bumps indeed significantly re-duces the emittance growth, see Fig. 3. The result for thecurved linac with zero BPM scale error is almost identicalto that for the laser straight machine. For larger scale errorsthe curvature however does not allow to use large values ofand thus deprives us from taking full advantage of thegood BPM resolution. 0 5 10 15 20 25 30 0.1  1  10  100  1000  10000Δε [nm]w1dfs,σscale=0.0dfs,σscale=0.1dfs,σscale=0.2dfs+bumps,σscale=0.0dfs+bumps,σscale=0.1dfs+bumps,σscale=0.2Figure 3: Emittance growth as a function of the correctorweight, if dispersion tuning bumps are used. A BPM reso-lution of  is considered.DYNAMIC EFFECTSThe beam will be guided around the curvature by usingthe corrector coils in the quadrupoles. Small variations ofthe strength of these correctors can arise from ripples ofthe power supply and lead to deflections of the beam withrespect to the nominal trajectory. We are focusing on theadditional effect due to the earth curvature, hence we studythis effect for a perfectly aligned linac. An additional effectis expected from the initial misalignments but this is ex-pected to be the same for a curved and a laser straight linac.We simulate the single- and multi-pulse emittance growth.The former is relevant if an intra-pulse feedback correctsthe beam trajectory at the end of the linac and full luminos-ity optimisation is performed at the interaction point. Thelatter is the emittance integrating over a few pulses and as-suming that no feedback is used. The main contribution isdue to the trajectory jitter, hence  growth correspondsto a jitter of 	.While the found emittance growth is small—see Fig. 4—one should be aware that the emittance is a relevant mea-sure of the luminosity only if the beam-beam offset andangle are optimised for luminosity [7]. Otherwise the lumi-nosity loss can be enhanced by the beam-beam effects[8].The required stability of a few times   is well withinthe state of the art.BENCHMARKINGIn order to benchmark the PLACET results the simula-tion of the curved linac has also been performed with MER-LIN [4] for a weight   . In this case no tuningbumps have been used but the plotted emittance is disper-sion corrected. As can be seen in Fig. 5 the agreement be-tween MERLIN and PLACET is quite good.CONCLUSIONWe have studied the impact of a curved tunnel on theemittance preservation in the main linac of ILC. In prin- 0 2 4 6 8 10 0  0.0002  0.0004  0.0006  0.0008  0.001Δεy/εy,0 [%]σDsinglemultiFigure 4: Emittance growth as a function of the dipole cor-rector power supply ripples . A perfectly aligned linacis assumed and the single-pulse as well as multi-pulse emit-tance growth are shown. 0 0.5 1 1.5 2 2.5 0  50  100  150  200  250  300Δεy [nm]Quadrupole no.PlacetMerlinFigure 5: Emittance along the linac comparing MERLINand PLACET results.ciple the same performance can be reached in both casesexcept that BPM calibration errors can singificantly impactthe performance of the beam-based alignment algorithm inthe curved linac. Scale errors above 10% are significantlyimpacting the emittance growth. Dispersion tuning bumpscan significantly reduce the emittance growth so that evenscale errors as high as 20% seem tolerable. But still smallervalues are strongly desired in order to take full advantage ofBPM resolutions in the order of . The required powersupply stability for the corrector coils has also been studiedand found to be not critical.REFERENCES[1]  			[2] W. Funk, D. Schulte, T. Shidara. GDE White paper “Com-ments on the Laser-Straight vs. Curved Tunnel” 2005.[3] D. Schulte et al. CERN/PS 2001-028 (AE) and PAC 2001.[4]  	[5] P. Eliasson, D. Schulte. EUROTeV-Report-2005-021[6] M. Ross. Private communication.[7] D. Schulte. PS/AE/Note 2002-181.[8] R. Brinkmann, O. Napoly and D. Schulte, PAC 2001.

Study of an ILC Main Linac that Follows the Earth Curvature

Study of an ILC Main Linac that Follows the Earth Curvature

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