1. Simulation of Positron Production and Capturing. W. Gai, W. Liu, H. Wang and K. Kim Working with SLAC & DESY

2. Start-to-end Model of the Positron Source e- Undulator Electron Gamma Shower code: EGSnrc Particle dynamic code: PARMELA Analytical + Monte carlo

3. AMD profile and PreAccelerator Filed Map AMD field:5T-0.25T in 50cm Accelerating gradient in preaccelerator: 12MV/m

4. Photon number spectrum and distribution functions The spectrum of photon generated by helical undulator is known as Photon number spectrum in terms of harmonics (1) Harmonics distribution function Energy distribution function (2) (3) (4) e- Undulator

5. Photons from Helical Undulator– polarization and radiation angle The amplitude of radiation from helical undulator in terms of harmonic can be obtained as From which the Stokes parameters are obtained as: (1) (2) (3) where   describes the linear polarization,  2 describes the linear polarization in coordinate system rotated by 45 o with respect to the original one for  1,  3 describes the circular polarization. After knowing its energy and originating harmonic, the radiation angle of photon is also determined as: An uniform distribution on azimuthal direction is assumed e- Undulator

6. Photons from helical undualtor– originating point and collimating In addition to distribution functions in previous slides: Uniform distribution along the length of undulator is assumed Temporal and transverse distribution is inherited from drive e- beam Collimating: With the originating point ( x 0, y 0, z 0 ) and direction vector (dx, dy, dz) assigned, the state of a photon after collimator is determined by its position on the collimator screen as: Where z c is the location of collimator. If r is greater than the collimator iris, the photon is then ignored and will not allowed to strike the target to produce positrons (1) e- Undulator

7. Undulator Based Positron Source e- Undulator Polarized source: For unpolarized source, the photon collimator and drift between target and undulator can be elliminated

8. Photon Spectrum and Polarization of ILC baseline undulator Results of photon number spectrum and polarization characteristic of ILC undulator are given here as examples. The parameter of ILC undulator is K=1, u=1cm and the energy of electron beam is 150GeV. Figure1. Photon Number spectrum and polarization characteristics of ILC undulator up to the 9 th harmonic. Only those have energy closed to critical energy of its corresponding harmonics have higher polarization e- Undulator

9. Positron polarization distribution after target without collimator with collimator The collimator is 2.5mm in radius and is 700m away from the end of a 100m long undulator. Photons are radiated uniformly along the undulator. For the case without collimator, the photon source is treated as a point source. Photon collimator screened out those photon with lower polarization and thus improved the positron polarization.

10. Comparison of the captured positron polarization spectrum: with/without collimator. Without collimatorWith collimator The capturing optics are the same for both with and without collimator. The collimator screened out those photons with lower polarization and thus improved the polarization of resulting positron beam. The polarization of captured positron beam is about 30% without collimator and 63% with the collimator setting used here. Better polarization but lower positron yield due to less photons were used

11. Yield contribution from different harmonics. 1 st harmonic contributed <15% to the positron yield 2 nd and 3 rd harmonic together contributed >45% Contributions from 4 th and 5 th harmonic are comparable to 1 st harmonic Positron yield is mostly contributed by high order harmonics The cutting angle of collimator is fixed at 3.85  rad e- Undulator

12. The Effect of Photon Collimator Figure 1. Figure 2. Figure 3 Yield and polarization strongly correlated to collimator configuration. For 150GeV drive beam with K=1 and lu=1cm, 60% polarization required at least 400m drift

13. Optimum yield for 150GeV undulator with u=1cm and different K Optimum yield dropping from about 1.1 down to <0.9 when K change from 1 to 0.8

14. Optimum yield for 150GeV undulator with  and different u Optimum yield decrease from ~1.1 down to ~0.4 when u increase from 1cm up to 1.6cm

15. Yield and Polarization for undulator with 250GeV drive beam Yield for polarized undulator based source using 250GeV drive e- beam with K=1.5 and B=1.76T ( u~0.91cm) is about 2.5 per 100m undulator The collimator has a fixed cut angle at 3.85  rad/  This angle is enough for 150GeV option but still a little bit bigger for 250GeV and results in a smaller polarization

16. Photon collimating Since the polarization of photon from hellical undulator has strong correlation between it’s radiation angle  and harmonics index. For undulator based positron source, a collimator with proper configuration is required in order to achieve the required polarization. For 150GeV option, the shortest drift between target and undulator is 400m where the hardedge radius of the collimator iris is about 1.5mm. For 250GeV option, since the yield is higher and thus the undulator is shorter, the drift could also become shorter. But for 250GeV drive beam energy, collimator iris will be smaller and this could makes it more difficult to align the collimator with the beam

17. Unpolarized e+ source For unpolarized e+ source, we don’t need collimator and drift of several hundreds meters. (you still get 30% polarization) Since we are using all the available photons, the e+ yield will be higher. For 150GeV drive beam, the yield is about 2.3 per 100m undulator. For 250GeV drive beam with the same undulator parameters where K=1, u=1cm, the yield is about 6.5 per 100m undulator. For K ~ 1.5 and B=1.76T, for 250GeV drive beam, the yield will be about 12 per 100m undulator

18. Yield for unpolarized source at different undulator parameters, 250GeV drive beam For yield of 1.5, the required length of undulator using K=1, lu=1cm and drive beam of 250GeV will be only 23m

19. Yield for unpolarized source at different undulator parameters, 150GeV drive beam For required yield of 1.5, using 150GeV with K=1, u=1cm, the unpolarized source required a length of about 65m 

20. Error Analysis  Sensitivity of Yield to beam jitter Yield and polarization as a function of drive beam transverse position - collimator: location 700m, iris radius 2.5mm Yield and polarization as a function of drive beam transverse position - collimator: location is 300m, iris radius= 1.155mm e- Undulator

21. Summary We studied the e+ yield in the immersed target case. Including both polarized (60%) and unoplarized cases. Many undulator and drive beam parameters investigated. Also studied the drive beam jitter and found it is not a severe problem. A lot more cases to be done.

22. Back-up

23. Summary on numerical modeling of helical undulator photon source A complete numerical model of helical undualtor photon source is established with correlations between drive beam profile, undulator length, collimator location and iris included. Using this model, we find that the majority of captured positrons are produced by photons from high order harmonics. 1 st harmonic contributed only less than 15% of the yield. By comparing the yield and polarization of resulted positron beam, we noticed that the optimum yield decreasing more quickly with undulator period u than with K. For the effect of transverse position jittering of drive electron beam, it depends on the location of collimator. The simulation results shows that for collimator with 5mm iris aperture and located at 700m, the yield change is not significant until the offset of the drive beam reaches 0.6mm. But for collimator with aperture of 2.31mm and located at 300m, the yield is decreasing immediately after the offset of drive beam transverse position is over 0.1mm and the polarization of positron beam goes below 0.6 when the offset is over 0.3mm. But in either case, transverse jittering of drive beam is not a problem as long as the collimator is not too close to the undulator

24. A possible separation optics e+ to SC Linac Momentum selection chicane with collimator Transverse emittance collimator Bunch compression chicane with collimator Longitudinal phase space rotation Linac e+ from PPA 28m To be inserted between preaccelator and SC linac. Only positrons within 15 0 RF phase capturing window will pass through. Having insertion lost

25. At exit of pre-acceleratorAt exit of momentum selection chicane At exit of bunch compressing chicane At exit of phase space rotation linacs PARMELA simulation shows after beam pass through the positron separation optics, there are still some particles staying in subsequent RF buckets. So RF deflector should be use to kick off these undesired particles.

26. Possible ways to improvement Recently, Yuri has come up with a scheme to enhance the yield by doing phase space shaping of e+ beam while doing spin rotation before inject beam into damping ring. From his results, the capture efficiency enhanced by 50%. If we combine Yuri’s scheme with the positron separation optics presented here, we can overcome the insertion lost and solve the problems associated with dumping 5GeV e+ beam in his original scheme.

27. Positron separation optics Since the energy spread e+ beam is too big at beginning it is very difficult to do separation at the beginning. We also don’t want to separate e+/e- too late because of the problems associated with dumping high energy e+/e- beam

28. Open questions Immersed or non-immersed target: Yield changes ~ 35% Magnetic field distortion and cancellation in immersed target, it is difficult to solve, but will try to work on it.

29. Multivariate Optimization Use Start-to-End Model to maximize positron yield delivered to the Damping Ring –Drive beam energy (ILC Baseline:150 GeV) –Collimator Angle (Drift Length and Collimator Radius) –Target Material and Thickness (ILC Baseline: 0.4 rl, Ti) –AMD profile ( 5T-0.25T in 50cm) –Accelerating gradient: 12MV/m in pre-accelerator 25MV/m in super conducting linac –Damping ring acceptance:  x +  y <=0.09m.rad.  E/E < 1%