Photon production at the interaction point of the ILC
aa r X i v : . [ phy s i c s . acc - ph ] M a r LAL/RT 08-01EUROTeV-Report-2007-014
February 2008
Photon production at the interaction pointof the ILC
R. Appleby
The Cockcroft Institute and the University of Manchester,Oxford Road, Manchester, M13 9PL, UK , P. Bambade
LAL, Univ Paris-Sud, CNRS/IN2P3, Orsay, France
Abstract
The intense beam-beam effect at the interaction point of the International Lin-ear Collider (ILC) causes large disruption of the beams and the production ofphotons. These photons, arising dominantly through beamstrahlung emission, areproblematic for the machine design as they need to be transported and dumpedin a controlled way. In this work, we perform simulations of the beam-beam inter-action to predict photon production rates and distributions for the different beamparameters considered at ILC. The results are expressed in terms of a set of conesof excluded power, allowing to define the beam-stay-clear requirements relevantfor different cases and contexts. A comparison is also made with theoretical expec-tations. The suggested photon cone half-opening angles are 0.75 and 0.85 mradin the horizontal and vertical planes, respectively. These cones cover all machineenergies and parameter sets, and include the low power Compton photons. Introduction
The International Linear Collider (ILC) [1] is an electron-positron collider with a centre-of-mass energy up to 1 TeV and a luminosity goal of 10 cm − s − . The achievement ofthis goal is challenging, and requires nanometre-sized colliding beams at the interactionpoint, achieved through emittance reductions in dedicated damping rings and strongfocusing before the interaction point. This, combined with the high bunch charge leadsto intense electromagnetic interactions when the beams collide, causing particles of eachbunch to be deflected by the space charge of the other. Such deflections strongly en-hance the angular divergence of the outgoing beams and significantly dilute their energydistributions, through radiation of so-called beamstrahlung photons. Re-interactionsinvolving these photons also produce additional secondary charged particles.The production of beamstrahlung, whilst exploitable as a diagnostic, is generallytroublesome to the design of the interaction region and subsequent extraction line. Thephotons are produced in the direction of the outgoing beam, with considerable power (inthe order of MWs), in a cone of some opening angle in the forward direction (typicallyup to a mrad), and must be dumped in a controlled way. They may irradiate parts of themachine, potentially quench superconducting magnets and produce backgrounds in theinteraction region detectors, through backscattering. Hence a detailed knowledge andcharacterisation of the beamstrahlung production is critical to successful linear colliderdesign.A further contribution to the photon spectrum arises from the so-called Comptonphotons. These correspond to quantum interactions between electrons and positrons ofthe colliding beams, where the accompanying photon radiation has high energy. Thedominant contribution is from the radiative Bhabha process, in the particular kinematicdomain involving the exchange of a virtual photon only slightly off mass-shell. Thehard part of this process can be described as Compton scattering of a beam particle onthis quasi-real photon, and mostly factorises from the part corresponding to its emissionoff the electron or positron on the other side. The total power corresponding to theseadditional photons is however only a few tens of Watts and they are radiated with anglescomparable to those of the beamstrahlung photons.In this report, comprehensive calculations of the beamstrahlung and Compton photonproduction for the newest ILC beam parameter sets are presented. The resulting photonangular distributions are obtained and a set of cone half-opening angles to representsuccessive total beamstrahlung powers are presented for each ILC parameter set. InSection 2 the computational methods and the ILC parameter sets under considerationare discussed. In Section 3 approximate analytical expectations of the photon cones arecalculated. They are compared to computational results in Section 4. Conclusions arepresented in Section 5, including the practical beam stay-clear requirements in terms ofcone half-opening angles. 2 ILC parameter space and computational methods
In this section, the current ILC beam parameter sets, the key parameters relevant tobeamstrahlung production and the method used to simulate the beamstrahlung andCompton photons are described.The latest ILC beam parameter sets [2] are similar to the previous working spacefor the 500 GeV machine whilst reducing the magnitude of the beam-beam interactionfor the 1 TeV case, resulting in smaller mean particle energy losses to beamstrahlungphotons, δ B , at that energy.The parameters for the new working space relevant to this work are shown in Table 1,where E, N b , N, L , P and σ x,y,z are the centre-of-mass energy, the number of bunchesper train, the number of particles per bunch, the luminosity, the total power containedin the beamstrahlung photons and the r.m.s bunch sizes in the horizontal, vertical andlongitudinal dimensions, respectively.Table 1: Key parameters of the new beam parameter sets used in this work, at 500 GeVand 1 TeV in the centre-of-mass.
Set Energy N b N [10 ] δ B L [m − s − ] P [MW] σ x , y , z [nm,nm,mm]Nominal 500 GeV 2625 2.05 0.024 2.06E38 0.258 639, 5.7, 0.3Low Q 500 GeV 5120 1.05 0.017 2.00E38 0.184 474, 3.5, 0.2Large Y 500 GeV 2625 2.05 0.027 2.03E38 0.287 474, 9.9, 0.5Low Power 500 GeV 1320 2.05 0.055 1.99E38 0.299 474, 3.8, 0.2High Lum. 500 GeV 2625 2.05 0.067 4.57E38 0.726 474, 3.5, 0.15Nominal 1 TeV 2625 2.05 0.052 2.77E38 0.897 554, 3.5, 0.3Low Q 1 TeV 5120 1.05 0.042 2.79E38 0.728 378, 2.5, 0.2Large Y 1 TeV 2625 2.05 0.063 2.08E38 1.080 367, 7.0, 0.6Low Power 1 TeV 1640 2.05 0.094 2.80E38 1.010 452, 2.7, 0.2High Lum. 1 TeV 2625 2.05 0.094 4.89E38 1.620 452, 2.5, 0.2The calculation of the beamstrahlung is performed using the beam-beam simulatorGUINEA-PIG [3]. This code models the interaction of two colliding flat Gaussian beamsin a consistent way, by calculating particle trajectories from Lorentz’s force law and re-computing the relevant electromagnetic fields as the bunches traverse eachother. Beam-strahlung emission and secondary particles produced during beam collisions, e.g. Comp-ton photons, can also be generated. The simulated data used in this work are availableat [4].Resulting photon distributions are presented in terms of cones with half-opening anglescorresponding to a given amount of total excluded photon power. This definition [5] isattractive because it can be directly related to the beam stay-clear requirements ofthe beamline, for each case in consideration of its specific tolerance (e.g. for quench3imits or irradiation). It is moreover less sensitive to statistical fluctuation and hencecan describe more correctly the impact of the far tails of the photon distribution. Analternative definition, expressed in terms of a maximum production angle and which isoften used in the ILC community, can be recovered by tending the excluded power tozero.In the case of primary beamstrahlung photon production, the maximum size of thehorizontal cone opening angle occurs for zero-offset bunch collisions. However the elec-tromagnetic field distribution in the vertical plane results in a maximum vertical coneopening angle at some vertical offset between the beams at the interaction point, suchthat the beamstrahlung parameter δ B is maximised. In the vertical plane, cone half-opening angles were therefore computed after performing vertical scans to determinethis (parameter-set dependent) worst-case offset [5]. In the case of Compton photonproduction, the rate of Compton electrons is on the other hand essentially proportionalto the instantaneous luminosity and so the flux of Compton photons falls rapidly withbeam offsets in both planes. Hence the worst-case for Compton photon production inboth planes is for zero beam offset at the collision point. The beamstrahlung photon angles produced by the beam-beam simulation can be com-pared to theoretical expectations. The rigid-beam model of two colliding bunches devel-oped in [6] makes the assumption of a Gaussian beam charge distribution for the threecoordinates (x, y, z): ρ ( x, y, x ) = N e (2 π ) / σ x σ y σ z exp (cid:18) − x σ x − y σ y − s σ z (cid:19) , (1)where e is the electron charge, which remains unchanged as the relativistic bunchescollide. In this model, the pinch effect is hence neglected, an approximation which is notjustified in the vertical plane at the ILC. The equations are valid for arbitrary transversebeam sizes, and in general σ x = σ y . The calculation of the beam-beam kicks proceeds bycomputation of the fields of the bunch, followed by calculation of the motion of particlesin the other bunch using the Lorentz’s force law.Individual beam-beam kicks arise from the interaction of single beam particles withthe opposite bunch’s field. For a beam particle located at position ( x, y ), the followingexpression can be used [6]:∆ x ′ − ı ∆ y ′ = 2 N r e γ ı √ π q σ x − σ y ) (w x + ıy q σ x − σ y ) − exp (cid:18) − x σ x − y σ y (cid:19) w x/R + ıyR q σ x − σ y ) ) , (2)4here r e is the classical electron radius and R = σ x /σ y . The complex error function isdenoted by w( z ) and is defined as:w( z ) = exp( − z )Erfc( ız ) , (3)where Erfc( z ) denotes the complementary error function, defined by Erfc( z ) = 1 − Erf( z ).The overall kick of the entire bunch in the field of the other bunch is simply theaverage of the individual kicks of its particles. This kick is described in terms of theoverall bunch offsets in the horizontal and vertical directions and is also zero for perfectlyaligned bunches. The expression which is obtained is the same as for the individual kick,with the substitutions ( x, y ) → ( X, Y ), where X and Y denote the horizontal and verticalbunch offsets, and 2 σ x,y → σ x,y :∆ x ′ − ı ∆ y ′ = 2 N r e γ ı √ π q σ x − σ y ) (w X + ıY q σ x − σ y ) − exp (cid:18) − X σ x − Y σ y (cid:19) w X/R + ıY R q σ x − σ y ) ) . (4)Because of the averaging, the maximum individual kick always exceeds the overallone. Since the radiated beamstrahlung photons are strongly peaked in the forwarddirection of the emitting particle, the maximum prodution angle for photons equals thatfor individual particles after adding the natural beam divergence of the incoming beamsprior to colliding, σ ′ x = p ǫ x /β ∗ x .Numerical results for the individual kicks are shown in Table 2 for the beam parametersets with the largest beam-beam effects. The individual and overall kicks are also shownas a function of horizontal beam offsets in Figures 1 and 2 for the Low Power beamparameter set at 1 TeV.Table 2: Photon production angles for the new ILC beam parameter sets [2]. E CM Parameter set σ x [nm] σ ′ x [mrad] Kick maximum [mrad] 3 σ ′ x +kick500 Nominal 639 0.032 0.280 0.376500 Large Y 474 0.043 0.379 0.508500 Low Power 474 0.043 0.378 0.508500 High Lumi 474 0.043 0.378 0.5081 TeV Nominal 554 0.018 0.324 0.3791 TeV Large Y 367 0.033 0.489 0.5891 TeV Low Power 452 0.023 0.397 0.4651 TeV High Lumi 452 0.023 0.397 0.4655 · -6 -2 · -6 · -6 · -6 x @ m D -0.0004-0.00020.00020.0004 ∆ x ¢ @ rad D Figure 1:
The individual particle kick for the 1 TeV Low Power beam parameter set. -4 · -6 -2 · -6 · -6 · -6 x @ m D -0.0002-0.00010.00010.0002 ∆ x ¢ @ rad D Figure 2:
The overall bunch kick for the 1 TeV Low Power beam parameter set.
Cones of excluded photon power calculated using GUINEA-PIG are presented in thissection. For the horizontal plane, zero-offset colliding beams are used, while for thevertical plane, the offset maximising the beamstrahlung power is determined by scan-ning. The natural beam divergences of the incoming beams prior to colliding are takeninto account automatically by this calculation, however the effect is minor since thecorresponding standard deviations are much smaller than individual deflection anglesand since they enter in quadrature in the excluded power computations. Figure 3 showsthe distributions obtained for the five beam parameter sets at 500 GeV in the centre-of-mass. The variation with beam parameters can be clearly seen, and sets with largeenergy losses to beamstrahlung and/or large pinch effects show the largest photon coneopening angles. The 1 TeV machine horizontal and vertical distributions are shown inFigure 4. 6
10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ] x’ [mrad]Horizontal cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi 10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ] y’ [mrad]Vertical cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi Figure 3:
The primary beamstrahlung photon distribution for the 500 GeV machine inthe horizontal plane (left) and the vertical plane (right).
10 100 1000 10000 100000 1e+06 1e+07 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ] x’ [mrad]Horizontal cone distribution at 1 TeVNominalLow QLarge YLow PowerHigh Lumi 10 100 1000 10000 100000 1e+06 1e+07 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ] y’ [mrad]Vertical cone distribution at 1 TeVNominalLow QLarge YLow PowerHigh Lumi Figure 4:
The primary beamstrahlung photon distribution for the 1 TeV machine in thehorizontal plane (left) and the vertical plane (right).
Tables 3 and 4 give the numerical values of the cone half-opening angles for the 500GeV and 1 TeV machines, respectively, for the beam parameters in Figures 3 and 4and corresponding to three successive criteria on excluded power, at 100, 10 and 1 W.Maximum values over the different beam parameters and centre-of-mass energies aresummarised in Table 5.Clearly, specifying a given amount of excluded power is context-dependent, and some-what arbitrary. The 100, 10 and 1 W criteria are suggested here as they correspondto typical order-of-magnitude tolerances for either activation of beam-line components(100 W) or quenching in super-conductive magnets (1-10 W) [7]. However, in principleany criterion thought to be relevant for a particular application can be specified fromthe curves in Figures 3 and 4. For completeness, cone half-opening angles for 1, 10 and100 kW criteria are also given in Table 6.Comparisons to the theoretical calculations presented in Section 3 can now be made.7able 3:
Horizontal and vertical beamstrahlung cone half-opening angles at 500 GeV forthe different parameter sets, and with 100 W, 10 W and 1 W definitions for thephoton cone.
Set Plane 100 W 10 W 1 WNominal [mrad] X 0.35 0.37 0.39Low Q [mrad] X 0.28 0.30 0.34Large Y [mrad] X 0.74 0.86 0.88Low Power [mrad] X 0.50 0.58 0.70High Luminosity [mrad] X 0.54 0.64 0.66Nominal [mrad] Y 0.47 0.52 0.55Low Q [mrad] Y 0.31 0.34 0.35Large Y [mrad] Y 0.54 0.58 0.60Low Power [mrad] Y 0.70 0.80 0.88High Luminosity [mrad] Y 0.82 0.99 1.09Table 4:
Horizontal and vertical beamstrahlung cone half-opening angles at 1 TeV for thedifferent parameter sets, and with 100 W, 10 W and 1 W definitions for thephoton cone.
Set Plane 100 W 10 W 1 WNominal [mrad] X 0.21 0.25 0.27Low Q [mrad] X 0.18 0.21 0.22Large Y [mrad] X 0.56 0.65 0.67Low Power [mrad] X 0.31 0.37 0.44High Luminosity [mrad] X 0.32 0.40 0.47Nominal [mrad] Y 0.33 0.38 0.43Low Q [mrad] Y 0.26 0.32 0.38Large Y [mrad] Y 0.44 0.53 0.59Low Power [mrad] Y 0.47 0.57 0.63High Luminosity [mrad] Y 0.50 0.63 0.72Table 5:
Horizontal and vertical maximum beamstrahlung cone half-opening angles, cov-ering all parameter sets and both energies, for 1, 10 and 100 W of excludedpower.
Plane 100 W 10 W 1 WHorizontal [mrad] 0.74 0.86 0.88Vertical [mrad] 0.82 0.99 1.098able 6:
Horizontal and vertical maximum beamstrahlung cone half-opening angles, cov-ering all parameter sets and both energies, for 1, 10 and 100 kW of excludedpower.
Plane 1 kW 10 kW 100 kWHorizontal [mrad] 0.64 0.49 0.30Vertical [mrad] 0.70 0.58 0.47Since they use the rigid beam model, these calculations are only valid in the horizontalplane and for cases with small disruption.Comparing Tables 3 and 4 indicates that the calculations predict the maximum hor-izontal angle of photon emissions reasonably well only for some of the parameter sets.For example, the 500 GeV Nominal theoretical maximum angle is 0.376 mrad, whichagrees well with the 0.35-0.39 mrad range computed from the beam-beam simulation forthe 100 - 1 W criteria. This is however not the case for the Large Y and High Luminositysets, where some differences are seen. Such differences are attributed to extreme collid-ing particle trajectories in GUINEA-PIG. These may originate from the input angulardistribution of the beams and may also result from some disruption occuring for theseparameter sets. In all cases, the GUINEA-PIG calculation gives larger values and shouldbe used for conservative results.Similar distributions for the Compton photons are presented in Figures 5 and 6, in thehorizontal and vertical planes and for the five parameter sets. While extending to similarangles as for beamstrahlung photons, the corresponding power is orders of magnitudeless. The maximum cone half-opening angles previously computed from beamstrahlungare hence not modified. P o w e r [ W ] x’ [mrad]Horizontal cone distribution at 500 GeV (Compton)NominalLow QLarge YLow PowerHigh Lumi 0.1 1 10 100 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ] y’ [mrad]Vertical cone distribution at 500 GeV (Compton)NominalLow QLarge YLow PowerHigh Lumi Figure 5:
Compton photon distribution for the 500 GeV machine in the horizontal (left)and vertical (right) planes. P o w e r [ W ] x’ [mrad]Horizontal cone distribution at 1 TeV (Compton)NominalLow QLarge YLow PowerHigh Lumi 0.1 1 10 100 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ] y’ [mrad]Vertical cone distribution at 1 TeV (Compton)NominalLow QLarge YLow PowerHigh Lumi Figure 6:
Compton photon distribution for the 1 TeV machine in the horizontal (left)and vertical (right) planes.
In this paper, the angles of photons emitted through the beam-beam interaction atthe International Linear Collider have been computed using both the rigid beam modeland the beam-beam simulator GUINEA-PIG. These calculations, and the subsequentunderstanding of the beamstrahlung, are crucial to the effective design of the interactionregion and extraction line.The rigid beam theoretical predictions tend to underestimate the photon cone openingangles for some of the beam parameter sets, particularly for cases with large disruption.GUINEA-PIG is hence used for conservative results.Cones of excluded photon power are defined corresponding to tolerances relevant todifferent aspects of beam-line design: 100 W for general activation and 10 - 1 W for super-conductive magnet quenching. Two contributions were studied, from beamstrahlungemission and from a Compton process involving the exchange of a slightly virtual photonbetween the incident electrons and positrons. By far the first contribution dominatesfor most of the angles. The results are summarised in Table 5.For the general design of the extraction line, the 100 W definition is applicable. In thiscase, half-opening angles of 0.75 and 0.85 mrad can be used as conservative definitionsof the required beam-stay-clear in the horizontal and vertical planes, respectively.
Acknowledgement
We would like to thank Daniel Schulte, Olivier Napoly, Olivier Dadoun, Mark Briscombe,Daniel Smallqy and C´ecile Rimbault for helpful advice and assistance, and special thanksto Deepa Angal-Kalinin for checking the manuscript and useful advice. This work wassupported by the Commission of the European Communities under the 6th Frame-work Programme ”Structuring the European Research Area”, contract number RIDS-011899, and by the Alliance programme of the British Council and Minist`ere des Affaires´Etrang`eres. 10 eferences
10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]]
10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]] x’ [mrad]Horizontal cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]]
10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]] x’ [mrad]Horizontal cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]] y’ [mrad]Vertical cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi10 100 1000 10000 100000 1e+06 1e+07 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]]
10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]] x’ [mrad]Horizontal cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi10 100 1000 10000 100000 1e+06 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]] y’ [mrad]Vertical cone distribution at 500 GeVNominalLow QLarge YLow PowerHigh Lumi10 100 1000 10000 100000 1e+06 1e+07 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]] x’ [mrad]Horizontal cone distribution at 1 TeVNominalLow QLarge YLow PowerHigh Lumi10 100 1000 10000 100000 1e+06 1e+07 0 0.2 0.4 0.6 0.8 1 P o w e r [ W ]]