A pair of idle cavity structures has been built at the Alfvén Laboratory, KTH, Stockholm for a second order compensation of the drive beam energy spread in the CLIC Test Facility II (CTF II) at CERN, Geneve. In this note, the theoretical background and the cavity design, together with the experimental results, are presented

Braun, H

Rosander, S

Valentini, V

CERN Document Server

OPEN-2000-01809/12/1999ORGANISATION EUROPEENNE POUR LA RECHERCHE NUCLEAIREEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH1211 Geneve 23, SwitzerlandCLIC Note 42509 December 1999Beam Loading Compensation of the CTF II Drive Beam using Idle CavitiesStaffan RosanderAlfvén Laboratory, KTH, StockholmMarco Valentini & Hans BraunCERN, PS/LP, Geneve, SwitzerlandA pair of idle cavity structures has been built at the Alfvén Laboratory, KTH, Stockholm for asecond order compensation of the drive beam energy spread in the CLIC Test Facility II(CTF II) at CERN, Geneve. In this note, the theoretical background and the cavity design,together with the experimental results, are presented.1. Beam-loading compensation in the CLIC Test Facility IIThe 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 CTF II isdescribed in [1] and [2] and some operational parameters of the CTF II drive-beam injectorare presented in Table 1.The drive-beam accelerator consists of two S-band structures which accelerate a bunchtrain of 48 bunches with a total charge of about 500 nC during 16 ns. The CTF drive-beamtrain extracts about 1 GW of power from the 3 GHz accelerating structures. This is far morethan the power input to the accelerators. The related energy has to be provided by the energystored in the structures and the heavy beam-loading has to be compensated.The effect of this substantial beam-loading is compensated for by operating the twoaccelerating 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 thebeam loading. Due to the sinusoidal time-dependency of the RF field, an energy spread ofabout 7% remains in the bunch train. The drive beam energy profile after acceleration has aparabolic profile with the leading and trailing bunches having the same energy and the centralbunches having a higher energy.In the CTF II, simultaneously to acceleration and beam-loading compensation, the drivebeam injector has to provide a way to establish the proper single-bunch energy-phasecorrelation required for magnetic bunch compression. The single-bunch energy-phasecorrelation can be controlled by using two accelerating structures, one operated at a frequencyCTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 2 of 10higher and the other at a frequency lower than the bunch repetition frequency. By running thetwo accelerators at the same field amplitude and injecting the train at opposite phase, thesingle-bunch energy spread introduced in the first structure is compensated by the second one.However, by using the correct phasing and a reduction of the field amplitude in the secondstructure, it is possible to introduce the same energy-phase correlation in all bunches.A detailed description of the beam-loading compensation system and of the hardware usedis given in [3], [4], [5] and [6].Table 1. Typical Operational Parameters of the Drive-Beam Injector.Number of bunches 48 Accelerating Field 35 MV/mBunch spacing 10 cm Residual train energyspread after acceleration~ 7%Bunch train charge 500 nC Correlated single bunchenergy spread~ 7%Energy 35 MeV Bunch length aftercompression (FWHM)5 ps2. Idle Cavities To further reduce the train residual energy spread, a pair of 3-cell idle cavities has beenconstructed at the Alfvén Laboratory, KTH, Stockholm. The cavities are tuned at frequencies31.2 MHz higher and lower than the bunch repetition frequency. Due to this frequencydifference, the beam-loading of the individual drive beam bunches does not add in phasealong the train. It is maximum after 24 bunches, i.e. in the middle of the 48 bunch train, and itis 90° out of phase for the last bunch. This way, the energy of the central part of the train islowered while the first and last bunch experience only their own wake. As a result, theresidual energy spread is further decreased. The idle cavity design has been optimised toreduce the train energy spread to less than 3% at the nominal charge. This is of the same orderof the energy spread expected from high order modes. The use of two cavities tuned at 31.2 MHz above and below the bunch repetition frequencyallows to conserve the energy-phase correlation of individual bunches.2.1 Design Criteria of the Idle CavitiesAs the bunch length after acceleration is shorter than 10 ps (FWHM), while the idle cavityresonant period is about 333 ps, the bunches can be regarded as infinitely short. Thus thedeceleration of the n-th bunch can be written as:¿¾‰flfi›‚‚„•¤¤'§ ’ ’ ƒ 110 2cos212nm bn mffqkW S (1)CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 3 of 10where q is the bunch charge, ’f is the frequency difference between resonant frequency, f0,and bunch repetition frequency, fb, and the loss factor, ko, is ko = R/Q*Z/4, where R is theshunt impedance (linac convention), Q is the quality factor and Z = 2Sf0.Employing the relation °°¿°°¾‰°°fl°°fi›‚„•¤'§‚‚„•¤¤'§‚„•¤'§ ƒ 2sin21sin121cos0 xxkjxkj(2)equation (1) reads ‚‚„•¤¤'§ ’‚‚„•¤¤'§ ’ ’bbnffffnqkWSSsin12sin0 (3)For the last bunch, n = 48, this expression should take the same value as for the first one, i. e.-’W48 = -’W1, thus:‚‚„•¤¤'§ ’ ‚‚„•¤¤'§ ’bb ffffsin95sin S (4)which is fulfilled in the following cases: °°fl°°fi› ’ ’ ’...  1 0, k      12... 1 0, k             295bbbffkffkffSSSSS (5)The simplest, non-trivial, solution givesbb ffff ’ ’ 195S (6)orMHz  23.3196r r ’ bffand so the idle cavity frequencies were chosen 2967.32 and 3029.78 MHz, respectively. It isinteresting to note that the necessary off-frequency, ’f, depends only on the number ofbunches in the bunch train and not on the beam intensity. This has the unavoidableconsequence that the effectiveness of the idle cavities is limited to the operation at the designbunch train length.CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 4 of 10Choice of the Shunt ImpedanceOn the other hand, the drive beam intensity does determine the level of compensationintroduced by the idle cavities. It is clear from Eq. (3) that the deceleration scales linearlywith the bunch charge.The highest correction according to Eq. (3) occurs for bunches 24 and 25,qkqkW 0025,24 *55.3096sin2sin °°¿°°¾‰°°fl°°fi›|’SS(8)and the lowest one for bunches 1 or 48,qkWW 0481  ’ ’ (9)For the typical operation conditions presented in Table 1, the bunch charge, q, approximatelyequals 500/48 nC. The residual energy spread, 7% of 35 MeV | 2.45 MeV, is totallycompensated by the difference between Eq. (8) and (9), i.e. 29.55*ko*q.  This is achieved fora total loss factor ko=8 V/pC, which corresponds to a total R/Q of the idle cavities of::    170055.29**MeV 45.2*44 00 qkQRshZZ(10)In order to allow operation at bunch train charges higher than 500 nC, it has been decided tolimit the compensation level and to accept a residual energy spread of 3-4% for a bunch traincharge of 500 nC. This corresponds to a total loss factor of 4 V/pC and to a total R/Q of850 :.Electric field in the Idle CavitiesIt is worthwhile to note that while the decelerating field experienced by the n-th bunch ismaximum at the center of the bunch train, the electric field in the idle cavities reaches amaximum at the end of the bunch train. The average electric field after the n-th bunch is: ƒ ' njjfion eqLkE1122 QS(11)where ko is the loss factor in the idle cavity, L is the length of the idle cavity, q is the bunchcharge, ’f  is the idle-cavity off-frequency and f is the bunch repetition frequency.Figure 1 shows the real and imaginary part and the modulus of the field as in Eq (11).It is clear that the decelerating field is maximum in the middle of the bunch train and that itvanishes for the first and last bunch. The maximum field occurs in the cavity at the end of thetrain and, for a bunch train charge of 500 nC, it is about 9 MV/m.CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 5 of 100 10 20 30 40 500246810real partimaginary partmodulusBunch NumberField [MV/m]Figure 1. Electric field in the idle cavities as a function of the bunch number along the train.Maximum deceleration occurs in the middle of the train.2.2 Design and Test of the Idle CavitiesA pair of 3-cell OFHC copper cavities were designed [7], constructed and tested at the AlfvénLaboratory with dimensions according to URMEL calculations performed at CERN. Themain design parameters are reported in Table 2. The cavity geometry is shown in Figure 2, thehigh frequency cavity is on the left side (i.e. the three far left cells) and the low frequencycavity on the right (i.e. the three far right cells).Table 2. Design and Measured parameters of the Idle CavitiesHigh Frequency Cavity Low Frequency CavityDesign Measured Design MeasuredFrequency 3029.78 MHz 3030.09 MHzat 23 °C2967.32 MHz 2967.72 MHzat 23 °C3029.75 MHzextrapolated at30 °C2967.37 MHzextrapolated at30 °CQo just above 12000 just below 12000R/Qo 425 490 ± 30 425 475 ± 30Number of cells 3ko per cell 0.68 V / pC cell 0.68 V / pC cellL of a cell 0.05 m/cellmode SCTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 6 of 10Figure 2. Idle cavity cross sectionThe measurements and the calculations revealed a coupling constant, k, of 7.39 and 7.03 permille for the high and low frequency cavities, respectively. Therefore, the outer cells weregiven respectively 5.56 and 5.25 MHz higher proper frequency (fout) than that of thecorresponding middle cell (fmid). In the S-mode, the coupled reactances thereby give each ofthe three cells of either cavity the same resonant frequency [8]21 kff out S(12)kff mid 1S(13)Thus, in this mode, all three r.f. field amplitudes of each cavity are expected to be equal.After pre-trimming and brazing of the cavity cells, only a slight change of the cell gaplengths remains to finally set the cell frequencies. This was done by moving the partitionwalls of the cavity assembly into position with an expandable special tool.The measured parameters (at 23°C) of the idle cavities are presented in Table 2. Thecavities match well the design specifications. The R/Q values, given in Table BB, were foundvia perturbation technique measurement of the electric field on axis [9]. The measured fielddistribution is shown in Figure 3, in which the two halves were measured at differentfrequencies.0,002,004,006,008,0010,0012,0014,00-10 10 30 50 70 90 110 130 150 170 190 210 230 250 270 290 310 330mmE-fieldhigh frequency cavity            low frequency cavityFigure 3. Idle cavities, axial E-field distribution in arbitrary units.CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 7 of 104.  OperationThe installation of the beam-loading compensation system has been completed at thebeginning of 1998 and the idle cavities have been installed at the beginning of 1999. Despitethe fact that the 3 GHz accelerating structures have been conditioned to only 36 MV/minstead of the design value of 60 MV/m, the beam-loading compensation system worked aspredicted by the theory. Its flexibility allowed operation at high current levels, which enableddemonstration of the two-beam accelerator scheme [2].Figure 4 shows a longitudinal phase-space image of a 24 bunch train with a total chargeof 120 nC. The measurement has been taken before the installation of the idle cavities. Thelongitudinal phase space has been measured with a streak camera from a transition radiationscreen in a spectrometer behind the accelerators. This way the energy spread is translated inposition spread. Only 24 bunches are shown because of the limited acceptance of the streak-camera.4 75 0B u n ch  N u m b er1 0 1 02 0 2 0Energy [MeV]Figure 4. Longitudinal phase space with beam-loading compensation before the installation ofthe idle cavities. Left side: measured; right side: predicted.Figure 5 shows the longitudinal phase space of the bunch train after the installation of the idlecavities in case of a train charge of 200 and 50 nC, respectively. Only the central part (i.e. 40bunches) of the bunch train is visible, due to the limited acceptance of the streak camera. Asexpected, the residual energy spread decreases as a function of the bunch train charge.CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 8 of 1041.545.543.55 44Bunch numberEnergy [MeV]4551485Energy [MeV]44Bunch numberFigure 5. Longitudinal phase space after the installation of the idle cavities. Top: drive beamcharge 200 nC, residual energy spread 5.9%. Bottom: drive beam charge 50 nC, residualenergy spread 7.2%.CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 9 of 100 10 20 30 40 5038394041Bunch NumberEnergy [MeV]Figure 6. Expected energy distribution along the bunch train with (+) and without (x) the idlecavities. Q = 400 nC, no correlation. The total energy spread is reduced to 4%.Table 3. Idle cavities performance for different bunch charges.DriveBeamCharge[nC]MeasuredEnergySpread[%]ExpectedEnergySpread[%]MeasuredEnergyMin-Max[MeV]PeakInducedDeceleration field[MV/m]400 4.3 4 38.3 - 40 7200 5.8 5.5 42.1 – 44.6 3.550 7.4 6.3 45 – 48.5 0.8Figure 6 shows the expected longitudinal phase space with and without the idle cavities for adrive beam charge of 400 nC (i.e. first case of Table 3).The measurements are compared with the predictions of the above-reported analyticalcalculations in Table 3. It is clear that the energy spread reduces with increasing charge aspredicted. In addition, there is a very good agreement between measurements and predictions.Without the idle cavities one would expect for the CTF II beam-loading compensationscheme that the energy spread is more or less constant at ~7%.In terms of beam performance, the installation of the idle cavities enabled thetransmission of 23% more drive beam charge through the 30 GHz decelerator in comparisonwith the previous performance. However, in the present CTF II set-up, the drive beamdecelerator is twice as long, thus achieving good transmission should be more difficult than inthe past.The idle cavities did not produce any problems with vacuum, electrical break-downs ortransverse wakefields.CTF II PERFORMANCE FIGURES IN THE 1998 RUNSPage 10 of 10 5. Conclusion The high transient beam-loading of the CTF drive beam (<I> = 30 A during 16 ns) has beencompensated by adopting a two-frequency beam-loading compensation system. In addition toproviding acceleration, the system reduced the total energy spread to 7% and allowed theestablishment of single-bunch energy-phase correlation of the order of 1% per degree ofbunch phase extension. The idle cavities performed as predicted and reduced the residual drive beam energyspread depending on the bunch charge. The installation of the idle cavities enabled thetransmission of 23% more charge through the 30 GHz decelerator.References1. The CLIC Study Group, CTF2 Design Report, CLIC Note 304 and CERN/PS 96-14,1996.2. H.H.Braun and 15 co-authors, “Demonstration of Two-Beam Acceleration in CTF II,”Proc. Linac ‘98, Chicago, US and CERN/PS/98-038, 1998.3. H.H. Braun, M. Valentini, Two-Frequency Beam-Loading Compensation in the DriveBeam Accelerator of the CLIC Test Facility, CLIC Note 390 and CERN/PS 99-016 (LP).Presented at 1999 Particle Accelerator Conference, New York, USA, 28 March - 2 April1999.4. M. Valentini, H. Braun, "Analytical Calculation of Beam-Loading Compensation in theHigh Charge Structures", CERN PS/LP, CTF note 98-05, 19-02-98.5. M. Valentini, "Interdependence between beam Loading Compensation, Bunch Charge andEnergy Gain in HCS", CERN PS/LP, CTF note 97-14,18-09-97.6. G. Bienvenu, J. Gao, “A Double High Current, High Gradient Electrons AcceleratingStructure,” Proc. EPAC ‘96, Sitges, 1996.7. H.H. Braun and S. Rosander, Resumé of discussion 6 – 7 Nov. 1997 at the AlfvénLaboratory, CTF Note 19978. D.E. Nagle, E.A. Knapp, and B.C. Knapp, Coupled Resonator Model for Standing WaveAccelerator Tanks, Rev. Sci. Inst. 38, No. 11 (Nov. 1967) 1583.9. See e. g. E.L. Ginzton, Microwave Measurements, p. 435 ff., McGraw Hill 1957.

Beam Loading Compensation of the CTF II Drive Beam using Idle Cavities

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