A new CLIC Test Facility (CTF3) at CERN will serve to study the drive beam
generation for the Compact Linear Collider (CLIC). CTF3 has to accelerate a 3.5
A electron beam in almost fully-loaded structures. The pulse contains more than
2000 bunches, one in every second RF bucket, and has a length of more than one
microsecond. Different options for the lattice of the drive-beam accelerator
are presented, based on FODO-cells and triplets as well as solenoids. The
transverse stability is simulated, including the effects of beam jitter,
alignment and beam-based correction.Comment: LINAC2000 Conference, Paper No MOA0

Schulte, D.

English

arXiv

A new CLIC Test Facility (CTF3) at CERN will serve to study the drive beam generation for the Compact Linear Collider (CLIC). CTF3 has to accelerate a 3.5 A electron beam in almost fully-loaded structures. The pulse contains more than 2000 bunches, one in every second RF bucket, and has a length of more than one microsecond. Different options for the lattice of the drive-beam accelerator are presented, based on FODO-cells and triplets as well as solenoids. The transverse stability is simulated, including the effects of beam jitter, alignment and beam-based correction

Schulte, Daniel

CERN Document Server

EUROPEAN ORGANISATION FOR NUCLEAR RESEARCHCERN – PS DIVISIONCERN-PS 2000-049 (AE)CLIC Note 452BEAM DYNAMICS SIMULATION FOR THE CTF3 DRIVE-BEAMACCELERATORD. SchulteAbstractA new CLIC Test Facility (CTF3) at CERN will serve to study the drive beam generation for the CompactLinear Collider (CLIC). CTF3 has to accelerate a 3.5 A electron beam in almost fully-loaded structures. The pulsecontains more than 2000 bunches, one in every second RF bucket, and has a length of more than one µs. Differentoptions for the lattice of the drive-beam accelerator are presented, based on FODO-cells and triplets as well assolenoids. The transverse stability is simulated, including the effects of beam jitter, alignment and beam-basedcorrection.XX International Linac Conference, 21-25 August 2000Monterey, California, USAGeneva, Switzerland17 August 2000BEAM DYNAMICS SIMULATION FOR THE CTF3 DRIVE-BEAMACCELERATORD. Schulte, CERN, 1211 Geneva, SwitzerlandAbstractA new CLIC Test Facility (CTF3) at CERN will serve tostudy the drive beam generation for the Compact LinearCollider (CLIC). CTF3 has to accelerate a 3.5 A electronbeam in almost fully-loaded structures. The pulse containsmore than 2000 bunches, one in every second RF bucket,and has a length of more than one µs. Different optionsfor the lattice of the drive-beam accelerator are presented,based on FODO-cells and triplets as well as solenoids. Thetransverse stability is simulated, including the effects ofbeam jitter, alignment and beam-based correction.1 INTRODUCTIONIn the nominal stage of CTF3, the drive-beam acceleratorwill have eight klystrons, each feeding two 1 m-long struc-tures. The structures are almost fully loaded, transferringmore than 90 % of their input power to the beam. The av-erage energy gain per structure is ∆E ≈ 9.1 MeV [1]. Thebeam pulse consists of ten short trains of about 210 buncheseach. The first train fills odd buckets, the immediately fol-lowing second train fills even buckets; this pattern is thenrepeated. An RF-deflector at half the linac frequency isused to separate the trains after acceleration [2]. The ini-tial beam energy is E0 ≈ 26 MeV, the final beam energyEf ≈ 170 MeV, the bunch charge q = 2.33 nC, its lengthσx ≈ 1.5 mm [3] and the transverse normalised emittancesare ∗x = ∗y = 100 µm.2 STRUCTURE MODELThe simulations below have been performed usingPLACET [4]. The long-range transverse wakefield is repre-sented by the lowest two dipole modes of each cell. Thesehave been calculated neglecting the coupling between cellsand the effect of the damping waveguides [5]. The damp-ing of the lowest dipole mode has been found [6] to be inthe range Q = 11 to Q = 19 for perfect loads. In the sim-ulation, the modes are confined to their cells, which allowsone to take into account the angle of the beam trajectoryin the structure. The loss factors used in the simulation are50 % larger than in [5]. This is to account for the effectof higher-order modes. Also, the damping is conservativein the simulation; Q = 30 and Q = 400 are used for thelowest and the second dipole band. The short-range lon-gitudinal [5] and transverse [7] wakefields have been cal-culated and are included in the simulation. Almost perfectcompensation of the long-range longitudinal wakefields ispredicted [1].Quadrupole wakefields may be important and have beenimplemented in PLACET. The corresponding modes havenot yet been calculated but need to be included in the sim-ulation as soon as they are available.3 LATTICESThree different lattices were investigated. One consists ofsimple FODO-cells, with one structure between each pairof quadrupoles. The other two lattices are based on triplets.In one case (called T1 below), one structure was placedbetween two triplets; in the other case two structures (T2).The weaker triplet lattice (T1) and the FODO lattice areroughly comparable in length and cost, whereas the strongtriplet lattice (T2) is significantly longer and more costly.In the FODO lattice, the phase advance is µ = 102◦per cell, with a quadrupole spacing of 2 m. In T2 one hasµx = 97◦ and µy = 110◦, and a distance of 4.2 m betweentriplets. The sum of the integrated strengths of the outertwo magnets is slightly larger than that of the inner one.With this arrangement, the horizontal and the vertical beta-functions are equal in the accelerating structures, and theenergy acceptance of the lattice is markedly improved. ForT1 the phase advances are µx = 84◦ and µy = 108◦ for atriplet spacing of 3 m. The transverse acceptance is 4.2 σfor the FODO lattice, 4.9 σ for T2 and 5.8 σ for T1.Since the beams have to be compressed after the accel-eration, the RF-phase cannot be used to optimise the beamtransport. It must be chosen to achieve the required com-pression and to limit the energy spread of the beam beforethe combiner ring to the latter’s energy acceptance. An RFphase ΦRF = 6◦ is used in the following.4 TRANSVERSE BEAM JITTERNo estimate of the transverse jitter of the incoming beamexists. Therefore, only the jitter amplification is calculated.In the simulation, each bunch is cut into slices; the beam isset to an offset of ∆x and tracked through the linac. Thenormalised amplification factor A for a slice is defined asA =σx,0∆x√(xfσx,f)2+(x′fσx′,f)2Here, σx,0 and σx,f are initial and final beam size, σx′,0and σx′,f are initial and final beam divergence, ∆x is theinitial beam offset and xf and x′f are the final position andangle of the centre of the slice. For a slice with nominalenergy and without wakefield effects, one has A = 1. The-3-2-10123-3 -2 -1 0 1 2 3(x’f/σx’,f) (σx,0/∆x)(xf/σx,f) (σx,0/∆x)-3-2-10123-3 -2 -1 0 1 2 3(x’f/σx’,f) (σx,0/∆x)(xf/σx,f) (σx,0/∆x)Figure 1: The amplifiaction factor of the beam at the end of thedrive-beam accelerator, using the FODO lattice, without a ramp(left) and with a ramp (right). A mono-energetic beam withoutwakefields should stay on the innermost circle.-3-2-10123-3 -2 -1 0 1 2 3(x’f/σx’,f) (σx,0/∆x)(xf/σx,f) (σx,0/∆x)-3-2-10123-3 -2 -1 0 1 2 3(x’f/σx’,f) (σx,0/∆x)(xf/σx,f) (σx,0/∆x)Figure 2: The beam at the end of the drive-beam accelerator in atriplet lattice. On the left-hand side T2, on the right-hand side T1.maximum amplification factor Aˆ is the maximum over allslices. The left-hand side of Fig. 1 shows the bunches atthe end of the accelerator using the FODO lattice. Differ-ent quadrupole strengths were used to find the best phaseadvance. Some bunches are kicked significantly; the maxi-mum amplification is Aˆ = 3.7. Without knowledge of theacceptance downstream and the size of the beam jitter, it isnot possible to decide whether the amplification is accept-able. Within the linac, even a large jitter of ∆x = σx doesnot lead to beam loss.The first few bunches in each train are kicked particu-larly hard. This can be prevented by adding charge ramps.Towards the end of a train that fills even buckets, the bunchcharge is slowly decreased from the nominal bunch chargeto zero. At the same time one increases the charge in theodd buckets from zero to nominal, to keep the beam cur-rent constant. Thus the two consecutive trains practicallyoverlap. On the right-hand side of Fig. 1, one can see thatin this case all bunches are well confined, with a maximumamplification of Aˆ = 2.In the triplet lattices, the horizontal plane has a largerjitter amplification than the vertical one. But even the hori-zontal amplifications are significantly smaller than in theFODO lattice. Figure 2 shows the examples of a pulsewithout charge ramps, the amplification factors being 1.8(T2) and 1.5 (T1). With charge ramps, they are reducedto 1.5 and 1.3. If the beam jitters significantly, the tripletlattices are markedly better than the FODO lattice.3456789101112130 5 10 15 20 25 30acceptance [σ]s [m]FODOT2T1Figure 3: The minimum acceptance along the linac, with a gra-dient error. For each lattice, 100 machines have been simulatedand their minimum acceptance at each point is plotted.5 BEAM-BASED ALIGNMENTTo keep operation as simple as possible, only one-to-one correction is considered. All elements are assumedto be scattered around a straight line following a normaldistribution with σ = 200 µm. In the FODO lattice,corrector dipoles are located after each quadrupole andbeam position monitors (BPM) are placed in front of eachquadrupole. In the triplet lattices, the corrector dipoles arepositioned after the triplets and the BPMs are positionedin front and after the triplets. The correctors are used tobring the average beam position to zero in the BPMs. Foreach case, 100 different machines are simulated. The smallgrowths of about 0.5 % are almost the same for all lattices.6 GRADIENT AND PHASE ERRORSThe limit on the variation of the bunch energy is 1 % [8],much smaller than the single-bunch energy spread. In nor-mal operation, the additional dispersive effects are there-fore small. Static local energy errors are of more concernand are discussed here.The initial and final beam energy can be well measured,and from this the average gradient can be derived. A localvariation of the gradient is more difficult to detect. It willlead to a quadrupole strength that is not adapted to the beamenergy. The worst case is too low a gradient in the first twostructures, which are fed by one klystron. In the simula-tion, 100 different machines with a gradient in the first twostructures that is too low by 10 % (20 %) are corrected withthe beam. The emittance growth found after correction is1 % (5 %) in the FODO lattice and 0.5 % (2 %) in T1, whichseems to be sufficiently low. In T2, the value for a 10 % er-ror is small, 2 %, but for an error of 20 % it starts to belarge: 14 %. The transverse acceptance is reduced to 3.8 σ(3.2 σ) in the FODO lattice, 4.7 σ (3.8 σ) in T2 and to 5.2 σ(5.1 σ) in T1. Figure 3 shows the acceptance for a gradienterror of 20 %. For the FODO lattice, and to a lesser degreealso for T2, one starts to worry about beam losses. How-ever, an error of 10 % seems acceptable with all lattices.To be able to use the FODO lattice or T2, it necessary to0123456-20 -15 -10 -5 0 5 10 15 20min acceptance [σ]∆G/G [%]FODOT2T1T2, weakFigure 4: The minimum acceptance of the linac, as a function ofthe RF-gradient error; 20 machines were simulated for each case.-3-2-10123-3 -2 -1 0 1 2 3(x’f/σx’,f) (σx,0/∆x)(xf/σx,f) (σx,0/∆x)-3-2-10123-3 -2 -1 0 1 2 3(x’f/σx’,f) (σx,0/∆x)(xf/σx,f) (σx,0/∆x)Figure 5: The amplification of beam jitter with and without thecharge ramp for the lattice T2 including the injector solenoid.measure the local gradient to better than 10 %, to be able tocorrect the lattice accordingly. For T1, a precision of 20 %is sufficient.The RF power produced by a klystron has a systematicphase variation during the pulse. One hopes to correct thiseffect globally, but local variations will remain. To esti-mate their importance, a linear change in phase of 20◦ overthe pulse is assumed for the two structures driven by oneklystron. The next pair has an exactly opposite phase vari-ation. The resulting bunch-to-bunch energy spread is 2 %,full width, which is not acceptable in the combiner ring;so a better compensation would be needed. In contrast, theemittance growth seems acceptable with about 1.5 % av-eraged over 100 machines for all lattices; the acceptanceis hardly decreased. This phase variation does not causesignificant transverse effects.7 ENERGY ACCEPTANCEDuring commissioning of the linac, large energy errorsmay occur. To study the sensitivity to this, 20 machineswere simulated for each lattice in the following way: thelinac is corrected with a nominal beam; then the incom-ing beam is assumed to be accelerated at a different gra-dient. Figure 4 shows the minimum transverse acceptanceof the three lattices as a function of the RF-gradient error.The final energy error is about 1.4 times larger than that ofthe RF-gradient, since the beam loading does not change.The FODO lattice and T1 have a comparable energy accep-tance, whereas that of T2 is slightly smaller. By reducingthe focal strength, the energy acceptance can be further im-proved at the cost of higher transverse wakefield effects. Byreducing the strength of T2 to µx = 83◦ and µy = 94◦, theenergy acceptance becomes larger than that of the FODOlattice. The maximum amplification of an initial jitter in-creases from 1.8 to 2.6 but is still smaller than the factor3.7 in the FODO lattice. With each lattice, the linac energyacceptance is largely sufficient during normal operation.8 SOLENOIDPLACET has been modified to also simulate the effectsof solenoids with acceleration. This allows to include thelast two structures of the injector which are placed insidea solenoid. Two triplets are used to match the end of thesolenoid to the T2 version of the drive-beam accelerator.The field of the solenoid is 0.2 T and its length is chosensuch that a horizontal jitter of the nominal beam leads to afinal horizontal offset. The end fields of the solenoid aremodelled as thin lenses. Neither space charge nor the dif-ference of the particle velocities from the speed of light aretaken into account, but the wakefields are considered, incontrast to calculations done with PARMELA [9].Figure 5 shows the amplification factor. While there issome contribution from the structures in the solenoid, theoverall amplification seems still acceptable.9 CONCLUSIONThe simulations show that the lattices considered here canbe acceptable; the best is the strong triplet lattice T1. Thetriplet lattice T2 seems to be a better choice than the FODOlattice. The FODO lattice is less expensive than T2, whichis much cheaper than T1. To find the best compromise,more information is needed. For the FODO lattice theramps have to be studied in more detail. For all lattices,the matching from the injector to the linac and from thelinac to the combiner ring needs to be understood.10 REFERENCES[1] I. Syratchev. Private communication.[2] D. Schulte. The Drive-Beam Accelerator of CLIC. Proceed-ings of Linac 1998, Chicago, USA and CERN/PS 98-042(LP) (1998).[3] L. Rinolfi. Private communication.[4] D. Schulte. PLACET: A Program to Simulate Drive Beams.Proceeding of EPAC 2000, Wien, Austria and CERN-PS-2000-028 (AE) (2000).[5] L. Thorndahl. In: The CLIC RF Power Source. CERN 99-06(1999).[6] E. Jensen, A. Millich and L. Thorndahl. Private communi-cation.[7] A. Millich. Private communication.[8] R. Corsini. Private communication.[9] F. Zhou. To be published as a CTF3-Note.

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