1. 2006.10.29 –11.03 Hawaii Multi bunch acceleration on LUCX system Ⅰ. LUCX project Ⅱ. Simulation results for Compton scattering Ⅲ. Calculation on beam loading and compensation Ⅴ. Results and summary Liu shengguang Masafumi Fukuda, Koichiro Hirano, Junji Urakawa

2. 2006.10.29 –11.03 Hawaii LUCX ( Laser Undulator Compact X ray source) is for generation x-ray photon by inverse Compton scattering. X-ray is for medical application ----K-edge digital subtraction angiography. In this application, 33KeV X ray photons are required. Collision angle between electron beams and the laser beams is 20 degree. The detector size is 4cm×4cm, 2m away from the collision point. Acceptance angle of the detector is 10mrad. Ⅰ. LUCX project (1)

3. 2006.10.29 –11.03 Hawaii Ⅰ. LUCX project (2)

4. 2006.10.29 –11.03 Hawaii Electron beamLaser pulse Energy43MeV1064nm (1.17eV) Intensity2nC/bunch (5nC/bunch) 1.25*10^10electron/bunch 17µJ/pulse 9.1*10^13photon/pulse Width (FWHM)10ps Bunch number100bunches/train 2.8ns spacing Beam sizeσ x =64um σ y =32um σ= 100um Repetition rate12.5Hz About 45% X ray photon number can be reserved by the detector : /bunch /train /sec Ⅰ. LUCX project (3)

5. 2006.10.29 –11.03 Hawaii Ⅱ. Simulation results for Compton scattering (1)

6. 2006.10.29 –11.03 Hawaii Because of the energy spread of electron beam, the peak position at the high energy edge decrease a little. If we want to shift the peak at 33keV, we should increase the energy of electron beam a little X-ray spectrum Ⅱ. Simulation results for Compton scattering (2)

7. 2006.10.29 –11.03 Hawaii Electron beam emittance affects the distribution structure of X-ray. But to the number of X ray on the detector, emittance is not much important. Emittance on Compton scattering Ⅱ. Simulation results for Compton scattering (3)

8. 2006.10.29 –11.03 Hawaii Comparing with the effect on the X ray number, the electron bunch length is much important than the beam emittance Bunch length on Compton scattering Ⅱ. Simulation results for Compton scattering (4)

9. 2006.10.29 –11.03 Hawaii Resonant Frequency 2856.000 MHz β 0.60 Filling Time 0.55 µs Qo 7900 R/Q 464 TTR0 1.87 MΩ Efull/Ehalf 0.77 RF Driving Frequency 2856.000 MHz RF Pulse Repetition rate 12.5 Hz Operation frequency 2856MHz Phase shift/cell 2/3π Electric-field distribution Constant gradient Structure length 3m Number of cells 84 cells + 2 coupler cells Quality factor 13,000 Shunt impedance 60M Attenuation parameter 0.57 Group velocity 0.0204–0.0065 c Filling time 0.83us Gun parameters Acc tube parameters Gun cavity and Accelerator tube Ⅲ. Calculation on beam loading and compensation(1)

10. 2006.10.29 –11.03 Hawaii Energy gain and beam loading Ⅲ. Calculation on beam loading and compensation(2)

11. 2006.10.29 –11.03 Hawaii Ⅲ. Calculation on beam loading and compensation(3)

12. 2006.10.29 –11.03 Hawaii C alculation result t0=0.916us V=4.72MeV/c Experiment result t0=0.908us V=4.65MeV/c Compensation on gun Ⅲ. Calculation on beam loading and compensation(4)

13. 2006.10.29 –11.03 Hawaii We can see that t is different, Δt is different. When a bunch inject into the structure, the RF power has been propagated in the structure for t time. And then the bunch spends Δt to catch up with the head of RF power. In fact, the catching up process is the acceleration process for the bunch. For the bunch that inject into the structure at moment t, the acceleration length is 0.0204 – 0.0065 c Energy gain calculation Ⅲ. Calculation on beam loading and compensation(5)

14. 2006.10.29 –11.03 Hawaii If the RF pulse is long and flat pulse, energy gain of electron bunch is linear to Δt, to c Δt. Energy gain Ⅲ. Calculation on beam loading and compensation(6)

15. 2006.10.29 –11.03 Hawaii In the theory of Traveling-Wave-Type RF-Pulse Compressor, Traveling wave type compressor Ⅲ. Calculation on beam loading and compensation(7)

16. 2006.10.29 –11.03 Hawaii For a slope RF pulse, of course, the propagation behavior is the same as the flat pulse. we can cut the pulse into n parts by time step dt. It is assumed that at t=0, the head of RF pulse begin to enter the structure. At time mdt (<filling time tf), a bunch enter the structure and begin acceleration. We can calculate the acceleration length dL for m parts. Average field gradient E of every part multiply its acceleration length during a dt step and sum up. The value is the energy gain for the bunch that enter the structure at time t, then normalize it. dt  dL Energy gain for slope RF pulse Ⅲ. Calculation on beam loading and compensation(8)

17. 2006.10.29 –11.03 Hawaii Traveling wave structure Ⅲ. Calculation on beam loading and compensation(9)

18. 2006.10.29 –11.03 Hawaii To a short RF pulse (width<tf), for example 500ns pulse. if the injection time of electron bunch is more than 500ns and less than 830ns, even through the whole RF pulse is in the structure, but the energy gain decrease a lot. This is another kind of attenuation of RF power in the process of propagation. Energy gain Ⅲ. Calculation on beam loading and compensation(10)

19. 2006.10.29 –11.03 Hawaii 600ns case for example Ⅲ. Calculation on beam loading and compensation(11)

20. 2006.10.29 –11.03 Hawaii calculation Ⅲ. Calculation on beam loading and compensation(12)

21. 2006.10.29 –11.03 Hawaii Good compensation results at the exit of accelerator tube are always as the plot show: Ⅲ. Calculation on beam loading and compensation(13)

22. 2006.10.29 –11.03 Hawaii Step 1 set parameter a to a suitable value (0.2<a<0.4) Step 2 solve the equation 1, then a formulas between p and t1 can be gotten— p1(t1) Step 3 solve the equation 2, then another formulas between p and t1 can be gotten---p2(t1) Step 4 solve p1(t1) and p2(t1), we can get the value p and t1 Step 5 using the value of p and t1 to check the energy at the exit of gun and Acc Step 6 to compare the calculation results for different parameter a. Ⅲ. Calculation on beam loading and compensation(14)

23. 2006.10.29 –11.03 Hawaii 600ns a=0.3, P=136.3MW, t0=0.2867us ACC: Max=43.5MeV ΔE=0.7MeV Gun: Min=3.70MeV ΔE=1.8MeV Case1 Ⅲ. Calculation on beam loading and compensation(15)

24. 2006.10.29 –11.03 Hawaii 600ns a=0.4, P=106.25MW, t0=0.286us ACC: Max=43.5MeV ΔE=0.7MeV Gun: Min=3.05MeV ΔE=1.4MeV Case2 Ⅲ. Calculation on beam loading and compensation(16)

25. 2006.10.29 –11.03 Hawaii 1000ns a=0.3, P=99.8MW, t0=0.2856us ACC: Max=43.5MeV ΔE=0.7MeV Gun: Min=3.17MeV ΔE=1.52MeV Case3 Ⅲ. Calculation on beam loading and compensation(17)

26. 2006.10.29 –11.03 Hawaii 1000ns a=0.4, P=77.5MW, t0=0.2846us ACC: Max=43.5MeV ΔE=0.7MeV Gun: Min=2.58MeV ΔE=1.18MeV Ⅲ. Calculation on beam loading and compensation(18) Case4

27. 2006.10.29 –11.03 Hawaii 500ns600ns1000ns RF power p (MW)106.2577.5 Injection time (us)0.286 0.2846 Parameter a0.4 Energy difference at ACC exit0.68MeV0.7MeV Energy difference at Gun exit1.4MeV Mini =3.05MeV 1.18MeV Mini =2.58MeV Ⅴ. Results and summary (1)Calculation the energy gain for multi electron bunches in the constant gradient structure, considering the propagation behavior of short (<filling time) slope RF pulse. Find a method to search for the RF power and injection time for the good compensation of the beam loading. (2)For high charge multi bunch acceleration as LUCX case, beam loading effect and effective compensation mostly take place in the ACC tube. For different length RF pulse cases, injection time is always at 0.28us~2.9us. (3)Two better compensation cases is showed in the follow table

28. 2006.10.29 –11.03 Hawaii End

29. 2006.10.29 –11.03 Hawaii t0ZΔzEt(Et0+Et1)/2E*dzE*dz/1.53228 0002.357194000 2.80.01736450.0173652.3215972.3571942.35430950.0408814140.02668012 5.60.034659250.0172952.3217392.3514252.34854540.0814985170.053187745 8.40.051884540.0172252.3218812.3456662.34279280.1218525980.079523715 11.20.069040660.0171562.3220222.3399192.33705170.1619449380.105688867 140.086127890.0170872.3221622.3341842.3313220.2017768120.131684034 16.80.103146530.0170192.3223022.328462.32560360.2413494890.157510043 19.60.120096860.016952.3224412.3227472.31989670.2806642330.183167719 22.40.136979170.0168822.322582.3170462.3142010.3197223010.208657883 25.20.153793740.0168152.3227182.3113562.30851670.3585249470.233981352 280.170540850.0167472.3228552.3056772.30284370.3970734150.25913894 30.80.187220780.016682.3229922.300012.2971820.4353689460.284131455 33.60.203833810.0166132.3231282.2943542.29153150.4734127750.308959704 36.40.220380230.0165462.3232642.2887092.28589230.511206130.333624488 39.20.236860310.016482.3233992.2830752.28026430.5487502360.358126606 420.253274320.0164142.3235342.2774532.27464740.5860463090.382466852 44.80.269622550.0163482.3236682.2718422.26904180.6230955610.406646018

30. 2006.10.29 –11.03 Hawaii