FONT collaboration P Burrows, G Christian, C Clarke, C Swinson, H Dabiri Khah, G White, S Molloy

1. Tony Hartin FONT collaboration • P Burrows, G Christian, C Clarke, C Swinson, H Dabiri Khah, G White, S Molloy The International Linear Collider at the IP – from feedback hardware to electromagnetic backgrounds

2. Hardware Ground motion and the need for stablisation IP feedback and the FONT project FONT results and BPM sensitivity Simulation Modification of GEANT for low energy transport 20 mrad crossing angle with different sets of accelerator parameters Origin of BPM spray Variation with Solenoid and DiD magnetic field Theory The background generators: GUINEA-PIG and CAIN New, non-linear sources of e+e- backgrounds at the IP Outline

3. Luminosity Loss at IP due to ground motion • Relative offsets in final Quads due to fast ground motion leads to beam offsets of several y (2.7 nm for ILC 500 GeV). • Correct using beam-based feedback system near IP or by active mechanical stabilization of Quads or both.

4. TESLA TDR: principal IR beam-misalignment correction Intra-train Beam-based Feedback Intra-train beam feedback is last line of defence against relative beam misalignment Key components: Beam position monitor (BPM) Signal processor Fast driver amplifier E.M. kicker Fast FB circuit

5. Dipole and kickers (FONT1 +) FONT2: beamline configuration BPMs

6. Beam starting positions beam start beam end Beam flattener on Feedback on 4 1 2 3 Delay loop on Latency 54ns, correction factor 14/1 FONT2 results: feedback BPM (Jan 04)

7. Copper strips with 1 mm gap to wall Noise from secondary charges crossing strip-wall gap ~1pm error for each charge absorbed or emitted. 1e6 hits per b.c. would be a problem! Noise form factor sinc(π.f.T) Secondary emission down to 100 eV needs to be considered Geant3 minimum transport is 10 keV! BPM noise from backgrounds

8. BPM Geant model of 20mrad design • Background primaries are traced through from the IP • Optimal position for the BPM can be established • BPM hits vary with parameter sets, geometry and magnetic fields. 93443

9. Geant3/4 mod for Low Energy Transport • Geant3 X-section parametrization wrong below 10kev cut • Recode Geant3 to parametrize real data from NEA site

10. Geant3 total BPM hits and emitted charges • LowE mods reveal significant increase in BPM hits at 100eV cut. • Generally Factor of 5 increase in BPM compared to default Geant cut of 1 MeV, and factor of 2 increase against Geant default minimum cut • Can define Geant areas (ROIs) around BPMS which are tuned for Low Energy particles • Worst case scenario (scheme14 in the 20mrad case) ~ 105 hits per strip per bc

11. Scheme 1 500 GeV TESLA Scheme2 USSC Scheme3 Nominal Scheme4 Low Q Scheme5 Large Y Scheme6 Low P Scheme7 High Lumi Scheme 8 1 TeV TESLA Scheme9 USSC Scheme10 Nominal Scheme11 Low Q Scheme12 Large Y Scheme13 Low P Scheme14 High Lumi Background Primaries – ILC parameter Sets • High Lumi sets produce the greatest numbers of background pairs • Guinea-Pig and Cain include L-L, B-H and B-W processes • Beam field is treated linearly i.e. equivalent photon method scaled by the number density of beam field photons • BUT.. The beam fields are intense – 10% of Schwinger critical field • What about non-linear sources of background pairs?

12. B Where does BPM spray originate from? (20mrad) • X,Y view at z=3.12m • E+ and E- have different trajectories • spray originates from annulus around extraction line

13. S B Relation of E distribution of BPM spray-producing pairs to Solenoid field • Increase in leads to energy peak shifting • With stronger magnetic field, (a)higher energy pairs, and (b) pairs with lower transverse momentum will produce spray on the mask hole edge Energy(MeV)

14. The impact of a Detector Integrated Dipole(20mrad)(Seryi & Parker, Phys Rev ST Accel Beam 8, 041001 (2005) • Introduced to offset Y displacement at the IP due to solenoid field • Steers more primaries into Lumi Cal (K. Busser). Extra BPM spray sources • 30% more spray hits delivered to the BPM

15.      k nk e e b       k k nk e e Unknown: Multiphoton Breit-Wheeler 1 2 b b k k 2 b b 1 Is there another non-linear source of pairs at the IP? • Known: multiphoton pair production • rate described by Sokolov-Ternov and onset governed by beam parameter Y=E/Ec~0.3. Scheme1 has Y=0.054, Scheme14 has Y=0.376 • 2nd order process rather than 1st order • Rules for onset are different • Calculation is complicated, but simplified when the photons are co-linear e- e+

16.     2 2 2 ( q nk ) m ( 1 ) Resonances in multiphoton B-W Pairs created in intense e-m field have a quasi-level structure and resonant transitions can occur (Zeldovich, 1967) 2nd order IFQED x-section can exceed normal x-sections by orders of magnitude (Oleinik, JETP 25(4) 697, 1967) 2nd order Breit-Wheeler process in CIRCULARLY POLARISED field shows the same feature Multiphoton Breit-Wheeler Resonances Multiphoton Bremstrahlung (non-resonant) Ordinary Breit-Wheeler hepwww.ph.qmul.ac.uk/~hartin/thesis

17. k b 1 2nd order: Substantial theoretical studies but no experimental efforts yet! BUT potentially more detectable because of resonances k k 2 b b 1 Experimental evidence for the IFQED processes e- e+ • 1st order: One photon pair production • Experiment E144 SLAC. 46 GeV beam with Nd:glass laser peak intensity 0.5x1018 Wcm-2. Up to 4 photons contributed to each event • Meyerhofer et al (1996) other non-linear phenomena such as electron mass shift observed e- e+

18. The field of the relativistic charge beams • With low disruption, approximate to a constant crossed e-m field perpendicular to direction of propagation • SIMPLIFICATION: Beamsstrahlung photons k1 and k2 emitted forward. Assume they are collinear • COMPLICATION: Symmetry of the field seen by the synchrotron photons

19. Including the external field in IFQED calculations • ‘Operator Method’: quantum interaction of electron and external field photons but electron trajectory is considered classical. Due to Baier et al (JETP 28(4) p.807, 1969) • Full quantum treatment: Horrendously complex but potentially doable with Vermaseren’s FORM • ‘Semi-classical method’: Dirac equation is solved exactly for interaction with a classical plane-wave e-m field. Most common method. Used originally by Narozhnyii, Nikishov and Ritus in the mid 1960s

20. IFQED – Dirac Equation Solution • Exponential dependency on external field 4-potential • Fourier Expansion in contributions of n external field photons • Different external field polarisations lead to different “form factor” functions Circular polarisation Bessel functions n Jn(Q) Linear polarisation Generalised Bessel–type functions Constant crossed field-Azimuthally symmetric Airy functions n Ai(n Q) • Constant crossed field –Nonazimuthally symmetric New ‘AiJ’ functions n AiJn(Q)

21. Calculation of Resonance widths • The Electron Self Energy must be included in the Multiphoton Breit-Wheeler process • This is a 2nd order IFQED process in its own right. • Renormalization/Regularization reduces to that of the non-external field case • The Electron Self Energy in external CIRCULARLY POLARISED e-m field originally due to Becker & Mitter 1975 for low field intensity parameter =(ea/m)2. Has been recalculated for general  • ESE in external CONSTANT CROSSED field is due to Ritus, 1972 • Optical theorem: the imaginary part of the ESE is the same form as the Sokolov-Ternov equations

22. Where do the resonances occur? • Beamsstrahlung photon ES >> 0.511 MeV • Beam photon EB < 0.511 MeV • Processes which give/take energy to the field allowed and mass shell can be reached for physical values • For collinear beamstrahlung photons, resonance condition is r (external field photons) ~ ES/EB Resonance Peak Resonance Width

23. And the PRELIMINARY results…..? Notes on the cross-section calculation • Full trace contains ~ 100,000 terms • Dramatically simplified by • Special “centre of mass-like” reference frame • Assume beamsstrahlung photons and beam field photons are collinear • Only insert Imaginary part of self energy to get resonance width

24. Results:Stimulated Breit-Wheeler (Non-Resonant) • Compare Stimulated Breit-Wheeler process with ordinary Breit-Wheeler process • Examine the resonant and non-resonant contributions to the cross-section separately • Nonresonant Stimulated Breit-Wheeler cross-section only a few percent of the ordinary Breit-Wheeler cross-section • Can be neglected as a source of extra pairs

25. PROVISO – calculation for special reference frame. Need to generalise the case! Results:Stimulated Breit-Wheeler (Resonant) • Differential cross-section can exceed the ordinary Breit-Wheeler process • Stimulated Breit-Wheeler Cross-section up to 2 orders of magnitude greater than ordinary breit-wheeler • Transverse production of pairs seems favoured

26. Summary and Future Work • FONT project continues with digital version and experiments planned at ATF2 (KEK) • GEANT tweaking • Modified Geant 3 for low energy transport • Ran pair files through Geant 3 simulation of BDS • BPM hits are within a factor of 10 of problem levels. More detailed studies are needed. Simulation support for planned ESA tests • LowE modification's reveal an increase in hits by a factor of 2 and were important to take into account • 2nd order, nonlinear interactions of beamsstrahlung photons with the beam fields should be taken into account because the cross-sections are potentially resonant and can exceed 1st order and “linear” ordinary cross-sections – established by substantial theoretical work by several groups • Preliminary calculations of the Stimulated Breit-Wheeler process (simplified case) suggests that this will be an issue at the ILC

27. Experimental detection of Stimulated Breit-Wheeler resonances low spec laser Focussed Tabletop TeraWatt Laser Australian Synchrotron 3 GeV electrons