Barlow RJ

Bungau A

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WAKEFIELD CALCULATION - COMPARISON BETWEEN SIMULATIONAND EXPERIMENTAL DATA∗Adriana Bungau† and Roger Barlow, The University of Manchester, Manchester, UKAbstractIn linear colliders the collimator wakefields have a sig-nificant effect on emittance growth, beam jitter and back-ground estimates. Each simulation code models the colli-mator wakefields using a different approach and a discus-sion of the formalism for incorporating wakefields into theparticle tracking code Merlin is included in this paper. Us-ing simple collimator types we present the different pre-dictions for bunch shape effects, and also for the wakefieldkicks. These kicks are also compared with experimentalresults from SLAC End Station A (ESA).INTRODUCTIONIn order to prevent beam losses near the interaction re-gion that could cause unacceptable background in the de-tector, collimators are placed close to the beam path. Thetight apertures of the collimators cause wakefields that leadto beam jitter and emittance growth. The wakefields areseparated into two components, a geometric componentand a resistive component. The geometric wakefields aredue to change in the vacuum chamber section at the colli-mator, with the walls assumed perfectly conducting. Theimage charge generated by a charge q displaced by y in acollimator of half gap a is equivalent to a charge q placedat a2/y from the center of the beam axis. When the leadingcharge reaches the transition, the image charge stops fol-lowing it and generates an electrostatic field on the particlesthat are behind the leading particle. The resistive wakes aredue to the finite resistivity of the collimator material. Fora collimator with tapering sections, both the tapered andthe flat sections contribute to the resistive wall wakefieldsbecause of the finite conductivity of the material. The lon-gitudinal component of the wakefield increases the energyspread while the transverse component causes emittancegrowth.WAKEFIELD IMPLEMENTATION INMERLINThe collimator wakefields have been implemented in theMerlin tracking code in order to study the effect of thewakefields on the linear collider performances. The ini-tial standard wakefield implementation in Merlin includedonly the monopole (longitudinal) and dipole (transverse)∗Work supported by the Commission of the European Communitiesunder the 6th Framework Programme “Structuring the European Re-search Area”, contract number RIDS-011899.† Adriana.Bungau@manchester.ac.ukwakes. But because the collimator apertures are tight andparticle bunches are close to the collimator edges, the near-wall wakefields play considerable role in single bunch dy-namics [1]. For bunches close to the axis, the longitudinaleffect is dominated by the monopole mode (m=0) and thetransverse effect is dominated by the dipole mode (m=1)and when considering near-wall wakefields, higher ordermodes must be considered. Higher order modes were im-plemented in Merlin and new clases were derived in thecode containing the extra feature and a detailed discussionof the implementation has been presented [2]. The formal-ism for wakefield implementation into Merlin makes sev-eral assumptions [3]:• all particles are relativistic so the effect of the chargeson each other is supressed by a power of γ and there-fore ignored.• the effects of the transverse velocity and accelerationare ignored (the position r ′ and r of the leading andtrailing particle are constant).• the collimator aperture is assumed to be circular (thehalf width or the half height, whichever is the smallestis treated as radius in this model).The total wakefield effect is a sum over all multiple con-tributions: the summation is over all particles in a bunchslice and then over all slices for all modes. The usualmonopole and dipole formulae are reproduced for m=0,1.Geometric WakesAt present, the code contains an implementation of a ge-ometric wake function which corresponds to a simple colli-mator geometry: a collimator with an upper flat section of agiven length and a smooth tapering angle. The wake func-tion for a steeply tapered collimator moving from apertureb to aperture a is given by the following expression [4]:Wm(z) = 2(1a2m− 1b2m)e−mza θ(z) (1)where θ(z) is a unit step function. The calculation ofthe geometric wakefield uses the Yokoya approximation forsmall tapering angle [5]. Therefore, in this particular case,the tapering angle can not be provided but the computationis correct for smooth transitions. The implemenation of thegeometric wakes does not take into account the length ofthe upper flat section, only the beam pipe radius and thecollimator half-gap are the parameters of interest.MOPP007 Proceedings of EPAC08, Genoa, Italy03 Linear Colliders, Lepton Accelerators and New Acceleration Techniques562A03 Linear CollidersResistive WakesFor the implementation of the resistive wakes, Merlinreads tables of numerical integration of Chao’s impedanceformula [6]:Z =2cb(λk− ikb2)−1(2)The advantage of this implementation is that one can domore complicated formulae of the impedance for differentradia, material conductivity etc.BUNCH SHAPE DISTORSIONMerlin simulations were performed in order to determinethe bunch shape distorsion in collimators. The beam wassent through the ILC-BDS beamline with an offset and theshift in the bunch centroid was recorded in all BDS colli-mators. One can see in Fig. 1 that for an initial offset of1 nm the shift of the bunch centroid varies from -0.3μm to0.9μm as the beam encounters various accelerator compo-nents in the beamline. If at the start of the BDS the beamshape was Gaussian, in the last collimators it is distortedas Fig. 2 shows. This bunch distorsion corresponds to thespoiler AB7. A highly distorted bunch at the interactionregion is of great concern for the collider luminosity.z(m)0 500 1000 1500 2000 2500offset (m)-0.6-0.4-0.2-00.20.40.60.81-610×Beam jitter in the ILC_BDS collimators initial offset - 1nmFigure 1: Beam jitter through the ILC-BDS beamline.x2-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 -0-310×y2-10-50510-610×Spoiler AB7 - 1 nm offsetFigure 2: Beam shape is distorted in the collimator AB7.COMPARISON BETWEEN SIMULATIONAND MEASUREMENTIn order to design the ILC collimators, a goal has beenset of a ∼10% agreement between the measured and pre-dicted transverse wakes [7].Wakefield Measurements at ESAWakefield measurements were performed at the StanfordLinear Accelerator Center (SLAC) at the End Station A(ESA) facility. A wakefield box was installed at ESA totest various collimators. It contains an inner “sandwich”with five slots through which the beam passes. The colli-mators are placed in four of them to be tested at one timewhile the fifth slot is used to allow the beam to pass withoutobstruction for other beam experiements. The collimatorsare placed in the beam path using a horizontal mover. Thebeam parameters at ESA are presented in the table.Table 1: Specifications of the ESA beam.Beam Property ValueEnergy 28.5 GeVCharge 1-2·1010e−Repetition Rate 10 HzBunch length 0.3 - 1.0 mmBunch height, width 100 μm, 1 mmThe collimators tested at ESA are presented in Fig. 3,Fig. 4 and Fig. 5 and Fig. 6. They are made of copper,apart from collimators 11 and 14 which are made of tita-nium, and all have a smooth surface apart from collimator10 which has a surface roughness of few μm. The dimen-sions are given in the pictures.Figure 3: Beam collimators at ESA.Merlin PredictionsSimulations were run in order to determine the geomet-ric and resistive kick for ESA collimators. The kick wascomputed by dividing the shift in the mean value of y ′ an-gle multiplied with the beam energy, to the offset and bunchProceedings of EPAC08, Genoa, Italy MOPP00703 Linear Colliders, Lepton Accelerators and New Acceleration Techniques A03 Linear Colliders563Figure 4: Beam collimators at ESA.Figure 5: Beam collimators at ESA.charge. The results are compared with the masured kick atESA [8]:There is a good agreement between simulation and ex-periment for collimators 1,2 and 3. The differences for col-limators 4 and 5 can be explained by the fact that theseare step collimators and Merlin assumes that they have asmooth tapering angle. These kicks are small comparedto the measured kicks. For the other collimators, the Mer-lin predictions are bigger than the measured kicks. Merlindoesn’t include surface roughness and the geometric effectis dominant.Figure 6: Beam collimators at ESA.Table 2: Comparison between wakefield simulation usingMerlin and collimator wakefields measured at SLAC EndStation A.Coll.no Geom.kick Resist.kick ESA Kick1 1.311 0.003 1.4±0.12 1.324 0.012 1.4±0.13 4.899 0.128 4.4±0.14 0.005 0.00004 0.9±0.25 0.199 0.0009 3.7±0.16 2.115 0.20 0.9±0.110 2.115 0.20 1.4±0.211 2.115 0.11 1.7±0.112 2.115 0.20 1.7±0.1CONCLUSIONAn implementation of the wakefields into the computercode Merlin has been discussed and beam jitter and bunchshape distorsion has been simulated. A comparison be-tween the Merlin predictions ane the wakefield kicks mea-sured at End Station A has been presented for a numberof collimators. It was found that there is a good agree-ment between simulation and experiment and the geomet-ric wakefield dominates. Future work includes implemen-tation of different wake functions corresponding to morecomplicated collimator geometries.REFERENCES[1] Near-Wall Wakefields for Optimized Geometry of TTF 2 Col-limator, I.Zagorodnov, T. Weiland, M. Dohlus, M.Korfer,TESLA Report 2003-23.[2] A. Bungau and R.Barlow, “Simulation of High OrderShort Range Wakefields”, EPAC’06, Edinburgh, June 2006,WEPCH123, p. 2209 (2006) http://www.JACoW.org.[3] A. Bungau and R.Barlow, “Emittance Growth Due to HigherOrder Angular Multipole Mode Wakefields in the ILC BDSCollimators”, PAC’07, Albuquerque, June 2007, THPAN079,p. 3402 (2007) http://www.JACoW.org.[4] Impedances and Wakes in High-Energy Particle Accelerators,B.W.Zotter and S.A.Kheifets, World Scientific (1998).[5] Impedance of Slowly Tapered Structures, K.Yokoya, CERN,Geneva, July 1990[6] The Short-Range Resistive Wall Wakefields, K. Bane,M.Sands, SLAC-PUB-95-7074, 1995[7] Theory and Measurements of the Transverse Wake Due toBeamline Collimators, S.Molloy et al., APS/123-QED, 2008.[8] Measurement of the Transverse Wakefields Due to VaryingCollimator Characteristics, S.Molloy et al., FRPMS074MOPP007 Proceedings of EPAC08, Genoa, Italy03 Linear Colliders, Lepton Accelerators and New Acceleration Techniques564A03 Linear Colliders

and R.Barlow, “Simulation of High Order Short Range Wakefields”,

Emittance Growth Due to Higher Order Angular Multipole Mode Wakefields

Impedance of Slowly Tapered Structures,

Impedances andWakes in High-Energy Particle Accelerators, B.W.Zotter and S.A.Kheifets, World Scientific

Measurements of the Transverse Wake Due to Beamline Collimators, S.Molloy et al., APS/123-QED,

Near-WallWakefields for Optimized Geometry of

The Short-Range Resistive Wall Wakefields,

the Transverse Wakefields Due to Varying Collimator Characteristics, S.Molloy et al.,

Wakefield calculations - comparison between simulation and experimental data

Wakefield calculations - comparison between simulation and experimental data

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