The CLIC Test Facility (CTF) is a prototype two-beam accelerator, in which a high-current "drive beam" is used to generate the RF power for the main-beam accelerator. The drive-beam accelerator consists of two S-band structures which accelerate a bunch train with a total charge of 500 nC. The substantial beam loading is compensated by operating the two accelerating structures at 7.81 MHz above and below the bunch repetition frequency, respectively. This introduces a change of RF phase from bunch to bunch, which leads, together with off-crest injection into the accelerator, to an approximate compensation of the beam loading. Due to the sinusoidal time-dependency of the RF field, an energy spread of about 7% remains in the bunch train. A set of idler cavities has been installed to reduce this residual energy spread further. In this paper, the considerations that motivated the choice of the parameters of the beam-loading compensation system, together with the experimental results, are presented

Braun, Hans Heinrich

Valentini, M

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TWO-FREQUENCY BEAM-LOADING COMPENSATION in the DRIVE-BEAM ACCELERATOR of the CLIC TEST FACILITYH.H. Braun, M. Valentini#, CERN, 1211 Geneve 23, CH                                                       # Email: marco.valentini@cern.chAbstractThe CLIC Test Facility (CTF) is a prototype two-beamaccelerator, in which a high-current “drive beam” is usedto generate the RF power for the main-beam accelerator.The drive-beam accelerator consists of two S-bandstructures which accelerate a bunch train with a totalcharge of 500 nC. The substantial beam loading iscompensated by operating the two acceleratingstructures at 7.81 MHz above and below the bunchrepetition frequency, respectively. This introduces achange of RF phase from bunch to bunch, which leads,together with off-crest injection into the accelerator, toan approximate compensation of the beam loading. Dueto the sinusoidal time-dependency of the RF field, anenergy spread of about 7% remains in the bunch train. Aset of idler cavities has been installed to reduce thisresidual energy spread further. In this paper, theconsiderations that motivated the choice of theparameters of the beam-loading compensation system,together with the experimental results, are presented.1 THE CLIC TEST FACILITY IICTF II [1] is an experimental facility of the CompactLInear Collider (CLIC) study dedicated to demonstratethe feasibility of the CLIC two-beam accelerator schemeand its associated 30 GHz technology [2]. A high-currentdrive-beam generates the 30 GHz power, while the mainbeam probes the accelerating field in the 30 GHzaccelerator. Some operational parameters of the drive-beam injector are presented in Table 1.The drive beam is generated by an S-band RF-photo-Table 1: Operational Parameters of the Drive-BeamInjector during 1998 Number of bunches  48 Bunch spacing  10 cm Bunch train charge  500 nC Energy  35 MeV Accelerating Field  36 MV/m Total loss factor  13.7 V/pC Beam line energy acceptance  14% Residual train energy spread  ~ 7% Correlated single bunch energy spread  ~ 7% Bunch length after compression(FWHM)  5 psinjector whose photo-cathode is illuminated by a shortpulse (8 ps FWHM), UV laser. Two S-band, disk-loadedaccelerating structures are used to provide accelerationto about 35 MeV. Since efficient 30 GHz powerproduction requires short bunches, a magnetic chicane,together with optimised phasing in the acceleratingstructures, is used to compress the bunches to 5 psFWHM. After bunch compression, the beam is injectedinto the 30 GHz decelerator where a part of its energy isconverted into 30 GHz power.2 BEAM-LOADING COMPENSATIONThe CTF drive-beam train of 500 nC during 16 nsextracts 1 GW of power from the 3 GHz acceleratingstructures. The related energy has to be provided by theenergy stored in the structures and the heavy beam-loading has to be compensated. In the case of moremoderate beam-loading, its compensation is provided bydedicated structures tuned at a frequency higher andlower than the bunch repetition frequency, while normalaccelerating structures are used for acceleration [3]. Inthe CTF case, the drive beam accelerator has to provideboth acceleration and beam-loading compensation. Beam-loading compensation can be obtained with asingle accelerating structure operated at a frequencyslightly higher than the bunch repetition frequency andby injecting the first bunch of the train before the crest.This produces a phase advance along the train, i.e. thesuccessive bunches arrive closer to the crest than theprevious ones, experiencing a higher accelerating fieldwhich approximately compensates the beam-loading.In the CTF II, simultaneously to acceleration andbeam-loading compensation, the drive beam injector hasto provide a way to establish the proper single-bunchenergy-phase correlation required for magnetic bunchcompression.The single-bunch energy-phase correlation can becontrolled by using two accelerating structures, oneoperated at a frequency higher and the other at afrequency lower than the bunch repetition frequency. Byrunning the two accelerators at the same field amplitudeand injecting the train at opposite phase, the single-bunch energy spread introduced in the first structure iscompensated by the second one. However, by using thecorrect phasing and a reduction of the field amplitude inthe second structure, it is possible to introduce the sameenergy-phase correlation in all bunches.0-7803-5573-3/99/$10.00@1999 IEEE. 3402Proceedings of the 1999 Particle Accelerator Conference, New York, 19992.1  TheoryThe energy gain of the i-th bunch (∆Ti) of a bunch trainin an accelerating structure operated at a frequency ν1,is:( )+−+−=∆∑−=1111112cos21212cosij bbobijqkiLETννpiφννpi                    (1)where E1 is the structure mean field, L is the structurelength, νb is the bunch repetition frequency, φ1 is thelaunching phase of the first bunch of the train into theaccelerator, ko is the beam loss factor (ko=ω r'L/4Q) andqb is the bunch charge. Eq. 1 can be written as a functionof the accelerator off-frequency (∆ν = ν1 – νb), and thesum can be written in a closed form:( )( ) ( )( )( )ψψφψsin2212sin12cos 11−−+−=∆ iqkiLET boi      (2)where ψ = pi ∆ν/νb. In Eq. 2 the bunch number index ican be treated as a continuous variable. By introducing acontinuous variable t to represent the time relative to thebunch centre, Eq. 2 can be modified to represent also theenergy of bunch slices at time t. The energy-phasecorrelation of the i-th bunch is then given by: ω-1d/dt ∆Ti.The two accelerating structures of the CTF drive beaminjector allow four free parameters, i.e. fields and phases(E1, E2, φ1 and φ2), which allow the fulfilment of fourconditions: minimum energy spread and equal energy-phase correlation along the train, maximum energy gainand achievement of the desired amount of correlation.The requirement of minimum energy spread and of equalcorrelation can be expressed mathematically byrequiring both bunch energy and correlation to beindependent of the bunch number in the middle of thetrain:021=∆+=NiiTdid   and   0   210t= ∆+==NiiTdtddid  (3)where the derivative is taken with respect to the bunchnumber index i, and N is the number of bunches in thetrain. As a result, the phase and the field of the secondaccelerator (φ2 and E2, respectively) are expressed as afunction of the phase and the field of the first accelerator(φ1 and E1, respectively), and of the off-frequency ∆ν:( ) ( )( ) ( )++++=1112cossincos2tgatg φαββφααφLEqk bo( )( )2112coscosφαφα−+= EEwhere α = pi (∆ν/νb)(N-1) and β = pi (∆ν/νb) N.28303234363840420 10 20 30 40 50Energy [MeV] w ithout compensationw ith compensationBunch NumberFig. 1: Bunch energy gain along the train.To maximise the energy gain, E1 is set to themaximum value that can be achieved. Then the choice ofφ1 sets the amount of energy-phase correlation. In thecase of the CTF II, for E1 = 36 MV/m and a requiredcorrelation of 1% per degree of bunch phase extension,φ1 is -60°, φ2 is +25°, E2 is 29 MV/m, and the trainenergy gain is about 30 MeV. The residual energy spreadis about 7%.The train energy profile after acceleration is shown inFig. 1 as a function of the bunch number. Also shown isthe energy gain without beam-loading compensation.The beam-loading compensation scheme reduces theenergy gain of the train head so that the total energyspread is reduced to about 7%.The ratio between the residual energy spread and theenergy gain in the accelerating structures depends onlyon the accelerator off-frequency and on the train length.In the case of the CTF II, ∆ν = 7.81 MHz, and N = 48,the relative energy spread is about 7% of the energy gainin the two accelerators.2.2  The choice of the accelerator off-frequencyTogether with the bunch train length, the choice of thefrequency difference between the accelerating structuresand the gun (∆ν) determines the bunch train residualenergy spread, the energy gain after beam-loadingcompensation and the versatility of the beam-loadingcompensation scheme. The frequency difference is thenchosen to minimise the residual train energy spread andto maximise the bunch energy gain in the structures.The train residual energy spread and the maximumenergy gain as a function of ∆ν in the case of the designparameters of the CTF injector are shown in Fig. 2. Themaximum energy gain increases with ∆ν and reaches aplateau at about 6 MHz, a larger ∆ν does not lead to anappreciable additional energy gain. On the contrary, theresidual energy spread increases more than linearly with∆ν. However, for a given final energy and for a givenbunch charge, the accelerator field required by the beam-loading compensation scheme scales inversely with ∆ν.In other words, a higher ∆ν allows beam-loadingcompensation with a lower accelerating field, at theexpenses of a higher residual train energy spread.3403Proceedings of the 1999 Particle Accelerator Conference, New York, 1999024681002468103 4 5 6 7 8 9EnergyspreadEnergygainEnergy spread [%] Energy gain [a.u.]Off-frequency [MHz]Fig. 2: Fractional energy spread [%] and maximumenergy  gain [a.u.].2.3  HardwareIn CTF II, the possible choice of the accelerator off-frequency was limited to either 5 or 7.81 MHz byengineering constraints related to the timing system. Thehigher off-frequency has been chosen to obtain a moreflexible beam-loading compensation system, effectivefor several combinations of bunch charges andaccelerator fields.Two special accelerating structures optimised forhigh-charge acceleration have been constructed at LAL,Orsay [4]. They are tuned at ± 7.81 MHz with respect tothe bunch repetition frequency, they have a large irisaperture and they have been optimised for a low r'/Q(2200 Ω/m) to maximise the stored energy.2.4  OperationThe installation of the beam-loading compensationsystem has been completed at the beginning of 1998.Despite the fact that the accelerating structures havebeen conditioned to only 36 MV/m instead of the designvalue of 60 MV/m, the beam-loading compensationsystem worked as predicted by the theory. Its flexibilityallowed operation at high current levels, which enableddemonstration of the two-beam accelerator scheme [1].Fig. 3 shows a longitudinal phase-space image of a 24bunch train with a total charge of 120 nC. Themeasurement has been taken with a streak camera from atransition radiation screen in a spectrometer behind theaccelerators. Only 24 bunches are shown because of thelimited acceptance of the streak-camera.Due to the gradients available to date in theaccelerating structures, the single-bunch energy-phasecorrelation has been controlled by varying the injectionphase of the train in the two accelerators, withoutlowering the field of the second one. This contradicts theprescription of the beam-loading compensation scheme(see Eq. 3) but produces the two-fold advantage ofincreasing the bunch train energy gain and ofintroducing a higher correlation in bunches in the bunchtrain tail. The latter contributes to obtaining equal bunchlengths along the bunch train, as late bunches are longer4750Bunch Number10 1020 20Energy [MeV]Fig. 3: Longitudinal phase space with beam-loadingcompensation. Left side: measured; right side: predicted.due to the beam-loading in the RF gun.3 IDLER CAVITIES To further reduce the train residual energy spread, a pairof 3-cell idler cavities has been constructed at the AlfvénLaboratory, KTH, Stockholm [5]. The cavities are tunedat frequencies 31.2 MHz higher and lower than thebunch repetition frequency. Due to this frequencydifference, the beam-loading is maximum in the middleof the train and vanishes for the first and last bunch. Thisway, the energy of the central part of the train is loweredand the residual energy spread is further decreased. Theidler cavity geometry has been optimised to reduce thetrain energy spread to less than 3% at the nominalcharge. This is of the same order of the energy spreadexpected from high order modes. First tests of the idlercavities with beam are foreseen for spring 1999.4 CONCLUSION The high transient beam-loading of the CTF drive beam(<I> = 30 A during 16 ns) has been compensated byadopting a two-frequency beam-loading compensationsystem. In addition to providing acceleration, the systemreduced the total energy spread to 7% and allowed theestablishment of single-bunch energy-phase correlationof the order of 1% per degree of bunch phase extension.5 REFERENCES[1] H.H.Braun and 15 co-authors, “Demonstration of Two-BeamAceleration in CTF II,” Proc. Linac ‘98, Chicago, US andCERN/PS/98-038, 1998.[2] J.P.Delahaye and 27 co-authors, “The CLIC Study of a multi-TeVLinear Collider,” this conference and CERN/PS/99-05,1999[3] “ATF Design and Study Report,” KEK 1995.[4] G. Bienvenu, J. Gao, “A Double High Current, High GradientElectrons Accelerating Structure,” Proc. EPAC ‘96, Sitges, 1996.[5] H. Braun and S. Rosander, Resumé of disussion at AlfvénLaboratory, CTF Note, 1997.3404Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Two frequency beam-loading compensation in the drive-beam accelerator of the CLIC Test Facility

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