1. Mike Jenkins and Ian Bailey

2. Positron Requirements of a New Collider CLIC SLCILC LHeC 6.0x10 12 e + /s 3.9x10 14 e + /s 4.0x10 16 e + /s 1.1x10 14 e + /s

3. Undulator-Based Positron Source

4. Based on OPERA 3D model created by Jim Rochford Image of ILC Undulator Prototype at RAL

5. Undulator-Based Positron Source Conversion Efficiency in Target (e + /γ) 7% Transport Efficiency through Source (FC) 80% Positrons within Damping Ring Acceptance (ILC) 67% e + /e - in Damping Ring2 γ/e - in Undulator200 ELI-NPCLICILCLHeC ~10 13 2.2x10 16 7.8x10 16 8.0x10 18

6. Efficiency of Positron Production

8. Ideal Helical Undulator Spectrum

9. Simulating Undulator Photon Spectra In order to test a non ideal helical undulator photon spectrum we need to be able to generate a photon spectrum from an arbitrary magnetic field map. HUSR developed at Cockcroft Institute by David Newton FluxCalc developed at Cockcroft Institute by Duncan Scott

10. HUSR: Particle Tracking HUSR utilizes Lie maps in the tracking of particles through a magnetic field z(m) x(m) y(m)

11. HUSR: Photon Spectra HUSR calculates the synchrotron radiation produced from a particle track at a number of observation points The electric field at each observation point is calculated using the retarded potential This field is then Fourier transformed to give the frequency spectrum of the observed radiation

12. Benchmarking HUSR

14. Optimising the Photon Spectrum

16. Short Undulators λ=11.5 mmλ=14.0 mm B (T)0.86 K0.921.12 The possibility of using a number of short undulators has been investigated Number of periods is 15 rather than 155 for ILC TDR Undulator module

17. Short Undulators @ 150 GeV

18. Short Undulators @ 250 GeV

19. Summary Undulator-based positron sources could provide the positron flux required by ILC and CLIC Further optimisation of positron source is possible Using new software tools we can now optimise the undulator Possibility to design an undulator to provide the required light for an experiment

20. Acknowledgements David Newton – University of Liverpool and Cockcroft Institute Duncan Scott – ASTeC and Cockcroft Institute Sabine Riemann, Andreas Schaelicke and Andriy Ushakov - PPS-Sim Group at DESY Jim Clarke and the HeLiCal collaboration

23. Photon Requirements LCLS CLIC LHeC ILC LCLS (1 KeV)CLICILCLHeC 1.2x10 15 2.2x10 16 7.8x10 16 8.0x10 18

24. NbTi Helical Undulator B 0 (T)0.86 λ u (m)0.0115 K0.92 γ/m/e - 2.15 Images of ILC Undulator Prototype at RAL * *Equation 1.9 From Klaus Flottmann’s Thesis

25. Nb 3 Sn Helical Undulator Based on OPERA 3D model created by Jim Rochford Z B 0 (T)0.985 λ u (m)0.01 K0.92 γ/m/e - 2.48

26. ‘Realistic’ Undulator Photon Spectra Spectrume + /e - (100m Undulator) Ideal0.87 Realistic0.93 *From Paper by B.M. Kincaid 1976, Eq 25

27. Growing Period Undulators z(m) x(m) y(m)

28. Off Axis Injection into Undulators z(m) x(m) y(m) z(m) x(m) y(m)

29. Summary Investigations into growing period undulators and effect of off axis electron trajectories is on going Photon and positron polarisation studies have been carried out Paper on undulator studies currently being written Positron source thesis to be submitted in Feb 2013