The ability of a particle collider to produce the required number of events, the luminosity, is usually used to size its performances. As demonstrated in many accelerators optimizing and calibrating the luminosity can be done using the Van Der Meer method which consist of shifting one beam with respect to the other while recording the event rate. In the LHC it is planned to perform those scans at the four interaction points using the data from the machine detectors as well as the ones from the experiments. A graphical user interface (GUI) has been developed for this purpose. We looked into procedures to quantify and if possible minimize the systematic errors coming from the measurements and the beam parameters and will discuss how we plan on using the relevant informations such as the vertex position or background measurements coming from the experiments

Alemany-Fernandez, R

Burkhardt, H

Lamont, M

White, S

CERN Document Server

LUMINOSITY OPTIMIZATION AND CALIBRATION IN THE LHCS. M. White, R. Alemany Fernandez, H. Burkhardt, M. Lamont, CERN, Geneva, SwitzerlandAbstractWe discuss luminosity monitoring, optimization and ab-solute calibration in the LHC. Interaction rates will be con-tinuously monitored both by detectors on the machine sideas well as by the four large LHC experiments. Horizontaland vertical separation scans will be used to optimize lu-minosity and to measure the beam sizes in the interactionregion. An application software has been developed for thispurpose. We describe the procedures which have been pre-pared and discuss expected systematic effects which maylimit the accuracy of the measurement.INTRODUCTIONThe event rate N˙ of a process of cross section σ and theinstantaneous luminosity L0 are related for head-on colli-sions of gaussian shaped beams byL0 = N1N2 f Nb2π√(σ21x + σ22x)(σ21y + σ22y)=N˙σ, (1)where N1 and N2 are the bunch intensities, f the revolutionfrequency, Nb the number of bunches per beam and σix,iythe effective transverse beam sizes. The number of bunchesand the revolution frequency are accurately known. Bunchintensities are expected to be measured with a precision ofroughly 1% [3]. We expect that the accuracy will be mostlylimited by the knowledge of the transverse beam dimen-sions at the interaction region.SEPARATION SCANSThe separation scans method for luminosity determina-tion was pioneered by Van Der Meer at the ISR [1]. The 0 50 100 150 200 250 300-6 -4 -2  0  2  4  6Nb of EventsSeparation (sigma)Gaussian fitSimulated DataFigure 1: Simulated luminosity scan for two bunches col-liding in early run conditions (β∗=11 m, 4×1010 p/bunch).size and shape of the interaction region is measured byrecording the relative interaction rates as a function of thetransverse beam separation. For gaussian beams, we willhaveL(d) = L0 exp[−d22σ2d], (2)where σd =√σ21i + σ22i and i = x, y for each separationplane, and a fit of the measured interaction rates as func-tion of the separation as illustrated in Fig. 1 will allow todetermine the effective beam size as well as the maximumachievable collision rate.BEAM PARAMETERS AND ABSOLUTECALIBRATIONThe absolute luminosity calibration based on machineparameters is of interest for the early LHC operation be-fore the pp cross-section has been precisely measured atLHC energies [2]. In pp collisions it will be easy to get highcounting rates and statistical errors are not expected to besignificant. We propose to perform the absolute luminositycalibration at lower intensity and with few bunches with-out crossing angle as planned in the earlier operation. Thisshould also allow to minimize measurement errors. Table 1shows the expected range of beam parameters from initialup to nominal operation. We also quote the event rate for across section of 10 mb as assumed for the LHC luminositymonitors (BRAN).Table 1: Single Bunch Luminosityβ∗ σ∗ Np L N˙(m) (μm) p/bunch (cm−2s−1) (Hz)11 74.36 4×1010 2.59 ×1028 2592 31.71 1.15×1011 1.18 ×1030 117730.55 16.63 1.15×1011 3.54×1030 35400Total rates and luminosities are increased by the num-ber of colliding bunches per beam which is already 43 and156 in early operation. Even in the early operation, a fewseconds will be sufficient to reach a 1% statistical accuracy.A crossing angle is required for operation with more than156 bunches to avoid parasitic collisions. The crossing an-gle reduces the luminosity by a geometric factorFc =√1 +(θcσz2σ∗)2, (3)where θc the crossing angle, σz the bunch length and σ∗the tranverse beam size at the IP. For nominal parameters,the crossing angle will reduce the luminosity by up to 20%Proceedings of PAC09, Vancouver, BC, Canada WE6PFP015Circular CollidersA01 - Hadron Colliders 2513and would result into an additional 2% uncertainty fromthe knowledge of beam parameters. We propose to per-form the luminosity calibration runs with at maximum 156bunches per beam. The bunch spacing is then sufficientlylarge, such that no crossing angle is required. The beam-beam effects and the hour glass effect respectively dependon the beam intensity and the ratio r = β∗/σz , it is possi-ble to bring those effects to a negligible level by workingat low intensity (≈ 4 × 1010 p/bunch) and with a β∗ largerthan 2 m.INSTRUMENTATIONWe now list the instruments [3] involved and discuss sys-tematic uncertainties.Beam Position Monitors (BPM)For the separation scans the only relevant information isthe angle and position at the IP which can be determinedvia a linear interpolation of the measurements made withthe BPMs installed next to Q1. They consist of strip lines(BPMSW) at the four IPs with an uncertainty on the zeroposition of 50 μm and in the case of IP1 and IP5 special but-ton pick ups were installed with an uncertainty of 10 μm.Beam position changes are expected in one plane whilescanning the other plane, therefore acquisition will have tobe done in both planes for each scan.Beam Current Transformers (BCT)The BCTs installed in the LHC will be capable of in-tegrating the charge of each LHC bunch. The presisionof these measurements for the nominal LHC beams is ex-pected to be of the order of 1%. An additional uncer-tainty could come from the longitudinal bunch distribution,unbunched particles or non colliding bunches would becounted in the average beam intensity but would not con-tribute to the luminosity. A careful bunch by bunch analysiscombined with a calibration at the end of the ramp wherethere is no unbunched components should provide a goodunderstanding of this measurement.Luminosity MonitorsThe LHC is equipped with collision rate monitors at eachIP, ionization chamber for IP1 and IP5 and CdTe detectorfor IP2 and IP8. It is also planned to use the luminositymonitors from the experiments for those special calibrationruns which could give better resolution for low intensity.The ZDC (Zero Degree Calorimeter) working in coinci-dence showed very good performances in terms of signaland background during the scans performed at RHIC.OPERATIONAL TOOLSA luminosity scan software as been developed in theframework of the LHC Software Architecture (LSA) [4] toperform these measurements allowing the operator to per-form separation or angle scans manually or automatically.Different features are available within the application:• Monitoring of the relevant devices (BPM, BCT, lumi-nosity monitor, orbit corrector).• Creation of the separation bumps to be trimmed viaLSA or the MADX online model.• Data exchange with experiments via the Data Inter-change Protocol (DIP).• Online analysis.• Acquisition of the measurements in a database for of-fline analysis.• Default settings for fast optimization.This application was developed such that all the toolsrequired to perform and analyse a separation or angle scanare available in the same software.MAGNET PERFORMANCEThe separation at the IP is generated via a four magnetclosed orbit bump. The magnets used to steer the beamsindependently are MCBC and MCBY [3] orbit correctors.It is possible to estimate the length of a full scan by lookinga their acceleration and ramping rate. The nominal settingfor those magnets were set to 0.67 A/s for the ramping rateand 0.25 A/s2 for the acceleration. Assuming a scan from-5 σ to 5 σ with 11 acquisition points of 10 s for the 2 m β∗optics each steps would last 17 s for an overall scan lengthof 3 minutes per plane. The same scan performed for the11 m β∗ optics would last 4 minutes. Hysteresis effectsin these magnets during the scan could be a source of un-certainty. In the case of the LHC it was shown that orbitdisplacements from hysteresis effects in these magnets are,in the worst case, of the order of 0.05 σ [6] which is withinthe precision of alignement we can get with the Van DerMeer method and can be minimized by always scanning inthe same direction.CALIBRATION SCANSThe LHC will operate with rounds beams, scans in bothvertical and horizontal direction should be enough to deter-mine the overlap distribution of the two colliding beams.The calibration scans will be done for the four IPs sepa-rately.Bump CalibrationThe knowledge of the length scale of the offest d be-tween the beams is required for absolute luminosity deter-mination. The measurement of the beam position at the IPcould be done via the BPMs described above but the exper-iments can provide us with a much better resolution fromthe vertex reconstruction. A bump calibration could be per-formed before the luminosity scan:WE6PFP015 Proceedings of PAC09, Vancouver, BC, Canada2514Circular CollidersA01 - Hadron Colliders• Perform a quick scan to recenter the beams.• Take measurement during n seconds to get the re-quired precision.• Move the two beams together to another position.• Repeat the first two steps again.• Compute the length scale from the two points.• Repeat the same procedure in the other plane.This method was used at SLAC [7] and gave a resolutionof 5 μm or better on the determination of the beam posi-tion. This would represent an error of 1-2% on the lengthscale for a β∗ of 2 m and would considerably reduce theuncertainty on the effective beam size measurement.SystematicsTable 2: Expected Uncertainties for Nominal LHC Run-ning Conditions and Conditions Used for CalibrationNominal CalibrationFc 2% negligibleDynamic effects 1% negligibleHour glass effect 1% negligibleBeam current less than 1% 1%Hysteresis effects negligible negligibleLength scale 1-2% 1-2%Relative Luminosity less than 1% 1%In addition to what is shown in Table 2 we can expecta small uncertainty due to non pp collisions backgrounds.The main extra uncertainty is expected to be associatedwith our knowledge of the bunch shape and dimensions.Extended non-gaussian tails for example would contributeto the bunch intensities but very little to the collision rates.We are quite confident that a total uncertainty of about 10%in the absolute luminosity calibration could be reached insmall number of calibration runs.OPTIMIZATIONThe main goal of optimization is to maximize the inte-grated lumonisity. It is forseen to use the same method foroptimization as for the calibration of the luminosity. How-ever optimization does not require as much precision as cal-ibration, an online study of the averages over the bunchesand over a smaller range of separation should be sufficientfor optimizing the luminosity. Since the collision rates arethe highest at the beginning the integrated luminosity willbenefit a lot from every minute saved in the early store. It istherefore necessary to build a fast and automated procedurein order to save as much time as possible, futhermore, it isvery desirable to minimize as much as much possible anysteering of the beam that could degrade the beam conditionduring the store.Early StoreAfter collapsing the separation bumps and an initial cor-rection using the BPMs the beams will not be perfectly cen-tered. A fast scan over a small range of separation with asmall number of acquisition points (-2 σ to +2 σ with 5 ac-quisition points typically) should be enough to center thebeams within 0.1 σ [2] in a few minutes which correspondto a relative change of luminosity with respect to the peakof less than 1% (as a reference the expected orbit spreadfrom beam-beam interactions at nominal beam conditionsis of the order of 0.3 σ).During the StoreThe orbit during the store will be affected by various ex-ternal perturbations such as the ground motion and, with-out corrections, those perturbations could result in a sepa-ration of up to 1 σ at the end of the store. A fully automatedprocedure included in the feeback system was successfullyused in RHIC [5] and could be well suited for LHC oncewe have a good understanding of the machine. In the firstmonth of operation it might be safer to manually performthis optimization using the same procedure as for the earlystore.CONCLUSIONWe describe plans for luminosity optimization and cali-bration in the LHC using transverse separation scans. Anonline application has been developed to control and moni-tor these scans. It will allow to determine the effective sizeand shape of the beams in collision and allow to minimizeany offsets between the colliding beams. The knowledgeof the transverse beam sizes can be used to predict the ab-solute luminosity. We expect that a systematic uncertaintyof about 10 % could be reached in a small number of cali-bration runs.REFERENCES[1] S. Van Der Meer, ISR-PO/68-31, KEK68-64.[2] H. Burkhardt, P. Grafstrom, ”Absolute Luminosity from Ma-chine Parameters”, LHC Project Report 1019, 2007.[3] ”The LHC Technical Design Report”, CERN-2004-003-V-1.[4] G. Kruk, S. Dehaye, M. Lamont, M. Misiowiec, W. Slinwin-ski, ”LHC Software Architecture [LSA] - Evolution TowardLHC Beam Commissioning”, ICALEPCS07, 2007.[5] A. Drees, T. D’Ottavio, ”Luminosity Optimization Using Au-tomated IR Steering at RHIC”, EPAC04, 2004.[6] N. Sammut, S.M. White, W. Venturini Delsolaro, H.Burkhardt,”Measurement and Effects of the Magnetic Hys-teresis on the LHC Crossing Angle and Separation Bumps”,EPAC07, Genoa, 2007.[7] W. Kozanecki et al., ”Interaction-Point Phase-Space Char-acterization using Single-Beam and Luminous-Region Mea-surements at PEP-II”, SLAC-PUB-13383, 2008.Proceedings of PAC09, Vancouver, BC, Canada WE6PFP015Circular CollidersA01 - Hadron Colliders 2515

Luminosity Optimization and Calibration in the LHC

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