Bane, Karl Leopold Freitag

Eriksson, L

Jobe, R Keith

McCormick, D

Ng, C K

Onoprienko, D V

Raubenheimer, T O

Ross, M C

Stupakov, G V

Tenenbaum, P G

Walz, D

CERN Document Server

TRANSVERSE WAKEFIELDS FROM TAPERED COLLIMATORS:MEASUREMENTS AND ANALYSISP. Tenenbaum, K. Bane, L. Eriksson, R.K. Jobe, D. McCormick, C.K. Ng, T.O. Raubenheimer,M.C. Ross, G. Stupakov, D. Walz, SLAC ∗D. Onoprienko, Brunel University, UKAbstractWe report on a series of measurements of the transversewakefield from tapered collimators. The collimators weredesigned to principally present a geometric impedance tothe beam, and to minimize impedances from resistivity orsurface features; in addition, the geometries of the colli-mators were selected to permit examination of the scalingbehavior of the wakefield due to collimator taper angle andminimum gap size. We present the measured near-centerwakefields of the collimators, as well as the effect of bunch-length variation. The measurements are compared to ana-lytic models and MAFIA simulations.1 INTRODUCTIONIn contemporary high-performance accelerators, colli-mators are commonly used to remove large-amplitude par-ticles from the beam and to protect downstream compo-nents from bunches which are following an unsafe trajec-tory; it is anticipated that future accelerators will continueto require mechanical collimators for these purposes. In or-der to accomplish machine protection or halo removal, thecollimators typically must be positioned quite close to thebeam; this in turn implies that the collimators can present alarge impedance, which can destroy the high-quality beamsrequired for applications such as x-ray lasers and linear col-liders.In principle, the geometric impedance presented by abeam collimator can be reduced by introducing a longitu-dinal taper. In practice, it is difficult to either simulate orcalculate the high-frequency impedance of a large, taperedcollimator with sufficient accuracy to satisfactorily modelits impact on beam dynamics, and experimental measure-ments of such objects are also scarce.In order to address the absence of experimental data, wehave designed, constructed, and installed a dedicated beamtest chamber for collimators at the 1.19 GeV point in theSLAC linac [1]. This chamber has been used to measurethe transverse wakefields of a series of tapered collimators.We report on the results of these measurements, and alsocompare them to recent analytic and simulation-based pre-dictions.∗Work Supported by the Department of Energy, Contract DE-AC03-76SF00515.2 APPARATUS AND MEASUREMENTTECHNIQUEThe test chamber is a rectangular vacuum chamberwhich can hold up to 4 test collimators at one time. Duringmeasurements, one of the collimators is positioned in thepath of the beam by a remote-controlled translation stage.Once a collimator has been positioned in the beam’s path,the wakefield is measured by varying the collimator’s ver-tical position and measuring the resulting vertical deflec-tion of the beam centroid on downstream beam positionmonitors (BPMs). The vertical position is varied using aremote-controlled high-precision translation stage built forthe Final Focus Test Beam (FFTB) project at SLAC; it hasa range of motion in the vertical of ±1.4 mm, and a posi-tioning resolution of 1 µm [2].3 COLLIMATOR APERTURESThe first set of collimators was designed to test the geo-metric wakefield of a tapered aperture. In order to achivean accurate measurement of the desired effect, it was nec-essary to minimize the impedance of each collimator fromother sources – notably the surface roughness and finiteconductivity of the apertures. This was accomplished byconstructing each aperture from oxygen-free, elementalcopper, and carefully machining each piece to achieve anadequately smooth finish.Each of the four collimators has a maximum size of 38mm high by 38 mm wide. Three of the collimators wereconstructed with a rectangular aperture at the minimum,and these collimators are tapered in the vertical but not thehorizontal. One of the collimators is tapered in the verticaland the horizontal to achieve a square aperture: this colli-mator is an approximation of a tapered round collimator,the transverse wakefield for which has been predicted byYokoya [3]. Table 1 indicates the geometry of the colli-mators, parameterized by taper angle α and minimum half-gap b1. Note that in previous publications, the parametersof collimators (1) and (3) were exchanged: this was due toan oversight during installation [4, 5]. Table 1 reflects thecorrect configuration of the apparatus.At the time of construction, the theory used to estimatethe deflections [6] indicated that the rectangular collima-tors would produce extremely large kicks – tens of micro-radians per millimeter of beam-to-collimator offset. Morerecently, it has become clear that the applicability of the ex-pressions used for those predictions are quite limited, andthat rectangular collimators with large width to height ratio0-7803-7191-7/01/$10.00 ©2001 IEEE. 418Proceedings of the 2001 Particle Accelerator Conference, ChicagoTable 1: Parameters of the tapered collimators. All rectan-gular collimators have a half-width, h, of 19 mm.Coll # 1 2 3 4Type Rect Square Rect Rectb1, mm 1.9 1.9 1.9 3.8α, mrad 168 335 335 298fall into three qualitatively different regimes [7]:• For extremely shallow tapers, in which√αh2/b1σz < 3.1, the transverse impedance ofthe collimator is purely inductive and is proportionalto αh/σzb21• For extremely steep tapers, for which √αb1/σz >0.37, the transverse impedance of the collimators isproportional to 1/b21 (this is known as the diffractiveregime)• For tapers between the inductive and diffractiveregimes, the impedance is proportional to√α/σzb31.The diffractive model predicts an impedance which is inde-pendent of taper angle, and constitutes an upper bound onthe impedance of a collimator with a given half-gap b 1. Theinductive impedance model, when applied to the rectangu-lar collimators in Table 1, predicts impedances which aremuch larger than those predicted by the diffractive model,which indicates that these collimators are far from the re-gion of applicability of the inductive model. All three rect-angular collimators are within the region where the diffrac-tive model is expected to be applicable.Like rectangular collimators, round collimators fall intoinductive or diffractive regimes of transverse impedance(although they do not have an intermediate regime betweenthese two, which arises in the rectangular collimator dueto its asymmetry). In this case the inductive regime hasa larger region of applicability, and the square collima-tor in Table 1 is believed to be modelled by the inductiveimpedance model. Note that all four collimators are nearthe transitions between different regimes; the accuracy ofthe analytic estimates is therefore somewhat limited.4 WAKEFIELD MEASUREMENTS ANDANALYSISThe majority of wakefield measurements were per-formed with electrons, at a bunch charge of approximately2× 1010, and an RMS bunch length of 650 µm, which cor-responds to full compression of the electron bunch from theSLAC damping ring. A subset of measurements was per-formed at lower charge (approximately 1.2×1010), anothersubset was performed at a larger bunch length (approxi-mately 1.2 mm RMS), and a third subset was performedwith positrons.4.1 Measurement ProcedureThe BPMs in sector 2 of the SLAC linac typically havesignificant DC offsets: during normal running, the RMS ofBPM values in the region is several hundred micrometers.These DC offsets must be subtracted from the measurementdata in order to accurately measure the beam kicks from thecollimator wakefields. The DC offsets are determined byreading out the BPMs for 100 pulses while the apparatus isheld stationery at its nominal zero point. The average of the100 pulses, called the “reference orbit,” is subtracted fromall subsequent data taken at different vertical positions ofthe collimator.The collimator vertical position is scanned over the rangeof the translation stage (±1.4 mm), typically in steps of 0.2mm. At each position of the collimator, the BPMs are readout for 12 to 25 pulses. On each pulse of scan data the ref-erence orbit is subtracted and the R matrices in sector 2 areused to fit the incoming and outgoing position and angleof the beam at the collimator z location: this is necessaryto include the effect of pulse-to-pulse beam jitter in sec-tor 2. Cuts are made on pulses which exhibit pathologiessuch as low bunch charge or poor quality of fit to the modelR matrices. The remaining pulses at each collimator posi-tion are averaged together, and an average deflection anglefor each position is determined. Figure 1 shows the mea-sured deflection angle as a function of beam-to-collimatoroffset for collimator 3. Note that over the range of moverpositions used, the wakefield shows the nonlinear “near-wall” behavior associated with collimator wakefields [6].Also shown in Figure 1 is a fit to an odd-power polyno-mial: y = p0 + p1x+ p2x3.COL-3: Short Taper, Nominal BeamChi2 / ndf = 12.31 / 12 0.1171 ±p0       = -0.2966  0.3432 ±p1       = 4.313  0.2327 ±p2       = 1.731 Distance to the Gate Center,  mm-1.5 -1 -0.5 0 0.5 1 1.5Wake Kick,  mkrad / mm-10-50510Wake Kick,  mkrad / mmFigure 1: Deflection angle versus beam-to-collimator offsetfor collimator 3.4.2 Measurement ResultsTable 2 shows the measured wakefield kick to the beamcentroid, in V/pC/mm, from each of the collimators. As inFigure 1, the results in Table 2 were obtained by perform-ing an odd-power third-order polynomial fit to the data, andcollecting the first-power coefficients; the exception to thisis collimator 4, which has such a large aperture that the cu-bic term was negligible. Table 2 also shows the expecteddeflection for the standard RMS bunch length of 650 µm;in the case of collimator 2, the analytic models for a round419Proceedings of the 2001 Particle Accelerator Conference, Chicagocollimator are used. While the predictions for all collima-tors are comparable to the measured values, in the caseof collimators 1 and 3 the actual deflection is somewhatsmaller than the prediction; this is to be expected, since thediffractive model essentially treats the collimator as unta-pered; the tapers in collimators 1 and 3, while steep, doreduce the geometric impedance somewhat.Table 2 also shows the measured wakefields for an RMSbunch length of 1.2 mm. Both over- and under-compressedbunches were used for this measurement, and both sets ofmeasurements are shown, along with analytic-model pre-dictions.Although additional data was taken for nominal bunchlength and reduced charge, these measurements simplyconfirmed that the deflection scaled linearly with charge,and so we have not included them here. Additional mea-surements taken with positrons were in qualitative agree-ment with the electron data (i.e., the deflection had the cor-rect sign for a transverse wakefield, but not for an elec-trostatic or magnetostatic effect); however, the beam con-ditions for the positron measurements were not well con-trolled, and so the positron measurements are also not in-cluded in Table 2.Table 2: Measured, theoretical, and simulation wakefield results for nominal and long-bunch conditions. A plus sign (“+”)in the bunch length indicates over-compression, a minus sign (“-”) under-compression.Collimatorσz , mm 1 2 3 4Meas 0.65 1.2± 0.1 1.4± 0.1 1.4± 0.1 0.54± 0.05Theo 0.65 2.5 1.4 2.5 0.6Sim 0.65 1.1 2.1 1.3 0.4Meas 1.2- 0.78± 0.13 1.2± 0.1 1.08± 0.09 0.49± 0.14Meas 1.2+ 0.83± 0.12 1.3± 0.2 1.04± 0.16 0.44± 0.10Theo 1.2 2.5 0.75 2.5 0.6Sim 1.0 0.85 1.1 0.4Sim 1.3 1.0Table 2 also includes the wakefield predicted by simula-tion studies of tapered collimators. The majority of thesesimulations used the program MAFIA [8], and are dis-cussed in greater detail elsewhere [9]. The simulation ofcollimator 2 used the program ABCI [10], and assumeda round geometry rather than a square one. The MAFIAsimulation results are generally quite close to the measuredwakefields; the ABCI simulation predicts a wakefield forthe square collimator which is 50% larger than the mea-sured value.5 CONCLUSIONSThe wakefields of a set of longitudinally-tapered colli-mators have been measured in the SLAC linac, and com-pared to analytic and simulation models. The measuredwakefields typically agree well with simulation results, andshow agreement at the level of a factor of 2 with improvedanalytic models. The measured wakefields are smaller andless sensitive to bunch length than was originally expected;this is because the longitudinal tapers are so steep that thecollimators are in the diffractive regime and not the induc-tive regime of transverse geometric impedance, a fact thatwas not apprehended at the time of construction.The apparatus used for these studies is a general purposetest stand for the measurement of collimator wakefields.We are improving the data acquisition and analysis proce-dures, and expect to achieve more precise measurements.In the near future, a tapered graphite collimator made byDESY will be studied, and a more general study of resis-tive wakefields will follow. Other tests, including a test ofan NLC prototype collimator and tests of impedance due tosurface finish, are also foreseen.6 ACKNOWLEDGEMENTSThe wakefield experiment could not have been per-formed without the efforts of SLAC’s technical experts, inparticular B. Brugnoletti, K. Dudley, and M. Ortega. Wewould also like to thank D. Burke and T. Markiewicz fortheir support of this experiment.7 REFERENCES[1] P. Tenenbaum et al, Proceedings PAC-99, 3453 (1999).[2] G.B. Bowden et al, NIM A368:579 (1996).[3] K. Yokoya, CERN-SL/90-88 (AP) (1990).[4] P. Tenenbaum it et al, Proceedings EPAC-2000 (2000).[5] P. Tenenbaum it et al, Proceedings LINAC-2000, 56 (2000).[6] G. Stupakov, SLAC-PUB-7167 (1996).[7] G. Stupakov, these proceedings.[8] R. Klatt et al, “MAFIA – a Three Dimensional Electromag-netic CAD System for Magnets, RF Structures, and Tran-sient Wake Field Calculations,” Proceedigs LINAC-86, 276(1986).[9] C.K Ng et al, these proceedings.[10] Y.H. Chin, “Users’ Guide for ABCI Version 8.7,” CERN-SL-94-02-AP (1994).420Proceedings of the 2001 Particle Accelerator Conference, Chicago

Transverse Wakefields From Tapered Collimators: Measurements And Analysis

Transverse Wakefields From Tapered Collimators: Measurements And Analysis

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