1. MAP Meeting, IUCFMarch 12-13, 20071 Progress in Barrier Stacking W. Chou, J.Griffin, K.Y. Ng, D. Wildman Fermilab Presented to MAP Meeting IUCF, Indiana March 12-13, 2007

2. MAP Meeting, IUCFMarch 12-13, 20072 Content of Talk Motivation Method Simulation Experiment

3. MAP Meeting, IUCFMarch 12-13, 20073 Fermilab Accelerator Complex

4. MAP Meeting, IUCFMarch 12-13, 20074 Booster – the Bottleneck The Booster is a 30 years old machine has never been upgraded. The 400-MeV Linac can deliver 25 x 10 12 particles per Booster cycle. The 120-GeV Main Injector can accept 25 x 10 12 particles per Booster cycle. However, the 8-GeV Booster can only deliver 5 x 10 12 particles per cycle.

5. MAP Meeting, IUCFMarch 12-13, 20075 Solution — Stacking A solution is to stack two Booster bunches into one Main Injector RF bucket. This is possible because the much larger momentum acceptance of the Main Injector. (bucket width = 18.9 ns) BoosterMI Mom. Acceptance 0.13 eV-s (±11 MeV)0.70 eV-s (±58 MeV)

6. MAP Meeting, IUCFMarch 12-13, 20076 Stacking Goal Goal for Run II – To increase protons per second (pps) on the pbar target by 50% –Baseline: 5 x 10 12 every 1.467 sec –Goal: 2 x 5 x 10 12 every 2 sec Goal for NuMi – To increase pps on NuMi target by 60% –Baseline: 3 x 10 13 every 1.867 sec –Goal: 2 x 3 x 10 13 every 2.333 sec Slip stacking can raise proton intensity from 5.0 x 10 12 per batch to 7.0 x 10 12. ( K. Seiya, et al., PAC’05 ) We are going to study barrier stacking here.

7. MAP Meeting, IUCFMarch 12-13, 20077 Barrier Stacking by J. Griffin Booster batch injected off- energy so that top of batch slips 42 bkts per booster cycle. Barrier moves to left at 42 bkts per booster cycle. After 1 booster cycle, first batch passes front of barrier. 2 nd batch is injected 42 bkts from 1 st batch. Strength of barrier is determined by δ f1 = δ f2. This is the only parameter in the model. No solution if energy spread is too large.

8. MAP Meeting, IUCFMarch 12-13, 20078 For the injection of Booster batch into MI, allowable maximum energy spread is ΔE = ±4.90 MeV. Corr. integrated barrier strength VT 1 = 3.142 kV-µs. Booster bunch area: ~0.10 eV-s, bucket width: 18.9 ns. If completely debunched, ΔE = ±2.64 MeV. For the bunch filling whole bucket,. ΔE = ±4.15 MeV If a harmonic cavity is installed, booster bunch can be lengthened with ΔE reduced. E.g., bunch at V rf = 5.0 kV and a 3 rd harmonic cavity reduces ΔE to ±5.18 MeV. E.g., bunch at V rf = 4.8 kV and a 2 nd harmonic cavity reduces ΔE to ±4.56 MeV. If ΔE can’t be reduced, method still works if barrier is allowed to move faster. However, this will reduce the number of batches to be injected.

9. MAP Meeting, IUCFMarch 12-13, 20079 Simulation of Stacked Injection 1 st batch injection2 nd batch injection

10. MAP Meeting, IUCFMarch 12-13, 200710 3 rd batch injection4 th batch injection

11. MAP Meeting, IUCFMarch 12-13, 200711 6 th batch injection5 th batch injection

12. MAP Meeting, IUCFMarch 12-13, 200712 8 th batch injection7 th batch injection

13. MAP Meeting, IUCFMarch 12-13, 200713 10 th batch injection9 th batch injection

14. MAP Meeting, IUCFMarch 12-13, 200714 12 th batch injection11 th batch injection

15. MAP Meeting, IUCFMarch 12-13, 200715 After 12 th Booster cycleAfter 13 th Booster cycle Best time to re-capture

16. MAP Meeting, IUCFMarch 12-13, 200716 Hardwares Task: To build two ±8 kV wideband RF cavities. (i.e., the barrier RF) There is no low-level RF. The on-and-off of the RF voltage is handled by a high voltage solid-state fast switches made by Behlke Co. (German). These fast switches have been applied to the design of an RF chopper built at Chiba by a KEK-Fermilab team. W. Chou, et al., Design and Measurements of a Pulsed Beam Transformer as a Chopper, KEK Report 98-10 (Sep. 1998).

17. MAP Meeting, IUCFMarch 12-13, 200717 Finemet Cavity as a Chopper (installed on the linac of HIMAC in Chiba)

18. MAP Meeting, IUCFMarch 12-13, 200718 Finemet Core (a nanocrystal magnetic alloy patented by Hitachi)

19. MAP Meeting, IUCFMarch 12-13, 200719 High-Voltage Fast Switch (MOSFET Switches made by Behlke Co.)

20. MAP Meeting, IUCFMarch 12-13, 200720 The Broad-Band Barrier RF Cavity W.Chou, et al., Barrier RF System and Application in MI, PAC’05

21. MAP Meeting, IUCFMarch 12-13, 200721 Building of the Barrier RF System Switch

22. MAP Meeting, IUCFMarch 12-13, 200722 Building the Barrier RF Cavity

23. MAP Meeting, IUCFMarch 12-13, 200723 Testing a RF Cavity One barrier Two barriers per MI period

24. MAP Meeting, IUCFMarch 12-13, 200724 Barrier Stacking Experiment Normal Inj. from Booster to MI at f rf = 52,811,400 Hz. Injection is on-energy. No drift at all. Barrier is off. 2 nd batch injected 84 bkts from first batch. Mountain-view is 256 MI turns per trace.

25. MAP Meeting, IUCFMarch 12-13, 200725 Off-Energy Injection with Barrier Off  Inject at f rf = 52,812,014 Hz (614 Hz > nominal).  Booster above transition, so beam energy < nominal.  2 nd batch injected 42 bkts from the first.

26. MAP Meeting, IUCFMarch 12-13, 200726 Computation of ΔE offset (Δf rf /f rf ) B = 1.163x10 -5 Booster slip factor η B = 0.022436 Mom offset Δp/p = -η B -1 (Δf rf /f rf ) B = 5.136x10 -4 Energy offset ΔE = -4.54 MeV However, once inside MI, which is at η MI = -0.008888, beam revolves at a lower frequency than nominal:

27. MAP Meeting, IUCFMarch 12-13, 200727 clock beam 11.56 MeV 4.54 MeV Because there is no low-level RF, the barrier and the mountain-view will be at the locked RF frequency. The movement of the barrier can be accomplished by adding a delay. f rf = 52,812,014 Hz f rf = 52,811,400 Hz normal

28. MAP Meeting, IUCFMarch 12-13, 200728 Turning on Barrier on the Right Side The beam is seen reflected from barrier on the right.

29. MAP Meeting, IUCFMarch 12-13, 200729 Stationary barrierOne barrier moving Barrier trigger = Mountain view = 52,812,014 Hz Adjusting Barrier Position and Speed

30. MAP Meeting, IUCFMarch 12-13, 200730 Moving Barrier, 4 Pulses, No Bunch Rotation Mountain view = 52,812,014 Hz, f rf = 52,812,014 Hz Consecutive batch spacing 42 buckets Final beam width of 4 pulses only ~3.5 μs, half of that w/o barrier 3.5 μs (unstacked 4 batches: 6.36 μs)

31. MAP Meeting, IUCFMarch 12-13, 200731 Moving Barrier, 6 Pulses, No Bunch Rotation Mountain view = 52,812,014 Hz, f rf = 52,812,014 Hz Consecutive batch spacing 42 buckets Final beam width of 6 pulses only ~5.5 μs, half of that w/o barrier (unstacked 6 batches: 9.54 μs) 5.5 μm Some reflected beam catches up with moving barrier.

32. MAP Meeting, IUCFMarch 12-13, 200732 Mountain view = 52,812,014 Hz, f rf = 52,812,014 Hz Consecutive batch spacing 42 buckets Final beam width of 6 pulses only ~5.5 μs, half of that w/o barrier Moving Barrier, 6 Pulses, with Bunch Rotation (unstacked 6 batches: 9.54 μs) 5.5 μs Some reflected beam catches up with moving barrier.

33. MAP Meeting, IUCFMarch 12-13, 200733 Moving Barrier, 8 Pulses, No Bunch Rotation Mountain view = 52,812,014 Hz, f rf = 52,812,014 Hz Consecutive batch spacing 42 buckets (The 8 injections were lousy but no time to improve it)

34. MAP Meeting, IUCFMarch 12-13, 200734 Recapture (no bunch rotation) Mountain view = 52,812,016 Hz, f rf = 52,812,016 Hz 2nd batch 42 bkts from 1 st injection Capture V rf = 850 kV in ~45 ms

35. MAP Meeting, IUCFMarch 12-13, 200735 First Few Turns of the First Batch Mountain view = 52,812,016 Hz, f rf = 52,812,016 Hz No bunch rotation

36. MAP Meeting, IUCFMarch 12-13, 200736 First Few Turns of the First Batch Mountain view = 52,812,016 Hz, f rf = 52,812,016 Hz With bunch rotation, B:BRLVL = +8.7 Not as dramatic as expected. Capture result almost the same.

37. MAP Meeting, IUCFMarch 12-13, 200737 beam 11.59 MeV 4.55 MeV  Barrier width is fixed at T 1 = 0.3 μs, height is reduced gradually from V = 12 kV until beam leaks out.  is confined, from which beam’s energy spread ΔE can be inferred. f rf = 52,812,014 Hz clock f rf = 52,811,400 Hz normal beam Beam’s Energy Spread ΔEΔE ΔE tota l barrier V T1T1

38. MAP Meeting, IUCFMarch 12-13, 200738 With BR, 9.5 kV —> ΔE = 6.42 MeVWith BR, 9.0 kV —> ΔE = 5.77 MeV  Thus half energy spread is 5.77 MeV < ΔE ≤ 6.42 MeV  But with BR off, need 11 kV to avoid leakage, ΔE ≤ 8.14 MeV.  Thus bunch rotation works, although not dramatically.

39. MAP Meeting, IUCFMarch 12-13, 200739 It is hard to imagine ΔE > 13.15 MeV for 6-turn beam. We are told that it should be from 8 to 12 MeV. With BR, 2-turns injection 11 kV —> ΔE > 8.14 MeV With BR, 6-turns 16 kV —> ΔE > 13.15 MeV

40. MAP Meeting, IUCFMarch 12-13, 200740 Re-capture Results First 3 turnsAfter capture V rf 786 kV926 kV Full Bunch Length5.10 ns14.0 ns Half Bunch Height0.025 V0.0111 V Bunch Area (xconstant) 0.099 eV-s0.807 eV-s Height x Width0.128 V-ns0.156 V-ns  Bunch area increases 8.15-fold.  Amount of charge captured proportional to Height x Width, or 0.156/0.128/2 = 61%.

41. MAP Meeting, IUCFMarch 12-13, 200741 Recapture V rf = 850 kV, f rf = 52,811,400 Hz bunch rotation (yes or no?), 6 Booster turns  Large beam loss. Maybe ΔE is much larger and cannot penetrate the moving barrier.  Beam passes through reflecting barrier on the right; strength of that barrier is not large enough.

42. MAP Meeting, IUCFMarch 12-13, 200742  Moving barrier: 6 kV, 0.3 µs, integrated strength 1.8 kV-µs.  Barrier is not strong enough to accel. top of beam to +ve energy.  Final energy spread is large —> beam loss in recapture.  At this moving rate, barrier V can increase up to V = 8.69 kV. f rf = 52,811,400 Hz nominal f rf = 52,812,014 Hz clock 4.6 MeV 11.6 MeV 6.4 MeV 17.5 MeV beam 0.15 MeV  Then final half spread is ΔE = 15.0 MeV.  This can be further reduced by increasing V and let barrier move faster. beam

43. MAP Meeting, IUCFMarch 12-13, 200743 We have been successful in –injecting into MI off-energy, –setting a barrier moving at a prescribed rate, –stacking so far up to 8 booster batches into a width of ~ 4 batches, –re-capturing the stacked beam, although with large increase in bunch area and large beam loss. Future improvement: –Better understanding of the beam and RF maneuvering. –Improvement in bunch rotation in Booster so as to reduce ΔE, which is the source of beam loss in recapturing. –To built a low-level RF, if possible, so that barrier and mountain view can be referenced to MI nominal frequency. –Study with more intense beam and more batches. Summary