1. Undulator Based ILC positron source for TeV energy Wanming Liu Wei Gai ANL April 20, 2011

2. Goal – A reasonable scheme for the 1 TeV option without major impact on the ILC configuration. Assumptions – Drive beam energy: 500 GeV – Target: 0.4 X0 Ti – Drift from end of undulator to target: 400m – OMD: QWT Approach: – Changing undulator parameters to according to the drive beam energy change. – Longer period, same field. (high K approach).

3. 3 Radiated Photo parameters from beam passing through a helical undulator:  The 1 st Harmonic critical energy is approximately inversely proportional to the square of K when K goes higher and also inversely proportional to length of undulator period. Since K is proportional to the length of undulator period, thus the 1 st harmonic critical energy is approximately inverse proportional to the cubic of the length of undulator period.  The 1 st Harmonic critical energy is proportional to the square of gamma  When drive beam increased up to 500GeV, we can increase the length of undulator period to maintain photon spectrum and thus minimize the change of design.

4. Energy deposition distribution inside target, ( u=4cm, B= 0.8565T, 500GeV drive beam energy, single bunch) For single bunch, the energy deposition has a hollow distribution as a result of high K and long period. The peak energy density is about the same of RDR undulator. It has the similar distribution as photon beam at the target. X(cm) z (cm)

5. Comparison with RDR 1 st harmonic (MeV) Num of photon per 100m Average photon energy(MeV) Photon power (kW) Energy density in target (J/cm^3) Power deposition in target(kW) YieldPol. (%) RDR ( u=1.15cm) 10.06194.610.41619356615.31.5~30 TeV candidate ( u=4cm) 5.28193.9610.532173.4600141.5~30

6. Photon number spectrum As shown in figure, for TeV operation, photon spectrum of undulator with u=3cm, has a 1 st harmonic critical energy most closed to RDR undulator with 150GeV but it has a larger portion of higher order harmonics and thus the polarization is only ~20%. For  u=4cm, its 1 st harmonic critical energy is about half of RDR with 150GeV and thus it has a larger high order harmonic portion but with a compressed energy distribution and thus a reduced contribution from high order harmonic when comparing with u=3cm.

7. Yield and Pol. for different undulator period length When the period is 4cm long, the positron source will have a yield of about 1.7 and the captured positron beam will have a polarization of about 33%

8. Photon Power and energy deposition in target per 1.5 positron yield The deposited power ~ 14kW undulator has a period of 4cm while the total photon power is about 172kW.

9. Deposited energy distribution in target, u=4cm, 500GeV drive beam energy, accumulated The accumulated energy deposition in the rotating target (900RPM, 2m diameter) is about 600J/cm^3 which is about the same of the number for RDR ( 566J/cm^3) X(cm) z (cm)

10. The suggested parameter From the above two slides, one can see that undulator with u=4cm and B field of 0.8565T will give us a positron source with yield of about 1.5 and polarization of 33% for 231m long undulator with a Ti target and QWT as OMD The above chosen parameters will also give us a similar photon beam spot size on the target as for RDR positron source. The energy deposition on target will be about 14kW which is also similar to the 15.3kW energy deposition for RDR with QWT. The peak energy density in target is about 600J/cm^3 which is about the same number for RDR (566J/cm^3) Chosen the above undulator parameter will give us a positron source for TeV operation with about the same performance of RDR positron source and thus nothing need to be changed except the undulator.

11. The impact on 500GeV drive beam from the chosen undulator parameters Code used: elegant Lattice: – Quads: Effective length 1m Strenth:0.09717 and -0.1109 alternating. Separation: 12m with space of quad excluded. – Undulator: u=4cm, B=0.8565T Sections with effective length of 11.08m between quads Initial beam parameters: –  nx =10e-6 m.rad,  ny =0.04e-6 m.rad –  x=46m,  y=9m – Energy spread: 1GeV or 0.2% – Average energy: 500GeV

12. Drive beam emittance evolution

13. Drive beam energy and energy spread

14. Summary Positron generation with higher drive beam energy (500 GeV) and longer period or larger K ( u =4cm, B=0.85 T) has been investigated. The simulation results show that the souce has similar performance as the RDR undulator with 150 GeV. We may suggest to have a positron source for TeV operation without changing the design of other part of ILC except replace the undulator. Technology is straightforward. As RDR positron source, the undulator will damp the drive beam emittance and cause the energy spread to increase. Effects on emittance growth from quad BPM misalignment will follow.