Measurements of transverse impedance in the SPS to track the evolution over the last few years show discrepancies compared to the analytical estimates of the major contributors. Recent measurements to localize the major sources of the transverse impedance using intensity dependent optics are presented. Some simulations using HEADTAIL to understand the limitations of the reconstruction and related numerical aspects are also discussed

Arduini, G.

Calaga, R.

Metral, E.

Papotti, G.

Quatraro, D.

Rumolo, G.

Salvant, B.

Tomas, R.

UNT Digital Library

BROOK••VENNATIONA.L LABORATORYBNL-81803..2009..CPTransverse impedance localization using intensitydependent opticsG. ArduinP, R. Calaga1, E. Metra}2, G. PapottP, D. Quatrar02,G. Rumolo2, B. Salvant2, R. Tomas2IBrookhaven National Lab, Upton, NY2CERN, Geneva, SwitzerlandPresented at the Particle Accelerator Conference (PAC09)Vancouver, B.C., CanadaMay 4-8,2009Coil ider-Accelerator DepartmentBrookhaven National LaboratoryP.O. Box 5000Upton, NY 11973-5000www.bnl.govNotice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC underContract No. DE-AC02-98CH10886 with the u.s. Department of Energy. The publisher by accepting themanuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up,irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow othersto do so, for United States Government purposes.This preprint is intended for pUblication in a journal or proceedings. Since changes may be made beforepublication, it may not be cited or reproduced without the author's permission.DISCLAIMERThis report was prepared as an account of work sponsored by an agency of theUnited States Government. Neither the United States Government nor anyagency thereof, nor any of their employees, nor any of their contractors,subcontractors, or their employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, completeness, or anythird party's use or the results of such use of any information, apparatus, product,or process disclosed, or represents that its use would not infringe privately ownedrights. Reference herein to any specific commercial product, process, or serviceby trade name, trademark, manufacturer, or otherwise, does not necessarilyconstitute or imply its endorsement, recommendation, or favoring by the UnitedStates Government or any agency thereof or its contractors or subcontractors.The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agency thereof.Transverse impedance localization using intensity dependent optics *Arduinfl , Calaga\ Metral2, G. Papotti2 , D. Quatraro2 , G. Rumolo2 , B. Salv<mt2 , R. Tomas21BNL, Upton, 2CERN~ Geneva, SwitzerlandAbstract ated with the perturbations in AK can be expressed asThe slope of the linear fit lJ..¢j IJ..N is used as the ef-fective '"phase-beat" observable due to multiple defocus-ing impedance sources. The location of sources are recon-structed using a linear least squares method,The phase-beat induced is equivalent to theF3-beat is morerobust because it is measured independent of the hardwarecalibration. The SPS is equipped with approximately 100bearn position monitors (BPMs) placed around the ring atapproximately 90C betatron phase advance and are capableof recording turn-by-tum beam positions for 1024 consec-utive turns. A Fourier transform of the BPM data immedi-ately after a transverse kick applied to the beam can be usedto deduce the linear optics. The phase advance is measuredfor varying intensities and fitted to a linear function similarto the tune shiftMeasurements of transverse impedance in the SPS totrack the evolution over the last few years show discrep-ancies compared to the analytical estimates of the m~iorcontributors. Recent measurements to localize the majorsources of the transverse impedance using intensity depen-dent optics are presented. Some simulations using HEAD-TAIL to understand the limitations of the reconstructionand related numerical aspects are also discussed.INTRODUCTIONThe super proton synchrotron (SPS) accelerates beamsfrom an injection energy of 26 GeV to top energy of450 GeV which is delivered to the Large Hadron Col-Eder (LHC). Table 1 shows some relevant parameters forthe SPS. As the injector to the LHC, the SPS underwentseveral hardware changes (for example: removal of leptoncavities, some kickers, installation ofnew extractions kick-ers etc ..) which modified its impedance. An impedancemeasurement campaign has been in place for several yearsto track the evolution due to modifications in the machinehardware [1].(2)(3)(4)Table 1: Some relevant parameters of the SPS beamsUnit Prototype[m][MHz] (6)where A is the model response matrix constructed by usingthe quadrupoies in the magnetic lattice. Additionally, thesolution can be obtained by imposing constraints on thequadrupoles to provide only a defocusing force similar toan impedance[GeV/c] 26[1011] 0.05- L3tl1m] 3.0[ns] 0.5526.12,26.1950200Beam momentumPlBunchEmittance, Ex,yBunch Length, (J'tBetatron Tunes, Qx,yAverage f3Main RF FrequencyA proposal to localize the contributions of the individ-ual sources of impedance was carried out successfully in2004 [2]. This paper will focus on the most recent mea-surements performed during 2007-08 runs to improve theunderstanding of the individual impedance sources andpotentially resolve any discrepancies between the knownmodel and measured impedance in the SPS. The effect ofthe transverse impedance on the complex tune shift to firstorder can be approximated as a defocusing quadrupole,where the gradient can be expressed as,The corresponding linear tune shift and ,B-beat associ-.. This work was partially performed under the auspices of the US De-partment ofEnergyAlternate methods using orbit bumps in sextupoles are alsoused which is discussed in Ref. [3]. Some benchmarks ofthis technique and reconstruction algorithms are performedwhich discussed in the foHowing section.SIrwruLATIONSTo benchmark the reconstruction algorithms, trackingsimulations using HEADTAIL [4] were performed us-ing the effect of single and multiple impedance sourcesin the nominal SPS lattice (26 GeV). For simplicity, thesources were placed at the existing kicker locations with animpedance of 0.5 MfUm per source. Approximately 105particles were tracked for 103 turns (similar to the data ac-quisition buffer capacity in the SPS). The centroid positionof the bunch transverse distribution was recorded as a func-tion ofeach turn for five different intensities. This data wasused to determine the coherent tune shift due as a functionof intensity. The estimated impedance from the linear slopeoftne tune shift agrees weB with the impedance in thesimulation.The tum~by-turnbeam centroid positions were recordedat aB the BPM locations which were used to deduce thephase advance between the consecu.tive BPMs as a functionof the five different intensities. The phase advances weresubsequently fitted with a linear equation 4 to determine thephase slope as a function of intensity. The phase advanceslope in the vertical plane is shown in Figure 1 which isreconstructed in the model using a linear response matrix.duce the bunch length and improve measurement sensitiv-ity ofthe beam trajectories.In addition to intensity scan with. baseline optics, twoother scenarios were carried also out. A 10r0m verticalthree-bump at "MKDV.11731" located at 550.619 m tolocaHy increase the effective impedance and a measure-ment to determine the impact of a finite momentum off-set (opjp =,4 X 10.... 3). The bunch lengths (40") and the RFvoltages during the tune measurements are listed in Table 2.31.81.81.8V UF2.22.52.52.54azConditionBaselineBaseline10mm V-bump1: / 3 ,., ]O~ .. 3up P::'7.: •• 1 X .Nov 2.2007Aug 4, 2008Aug 5, 2008Aug 5, 2008A dipole kick is imparted to the single bunch during theinjection plateau for aU intensities after approximately 500ms and a synchronized BPM acquisition system records thebeam trajectories for 103 turns. For the tune measurement,a dedicated high resolution BPM is available. There areadditionally about a 100 BPMs placed around the latticewhich are capable of recording 103 subsequent turns. Fig-ure 2 shows the tune derived from an average of all func-tioning BPMs in the ring for aU intensities and the threedifferent conditions. It should be noted that RPM gain hasto be substantially increased in order to measure the tra-jectories at low intensities « 2 x 1010) which result inlarger error bars. The fitted linear slopes and the computedimpedance estimates from the tune shift with intensity islisted in Table 3.Table 2: Bunch lengths and RF voltages for the differentbeam conditions for the intensity dependent tune scan mea-surements.DateIFO~r~~~::::The response matrix is solved for two cases, one withfocusing and defocusing elements (QF, QD), and the otherwith only defocusing elements (QD) while constraining thesign of the gradient to produce a defocusing effect. The re-construction from the turn-by-tum tracking data is able toidentity the region of dominant impedance sources as ini-tially input in the simulations (see Fig 1). However, thestrength is distributed among the neighboring quadrupolesused in the reconstruction. Therefore, the exact location,amplitude and the sign of the impedance reconstruction islimited to the variables used and cannot be easily inferredfrom this technique. Additional methods using system-atic orbit bumps maybe required to identity the amplitude.These benchmarks revealed that the reconstruction with-out constraints yields a robust solution with less parasiticsources distributed around the ring unlike the reconstruc-tion with constraints as assumed in Ref [2].3 0(longiWdinej Pos~io" ikmJFigure 1: Bottom: Slope of the vertical phase advance be-tween consecutive BPMs determined from a linear fit as afunction of intensity. Top: Source localization from phaseadvance slope using linear response matrix. The top barplot represents the location of the impedance sources usedin the simulation.il\WEDANCE MEASURE:MENTSFigure 2: Tune shift determined from an interpolatedFourier transform of all SPS BPM trajectories acquiredover 1024 turns after a transverse kick was appliedSingle bunches were injected into the SPS with varyingintensities and the chromaticity was set to rv2-3 units tokeep the beam stable at the highest intensities while sus-tain coherent betatron oscillations for sufficient number ofturns. Appropriate voltage matching at injection was re-quired to suppress the strong injection oscillations and the200 MHz RF system was ramped up subsequently to re-There is a clear difference in the measured tune shifts be-tween the baseline measurements of 2007 and 2008 proba-bly due to the shorter bunch length as an effect of elevatedvoltage any residual closed orbit effects. The case with thevertical orbit bump clearly shows an increase in the tuneshift slope which experimentally supports the use of localate rom ouner trans orm 0 approxunate y turn~ y-tum aYear Condition Slope Qo i Imp [Mf2/m]Nov 2, 2007 oplp = 0 -0.0188 (± 1.4%) 0.20 (± 0.1%) ! 20 (± 03)Aug 4, 2008 r5p/p =~, () -0.0155 (± 1.2%) 0.18 (± 0,07%) I 17 (± 0.2)Aug 5~ 2008 V-Bump ~~ 10 mm -0.018 (± 1.2%) 0.18 (± 0.2%) I 21 (± 0.3)Aug 5, 2008 op!7)::" 3.7 X 10---3 ..0.011 (± 3.4%) 0.19 (± 0.9%) 15 (± 0.5)Table 3: Coherent tune shift and the corresponding impedance estimates for different machine configurations. The tuneshift is calcul d f: F f f 1 103 b BPM d taACKNO\VLEDGEMENTSWe would like to thank the help of the OP group andJ. Wenninger for their help in machine setup.Figure 4: Slope of the horizontal (left) and vertical(right) phase advance shift with intensity and correspond-ing quadrupole perturbations to reproduce the observedphase-beat for baseline SPS lattice.3 4Longitlldirnll Po,,~Io" tkmj3 4Longillldinal Po.n Il<m!_3L--,---,osources cannot be easily inferred from such a technique.However, the MKD & MKE kickers (r'VO.5 km) clearly re-veal themselves as one of the m~or contributors in the ver-tical plane. In addition two other locations near 1.5-2 kmand 5-5.5km regions indicate potential sources. Although,the reconstruction in the horizontal plane is distributed, theregion near 2 km indicate potential sources. Dedicatedmeasurements at these specific locations using systematicorbit bumps are planned for future.orbit bumps. The case with the momentum of£~t showsnot only the overall tune shift (chromaticity), but also aneffective reduction of the measured impedance which un-der study.DISCUSSION·.. ~r-~~-~~~ ...,,"-~:':t ~M.?WAfhW4 ~a:~,,~P"t'..,_~._ ~_t ~.. lM 1. \I'J " . ,!+?:=*~:;~·;Jl:t" 'I : ( 1~ ;) ~ :> is .e ~ ~ !l~",~P.:r:,2iWl~~Figure 3: Phase advance between consecutive BPMs cal-culated from the linear fit of the intensity dependent optics.A comparison of phase slope two measurement performedin 2007 and 2008 is shown in the bottom plot. Note thatBPMs with faulty data have been removed.The recorded slopes at aU BPM locations are used tocompute the effective quadrupole perturbations in the lat-tice (see section) to emulate the observed phase-beat withthe aid of a linear response matrix. The quadrupole pertur-bation vector can be used to infer the approximate locationof the largest impedance sources as shown in Figure 4 forbaseline SPS lattice.INTENSITY DEPENDENT OPTICSAs a virtue of betatron oscillations sampled aroundthe lattice, the betatron phase advdnce between consecu-tive BPMs can be measured from the Fourier transform.The tune shift observed with intensity can be expressedas the accumulated phase advance shift around the ring,~Q = 2~ En 8</>(n~ 1)-->;<· This approach was carried outin Ref. [2] to determine the linear slope in the betatronphase advance as a function of intensity. Figure 3 showsthe lattice phase advance between consecutive BPMs cal-culated from the fit intercept and the corresponding slope.The three cases: baseline, lOmm vertical three-bump at"MKDV.11731" located at 550.619 m and a finite momen-tum offset (6IJ/p = 4 x 10--3 ) and compared to baselineoptics model of the SPS.Local impedance reconstruction using intensity depen-dent optics from recent measurements (2007-08) and pre-vious measurements (Ref. [2]) point to localized sources(Figure 4). The case with no constraints yields a ro-bust reconstruction with fewer spurious sources distributedaround the ring. The amplitude and sign of the impedanceREFERENCES[1] E. Metral et at, in EPAC08, Genova, Italy, 2008.(2) G. Arduini, in EPAC04, Lucerne, Switzerland, 2004.[3] R. Calaga, ABP note, to be submitted.[4] G. Rumolo, F. Zimmermann, PRST-AB 5, 121002 (2002).

Transverse impedance localization using intensity dependent optics

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Transverse impedance localization using intensity dependent optics

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