We report on measurements of coherent tune shifts, head-tail growth rates, and current-dependent betatron phase advances at the CERN SPS in the year 2000. Comparing results obtained at two different energies shows that there is no notable contribution from space charge. Within the measurement resolution the impedance is the same as in 1999, consistent with the expected small effect from changes to ony a small number of pumping ports. In 2000, data were taken over an expanded range of chromaticities, which increases the sensitivity to the impedance frequency distribution. Measuremeents of the current-dependent phase advance around the ring help localizing the most important impedance sources

Arduini, Gianluigi

Burkhardt, H

Cornelis, Karel

Klem, J T

Zimmermann, Frank

Zorzano-Mier, M P

CERN Document Server

MEASUREMENTS OF THE SPS TRANSVERSE IMPEDANCE IN 2000G. Arduini, H. Burkhardt, K. Cornelis, J. Klem, F. Zimmermann, M.-P. Zorzano, CERNAbstractWe report on measurements of coherent tune shifts,head-tail growth rates, and current-dependent betatronphase advances at the CERN SPS in the year 2000. Com-paring results obtained at two different energies shows thatthere is no notable contribution from space charge. Withinthe measurement resolution the impedance is the same asin 1999, consistent with the expected small effect fromchanges to only a small number of pumping ports. In 2000,data were taken over an expanded range of chromaticities,which increases the sensitivity to the impedance frequencydistribution. Measurements of the current-dependent phaseadvance around the ring help localizing the most importantimpedance sources.1 INTRODUCTIONAs part of the SPS upgrade as LHC injector the trans-verse impedance is being reduced by shielding of more than1000 vacuum pumping ports, which represented about twothirds of the total impedance [1], and by removing leptoncomponents. About 20% of the pumping ports were al-ready shielded during the winter shut down 1999/2000.To monitor the effect of the ongoing vacuum-chambermodifications, a measurement program for the SPS trans-verse impedance was launched in 1999 [2]. The 2000 mea-surements aimed to (1) reproduce the 1999 data, (2) possi-bly discern a first small improvement, (3) further developmachine set up and measurement procedure, (4) quantifycontributions from space charge, and (5) explore comple-mentary measurement approaches.All our studies were performed with a single protonbunch. Relevant SPS parameters are listed in Table 1.Table 1: Relevant SPS parameters.variable symbol valuemomentum p 26 GeV/ccircumference C 6916 mbetatron tune Qx,y ∼ 26.6momentum compaction αC 1.856× 10−3bunch population Nb 1− 10× 1010rms bunch length σz 150 mmrms geom. tr. emittance x,y ∼ 0.25 µmave. beta function β ∼ 40 mThe impedance is described by a broadband resonatorZ⊥(ω) =ωrωR⊥1 + iQ(ωrω − ωωr) , (1)with resonant frequency ωr/2π = 1.3 GHz and qualityfactor Q = 1 [3]. Its effect is a complex tune shift [4]∆ωβ = − Nb ec4√π ωβ (p/e)T0 σz i(Z⊥)eﬀ (2)where T0 is the revolution frequency, ωβ the angular beta-tron frequency (including the integer part of the tune), and(Z⊥)eﬀ the effective transverse impedance. The latter isobtained by convoluting the impedance of Eq. (1) with aGaussian bunch spectrum h0(ω) = exp(−ω2σ2t ) that isshifted in frequency, ω → ω − ωξ, by ωξ = ξωβ/η, whereξ = Q′/Q = ∆QQ /∆pp denotes the chromaticity, and η theslippage factor. In Eq. (2), we have assumed a constant betafunction β = c/ωβ .We estimate the imaginary part of Z⊥ by measur-ing the coherent tune shift with current, and using(σz ∆Qx,y/∆Nb) ∝ ImZeﬀ ∼ R⊥/Q. The real partis obtained from the growth (or damping) rate 1/τ of thel = 0 head-tail mode, measured as a function of chromatic-ity ξ, via (−σz/(τNb)) ∝ Re(Z⊥)eﬀ ∼ ωξ/ωr R⊥/Q2.The ’∼’ signs indicate a proportionality in the limit oflong bunches (ωrσz  c). Note that the relation betweenimpedance and coherent tune shift given above strictly ap-plies only for the case of cylindrical symmetry [5]. In thecase of asymmetric structures, as in the SPS, part of thecoherent tune shift arises from ‘detuning’ or ‘incoherent’wakes, which are excited even if the beam is centered inthe chamber. To mark this difference, we add a superindex‘∆Q’ to impedance numbers computed from the tune shift.2 BEAM PARAMETERSImpedance measurements are ideally done at identicalconditions, varying only the intensity in case of the coher-ent tune shift measurements or chromaticity in case of thegrowth/decay rate measurements. The 200-MHz rf-voltagefor the measurements was fixed to a relatively high value,so as to obtain shorter bunches and to enhance the measur-able effect. The rf voltage during injection is lower (typi-cally 1.7 MV), and adapted for optimal matching. Betweeninjection/capture and the measurements the rf-voltage isramped adiabatically over a time span of about 80 ms. Fig-ure 1 illustrates the voltage ramping and bunch-length re-duction after injection.At the moment of the measurements within the SPS cy-cle, the 200-MHz rf voltage was about 2.6 MV for the stud-ies at 26 GeV/c and 4.3 MV at 120 GeV. In order to es-tablish stable beam parameters and to obtain reproducibleresults, we systematically monitor the bunch lengths andthe transverse emittances. A good knowledge of the bunchlength is also required for converting the measured tuneshifts or growth rates into an impedance value; see Eq. (2).Figure 2 summarizes bunch length measurements in 2000.0-7803-7191-7/01/$10.00 ©2001 IEEE. 2054Proceedings of the 2001 Particle Accelerator Conference, ChicagoFigure 1: Scope signals illustrating the rf ramp and bunchshortening prior to the measurement. Top trace: rf voltage;medium trace: peak current signal (inversely proportionalto the bunch length); bottom trace: dc current signal. Theinitial decay of both peak and dc currents indicates somebeam loss immediately after injection.σt [ns]02/06/00, 26 GeV19/07/00, 120 GeV02/10/00, 26 GeV0 1 2 3 4 5 6 7 8 9 10N  [1010]00.10.20.30.40.50.60.7Figure 2: R.m.s. bunch lengths in units of ns measured as afunction of bunch population in 1010 for the three study pe-riods in the year 2000. The values correspond to the stan-dard deviation of a Gaussian that was fitted to the signalfrom a wide-band pick up, recorded on a scope. The verti-cal error bars reflect the r.m.s. spread of several measure-ments taken at the same intensity. The systematic error inthe Gaussian fit for a single measurement is about 0.003ns (not shown). The horizontal error bar approximates thecycle-to-cycle intensity fluctuation.The bunch intensities were varied between 1 and 10 ×1010 protons by vertical scraping in the SPS. We used therotational wire scanner to monitor the emittances. The hor-izontal emittance was rather constant. The vertical emit-tance varied by more than a factor of 10, due to the scrap-ing. To minimize the bias of our measurement from thiseffect, we empirically adjusted the octupole magnets so asto cancel the detuning with amplitude.3 TUNE SHIFT AND GROWTH RATETune spectra are obtained by applying a fast Fouriertransform (FFT) to samples of 212 = 4096 successiveturns. Precise tune values are calculated off-line us-ing an optimized algorithm with windowing and peak-interpolation. A result for 120 GeV is shown in Fig. 3.The scattering of individual measurements implies an un-certainty of 4× 10−5 on individual tune measurements.0.5770.5780.5790.580.5810.5820.5830.5840.5850.5860.5870 1 2 3 4 5 6 7 8 9 101e10 protons per bunchVqv   211.1    /   211P1  0.5848P2 -0.5693E-03χ 2=211.05 ndeg=211slope=-0.000569 +/-0.000008tune error set to 0.00024 and scaled above 5  normalized for χ 2/n=10.5770.5780.5790.580.5810.5820.5830.5840.5850.5860.5870 1 2 3 4 5 6  mA bunch.currFigure 3: Vertical coherent tune shift versus bunch popula-tion at 120 GeV (19/07/00).Figure 4: Impedance values R(∆Q)⊥ , x(y) inferred from allmeasurements in 1999 (first 4) and 2000 (the last 3), byfitting to a broadband resonator with resonant frequencyωr/2π = 1.3 GHz and quality factor Q = 1 [3]. Trianglesare the R⊥ values obtained from the growth rate measure-ments; squares and circles representR∆Q⊥ inferred from thecoherent tune shift. The 6th measurement was performedat 120 GeV, all others at 26 GeV.Together with the measured bunch length and theknowledge of the beam energy, the effective transverseimpedance can be computed from Eq. (2). The results areshown in Fig. 4 (the circles and squares), which suggeststhat Im(Z⊥)eﬀ was measured reproducibly on the 10–20%level. The average vertical values in 1999, R∆Q⊥,y = 28± 2MΩ/m, and in 2000, R∆Q⊥,y = 26 ± 3 MΩ/m, are compati-ble with each other, and might indicate a small impedancedecrease by about 10%. The corresponding values in thehorizontal plane are R∆Q⊥,x = −2.6 ± 0.2 MΩ/m for 1999,and R∆Q⊥,x = −0.9 ± 1.8 MΩ/m for 2000. The horizon-2055Proceedings of the 2001 Particle Accelerator Conference, Chicagotal tune shift is almost zero. This is the expected result fora flat chamber, where effects of coherent and incoherentwakes cancel each other [5]. If scaled by the momentum,the 120-GeV impedance measurement (no. 6 in Fig. 4), isconsistent with the 26-GeV value. Hence, the space-chargecontribution at 26 GeV appears to be small.Growth rates were measured with the same set up, butby varying the chromaticity instead of intensity. Figure 5shows a result at 120 GeV. The data are compatible witha straight line, as expected for |ωξ|  ωr. The top scalein Fig. 5 is directly in units of frequency. By fitting thereal part of the effective impedance, the measured slopecan be translated into a value of R⊥, via Eq. (2). Resultsof the growth rate measurements are also depicted in Fig. 4(the triangles). The corresponding average impedances areR⊥,y = 11.1± 2.7 MΩ/m, and R⊥,x = 3.7± 0.3 MΩ/m.The incoherent wake fields in the vertical and horizontalplanes are of equal magnitude, but of opposite sign [5]. As-suming βx ≈ βy at the wake-field locations, the followingrelation should hold: R⊥,y =[R∆Q⊥,y − (R⊥,x −R∆Q⊥,x)].The two sides of this equation evaluate to 11 and 20 MΩ/m,respectively, which suggests that the actual resonator Qvalue is about 2, rather than 1.2000/12/18   16.08-1-0.75-0.5-0.2500.250.50.751-1 -0.5 0 0.5 1exec Growth date=20_07_2000 plane=V shiftx0=0.2402 ps=yesdata in file imp3_results_all H. Burkhardt  lxplus012  62.41    /    60P1 -0.3927E-04P2  -1.401chromaticity setting1000 * 1/τ  in turns  (normal. to 10**10 prot)fit f(x)=p1+p2*xwhere p1=-3.92655E-05 +/- 0.00583971where p2=-1.40064 +/- 0.0205126 scaled for Χ2/n=1zero chromaticity is at setting 0.240172 +/- 0.00416931-1-0.75-0.5-0.2500.250.50.751-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8E=120GeV  η=0.00179463fξ in GHzFigure 5: Growth rate of vertical head-tail mode (in unitsof 10−3 turns−1) measured as function of chromaticity ξ at120 GeV on 19/07/2000.4 IMPEDANCE LOCALIZATIONThe SPS is equipped with about 100 position monitorsper plane. These can be read out in multi-turn mode,thereby providing the possibility for localized impedancemeasurements as pioneered in LEP [6, 7]. From multi-turndata at all BPMs, the accumulated phase advance aroundthe ring can be computed [8]. Repeating this measurementfor two different beam currents and subtracting the two re-sults then yields the change in the phase advance with beamcurrent. An example is shown in Fig. 6. With present errorsit is hard to draw a definite conclusion. But there could bea first indication of steps (non-negligible local impedancecontributions) in the injection, rf and extraction area (lo-cated roughly at 1000, 3000 and 6000 m).cham2001/impedance/SPS_verticalPhaseAdvancem2.eps∆µ / 2π  / ∆Nprotons [1010 ]s [m]        (23 Multiturn data sets 02/06/2000 J. Klem)1000 2000 3000 4000 5000 6000 7000- 0.006- 0.005- 0.004- 0.003- 0.002- 0.0010.001Figure 6: Change of the accumulated vertical phase ad-vance around the SPS ring with bunch intensity [7].5 OUTLOOKIn 2001 we should be able to quantify the impedancereduction achieved by the SPS upgrade programme. In ad-dition, we will try to further extend the range of chromatic-ities in the growth-rate measurements, so as to enhance thesensitivity to resonant frequencies of individual impedancecomponents. According to a preliminary measurement in2001, the signal of the head-tail monitor [9] strongly varieswith beam current. This could be exploited for a direct ob-servation of the impedance effect on the l = 1 head-tailmode. Together with the coherent tune shift of the l = 0mode, this might allow us to distinguish experimentally thecoherent and incoherent wake contributions.Further informations can be found in Refs. [10].6 ACKNOWLEDGEMENTSWe thank P. Baudrenghien, L. Normann, M. Albert,J. Gareyte, D. Brandt, L. Vos, G. Rumolo, R. Jones, andthe PS division for help and discussions.7 REFERENCES[1] L. Vos, CERN SPS/86-21 (MS).[2] G. Arduini, et al., EPAC2000 Vienna (2000).[3] D. Boussard, J. Gareyte, Improvement Report no. 181 (1980).[4] F. Sacherer, Proc. 1976 Erice, CERN 77-13m, p. 198 (1977).[5] J. Gareyte, CERN SL/AP forum, 3. April 2001; K. Yokoya,Part. Acc. 41, p. 221 (1993); V. Danilov, VLHC workshop,SLAC, March 2001.[6] D. Brandt, et al., IEEE PAC95 Dallas (1995).[7] J. Klem, et al., Proc. EPAC 2000 Vienna (2000).[8] P. Castro et al., IEEE PAC 93, Washington, p. 2103 (1993).[9] D. Cocq et al., 8th WBI, Stanford, p. 281 (1998).[10] G. Arduini et al., SL-Note-2001-002 MD; and H. Burkhardt,Chamonix XI, CERN-SL-2001-003 DI (2001).2056Proceedings of the 2001 Particle Accelerator Conference, Chicago

Measurements of the SPS transverse impedance in 2000

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