Compensation of Transient Beam-Loading in CLIC Main Linac

1. Compensation of Transient Beam-Loading in CLIC Main Linac Alexej Grudiev, Oleksiy Kononenko CLIC Meeting, August 27, 2010

2. Contents • Introduction • Calculation of unloaded/loaded voltage in AS • Drive beam generation scheme • Optimization of the pulse shape - using the reference pulse - direct energy spread minimization • Conclusions and further steps

3. Motivation: Energy Spread Constraints *CLIC-Note-764

4. Motivation: Energy Spread Constraints *CLIC-Note-764

5. Energy Spread Minimization Scheme • Unloaded Voltage in AS • generate drive beam profile • include PETS bunch response (with/without reflections) • calculate unloaded voltage Klystron (reference) pulse • Loaded Voltage in AS • calculate AS bunch response • calculate total beam loading voltage • - add to unloaded voltage Method 1. Minimize the difference with the reference klystron pulse Method 2. Minimize energy spread for the CLIC Pulse directly

6. Beam Loading: Steady State *Beam loading for arbitrary traveling wave accelerating structure. A. Lunin, V. Yakovlev

7. Unloaded Voltage in T24 structure Z Considering T24 CLIC main accelerator structure

8. Unloaded Voltage in AS (FD) EUz (z,f) → [ exp ( ± i *z *ω/c ) ] → [ ∫ dz ] → VU (f)

9. Unloaded Voltage in AS (TD) V(t)= ifft(V+(f))

10. Unloaded Voltage in AS for a Rectangular Pulse Vp(t)= conv( V(t) , p(t) )

11. Beam Loading: Plane Wave Approach Plane Wave Approach: - takes into account dispersion - takes some time to calculate since Fast Sweeps in HFSS are not supported for the projects which involve plane wave sources, need to use Discrete Sweep - has rather good correlation with the CST WakeField Solver E0 k Thanks for the idea to Valery Dolgashev (SLAC)

12. Beam Loading: Coupling Impedance Ez(z,f) → [ exp ( ± i *z *ω/c ) ] → [ ∫ dz ] → V(f) → [IHFSS = 2*π*r * E0 / Z0] → Z(f)

13. Beam Loading: Wake Potential Wbunch = ifft(Z+)

14. Beam Loading: Voltage Vbeam=q *∑ Wbunch(t+Tbunch)

15. Drive Beam Generation Complex *CLIC-Note-764

16. Drive Beam Combination Steps fbeam= 4 * 3 * 2* fbuncher 12 GHz 3 GHz 1 GHz 0.5 GHz

17. PETS: Single Bunch Response kindly provided by Alessandro Cappelletti, Igor Syratchev (CERN)

18. PETS: Generated Rectangular Pulse No delays, just nominal (~240ns) switch times in buncher trise ≈ 1.5 ns

19. Rectangular Pulse in Main Linac Energy Spread ≈ 6%

20. Method N1. Reference Pulse • Unloaded Voltage • Loaded Voltage • Note: unfortunately we can’t use any deterministic algorithm for the optimization. Pulse shape dependence on the delay times is significantly nonlinear so it seems like only probabilistic algorithms can be used here. • Exhaustive search is also not a good idea either, because the total number of the possible combinations is ~ 1024 • Klystron Pulse • (reference pulse) • CLIC Pulse • Minimization of the Energy Spread • in Main Beam

21. Reference Pulse Shape Arise ≈ 0.62A

22. Trapezoidal Pulse in Main Linac Energy Spread ≈ 0.17%

23. Comparison of the Ramp Types Energy Spread ≈ 0.17 % Energy Spread ≈0.15 % Energy Spread ≈0.14 %

24. Comparison of the Rise Times Energy Spread ≈ 0.60 % Energy Spread ≈ 0.17 % Energy Spread ≈0.04 % Energy Spread ≈ 0.03 % Note: efficiency ~ tB/tP , so increasing tr we decrease the efficiency. tr = 81 ns, efficiency decrease by a factor of 0.8

25. Approximating the reference pulse by the CLIC one • Brief Description: • generate ‘reference’ pulse • generate random pulses • find the minimal difference • adjust delay step • - check energy spread • Disadvantages: • need to know the reference pulse • - no guaranty it can be approximated by the CLIC pulses

26. Pulse Shape Optimization Utility

27. Optimized Pulse Shape Corresponding switch delays in buncher

28. Optimized Pulse in Main Linac Voltage Spread ≈ 0.22 % Voltage Spread ≈ 0.17 %

29. PETS: Single Bunch Response *Alessandro Cappelletti, Igor Syratchev

30. Full PETS Bunch Response Calculations The same switch delays as for the simplified bunch response in PETS

31. Full PETS Bunch Response Calculations Voltage Spread ≈ 0.25 % Voltage Spread ≈ 0.22 %

32. Method 2. Energy Spread Minimization • Unloaded Voltage • Loaded Voltage • Klystron Pulse • (reference pulse) • CLIC Pulse • Minimization of the Energy Spread • in Main Beam

33. Method 2. Energy Spread Minimization Unloaded Voltage VU(t) = conv ( pCLIC, rAS) pCLIC(t,Tswitch) rAS(t) Loaded Voltage VL(t) = VU(t) + VBEAM(t) pCLIC(t,Tswitch) NB rows

34. Energy Spread Minimization in CLIC • Brief Description: • fix injection time • generate random pulses • find the minimal energy spread • adjust delay step

35. PETS: Single Bunch Response *Alessandro Cappelletti, Igor Syratchev

36. Optimized Pulse Shape for theSimplified PETS Bunch Response Voltage Spread ≈ 0.08 % Note: factor 3 better than using the reference pulse method!

37. Optimized Pulse Shape for the Full Bunch Response in PETS Energy Spread ≈ 0.08 %

38. Possible CTF3 Experiment • Remark: number of AS in CLIC >> number of AS in TBTS, so energy spread from CALIFES seems to be too high for now to see the influence of the pulse shape optimization, however we can try not to increase the one

39. Conclusions • Beam loading model based on the plane wave approach seems to be a reasonable one • Two developed methods of the pulse shape optimization are presented. It is demonstrated that the direct method gives better results and within the acceptable level of 10-4 • Pulse shape optimization which takes into account reflections in the tail of the PETS bunch response gives the same level of the energy spread • Final value of the energy spread depends on many parameters and also on the optimization algorithm

40. Further steps • Moving to the TD26 (CLIC baseline) accelerating structure • Possible different optimization techniques usage, i.e. genetic algorithm in the case if the energy spread is not within the acceptable level • CTF3 experiment for the beam loading compensation

41. Thank You for the Attention!