Compensation of multi-bunch beam loading is of great importance in the main
linac of the Compact Linear Collider (CLIC). The bunch-to-bunch energy
variation has to stay below 1 part in 1000. In CLIC, the RF power is obtained
by decelerating a drive beam which is formed by merging a number of short bunch
trains. A promising scheme for tackling beam loading in the main linac is based
on varying the lengths of the bunch trains in the drive beam. The scheme and
its expected performance are presented.Comment: LINAC 2000, paper ID MOA0

Schulte, D.

Syratchev, I.

English

arXiv

Schulte, D

Syratchev, I

CERN Document Server

Beam loading compensation in the main linac of CLIC

Compensation of multi-bunch beam loading is of great importance in the main linac of the Compact Linear Collider (CLIC). The bunch-to-bunch energy variation has to stay below 1 part in 1000. In CLIC, the RF power is obtained by decelerating a drive beam which is formed by merging a number of short bunch trains. A promising scheme for tackling beam loading in the main linac is based on varying the lengths of the bunch trains in the drive beam. The scheme and its expected performance are presented

arXiv:physics/0008132v1  [physics.acc-ph]  18 Aug 2000BEAM LOADING COMPENSATION IN THE MAIN LINAC OF CLICD. Schulte and I. Syratchev, CERN, 1211 Geneva, SwitzerlandAbstractCompensation of multi-bunch beam loading is of great im-portance in the main linac of the Compact Linear Collider(CLIC). The bunch-to-bunch energy variation has to staybelow 1 part in 103. In CLIC, the RF power is obtainedby decelerating a drive beam which is formed by merginga number of short bunch trains. A promising scheme fortackling beam loading in the main linac is based on vary-ing the lengths of the bunch trains in the drive beam. Thescheme and its expected performance are presented.1 INTRODUCTIONMulti-bunch beam loading is a strong effect in the mainlinac of CLIC. It needs to be compensated with help of theRF to avoid extreme variations of the beam energy alongthe pulse. Several approaches to solve the problem exist.All of them are based on manipulations of the drive beamwhich generates the RF power.The first possibility is to reduce the bunch charge in thefirst part of the drive-beam pulse [1]. In this scheme, thefirst bunch has about 70% of the nominal charge. Thecharge is then slowly increased from one bunch to the nextuntil it reaches the nominal value. This charge ramp cre-ates a ramp in the RF voltage. By carefully shaping thecharge ramp, one can achieve beam-loading compensation.In principle, this compensation can be perfect. However, itmay be very difficult to control the bunch charge with therequired precision so as to achieve the required compensa-tion of the gradient variation ∆G/G0 ≤ 10−3 (G0 is thenominal gradient).Another method is described in reference [2]. It achieves∆G/G0 ≈ 2 × 10−3. It requires additional hardware andmay compromise the stability of the drive beam in the de-celerator.In a third option, presented in this paper, one creates aramp in the current of the drive-beam pulse comparable tothe first option. But instead of varying the bunch charge,one varies the number of bunches per unit length of thepulse. This can be achieved by modifying the drive beamin the drive-beam injector [3]. To understand this, it is nec-essary to understand the drive-beam generation, which isdescribed below.2 THE DRIVE-BEAM GENERATIONThe drive beam is produced and accelerated at a frequencyof about 937MHz. In the injector of the drive-beam linac,one has a sub-harmonic buncher which can be switched toFigure 1: Schematic layout of the delay loop after the drive-beam accelerator in CLIC. The two RF-deflectors are shown asrectangles.fill either odd or even buckets. In the drive-beam accel-erator, the beam then consists of short trains of bunchesthat fill every second bucket. The first train fills the oddbuckets, the immediately following second train fills theeven ones, and this pattern is then repeated [4]. The cur-rent in the drive-beam accelerator, and consequently thebeam loading, therefore remains constant. After acceler-ation, the trains are separated using an RF-deflector run-ning at half the linac frequency. The first train is deflectedinto a delay loop and merged with the second one in a sec-ond RF-deflector, see Fig. 1. The newly created pulses areseparated by gaps that allow conventional deflectors to beswitched on and off.They are sent into two combiner rings [5]. These ringshave a circumference equal to the distance between twopulses plus (or minus) a quarter wavelength. This allowsto merge four pulses to form a single one, using an RF-deflector. The new pulse has four times as many bunchesas each of the initial ones, with a distance between thebunches that is four times smaller. The bunches comprisingthe four pulses have been inter-leaved by this operation sothat the first bunch of each of the initial pulses is one of thefirst four of the final pulse.The first ring is followed by a second one, four timeslarger, which merges four of the pulses of the first ring.At the end, the bunch-to-bunch distance has been reducedfrom the initial 64 cm to only 2 cm. In the following, each64 cm long section of the beam pulse is called a bin and itcontains 32 bunches. The bunches that were in the first binof each initial train are in the first bin of the final pulse. Thebunches that were in the second bin of an initial pulse arein the second bin of the final pulse, and so on.trainbinNominal SwitchingDelayed Switchingbefore firstRF−deflectorafter secondRF−deflectorbefore firstRF−deflectorafter secondRF−deflectorFigure 2: The scheme of delayed switching. In this example,each train contains 5 bins (an arbitray number chosen for bettervisibility). In the upper case the phase is switched at the nominaltime, creating a rectangular pulse. In the lower case the phaseswitch is delayed to create a ramp.3 DELAYED SWITCHINGIn order to create a current ramp in the final pulse, the firstfew bins of this pulse must contain a smaller number ofbunches than nominal. This in turn requires that some ofthe pulses after the delay loop have less than the nomi-nal two bunches per bin. This can be achieved by delay-ing the switching of the sub-harmonic buncher. The effectof the nominal switching is illustrated in the upper part ofFig. 2. The two trains before the delay loop and the pulseafter this loop are shown. In the delay loop, the bunchesof the first train are delayed by one nominal train length.In the lower part of the figure, the sub-harmonic buncheris switched slightly later. The bunch that, in the nominalscheme, would have been the first one of the second train istherefore appended to the first train. The second train startsone bunch later than nominal. As a consequence, the pulseafter the delay loop contains only one bunch in the first bin.The last bunch of the first train is appenended after at theend of the pulse.The additional tail of the pulse creates no problem in thecombiner ring, as long as the distance to the first bin ofthe next pulse is long enough to switch the ejection kickersof the rings on and off. In the drive-beam decelerator, theadditional tail is not important, since it will just add a littletail to the RF-pulse produced in the power extraction andtransfer structures (PETS).The switching time can be individually chosen for eachtrain, so a rather fine ramp in the final pulse can be created.This solution does not require any additional hardware; onemust only be able to switch the sub-harmonic buncher atnon-regular intervals.4 NUMERICAL RESULTSTo achieve beam-loading compensation in the CLIC mainlinac, 11 of the 32 initial trains need to be delayed in thedrive-beam linac. The maximum delay necessary is 11bins. The gradient seen by the main-linac bunches can be00.20.40.60.810 20 40 60 80 100 120 140 160G/G0t [ns]Figure 3: Shape of the RF pulse which is produced by the drivebeam if delayed switching is applied.-0.015-0.01-0.00500.0050.010.0150.020.0250.030 20 40 60 80 100 120 140 160∆G/G0 [%]bunch numberFigure 4: The deviation from the nominal gradient as seen byeach bunch in the main linac.simulated with ASTPC [6]. In this program, the transienteffects in the PETS of the drive-beam decelerator, as wellas in the main-linac accelerating structures are taken intoaccount. Each structure is represented by a series of reflec-tors that are located at the cell boundaries. This makes itpossible to simulate precisely the beam acceleration in thetime domain.The gradient errors depend on which of the trains aredelayed. To find a good choice, a number of different de-lay patterns was created randomly. These were evaluatedwith the program and the best case was accepted. For thiscase, Fig. 3 shows the RF-pulse as it is produced by thePETS. This pulse leads to a bunch-to-bunch gradient errorin the main linac that remains below ∆G/G0 = 5× 10−4,see Fig. 4. This is better than the required precision of∆G/G0 ≤ 10−3.The method described achieves a constant amplitude ofthe accelerating field in the main linac. The main beam is,however, not accelerated on the crest of the RF wave, butat a small phase in the main part of the linac, ΦRF = 6◦.At the end of the acceleration, this phase is even larger,ΦRF = 30◦. Since the amplitude is increased in the RFphase and the beam loading is in phase with the beam, this00.511.522.533.540 50 100 150 200 250 300 350Amplificationquadrupole numbercase 1case 2Figure 5: The maximum amplification of an initial beam jit-ter along the decelerator. The case of a rectangular current pulse(case 1) is compared to the one with a ramp in bunch number (case2).leads to an effective phase shift of the total acceleratingfield during the first part of the main-linac pulse. In orderto prevent this, one can think of shifting the delayed trainsbefore they are merged with the other ones. The shift has tobe such that the bunches are in phase with the main beam.In this case, not only the amplitude but also the accelerationphase is maintained.5 SIMULATION OF THE DRIVE BEAMTo estimate the impact of the beam-loading compensationon the stability of the drive beam in the decelerator, simu-lations are performed using PLACET [7]. A lattice is cho-sen in which each six-waveguide structure feeds three mainlinac structures.As a measure of the stability, the maximum amplificationof an initial jitter is used, which is determined as follows:in the simulation, each bunch is cut into slices. The beam isoffset and then tracked through the decelerator. The maxi-mum offset that the centre of any slice reaches, divided bythe initial offset, is the maximum amplification. Figure 5shows this amplification of a transverse jitter along thedrive-beam decelerator. If no transverse wakefields werepresent, the final amplification factor would be A =√10from the adiabatic undamping of the motion. As can beseen, a rectangular current pulse (case 1) is close to thiscase. The bunch ramp increases the amplification some-what (case 2). This seems tolerable. Most of the effect isdue to the trailing bunches.If the delayed trains are shifted in phase, so as to preventphase shift of the acceleration field, the wakefield effects inthe drive-beam decelerator may become worse. The sim-ulation shows that also in this case, the jitter amplificationis almost the same as without the shift; they could not bedistinguished in the plot. The method therefore seems to bepractical. But other methods, such as a slow phase changealong the train, might achieve the same result.-0.0200.020.040.060.080.10.120 20 40 60 80 100 120 140 160∆G/G0 [%]bunch numberFigure 6: Deviation from the nominal gradient, as seen by themain-beam bunches in CTF3.6 APPLICATION TO CTF3Delayed switching could also be used in CTF3, the newCLIC Test Facility, which will be constructed at CERN.In this case, the switching time will be longer, about 4 ns.Since only ten pulses are merged to form the drive beam,one only delays three of them. Again, different cases weresearched for an optimum. The achieved compensation isvery good, about ∆G/G0 ≈ 1.2× 10−3, see Fig. 6.7 CONCLUSIONThe method presented, to compensate the beam loading inthe main linac, achieves the required precision of betterthan one part in 1000. It is very simple, can be adjusted todifferent switching times, and requires no additional hard-ware. It seems to be the method of choice for CLIC.8 REFERENCES[1] L. Thorndahl. Drive Beam Bunchlet Trains for Multibunch-ing. CLIC-Note 291 (1995).[2] R. Corsini, J.-P. Delahaye and I. Syratchev. CLIC MainLinac Beam-Loading Compensation by Drive Beam PhaseModulation. CLIC-Note 408 (1999).[3] D. Schulte. Pulse Shaping and Beam-Loading Compensa-tion with the Delay Loop. CLIC-Note 434 (2000).[4] D. Schulte. The Drive-Beam Acclerator of CLIC. Proceed-ings of LINAC 1998, Chicago, USA and CERN/PS 98-042(LP) (1998).[5] R. Corsini and J.-P. Delahaye. The CLIC Multi-Drive BeamScheme. CLIC-Note 331 (1997).[6] I. Syrachev and T. Higo. Numerical Investigation of Tran-sient Beam Loading Compensation in JLC X-Band MainLinac. KEK-Preprint-96-8 (1996).[7] D. Schulte. PLACET: A Program to Simulate Drive Beams.Proceeding of EPAC 2000, Wien, Austria and CERN/PS2000-028 (AE) (2000).

Beam Loading Compensation in the Main Linac of CLIC

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