1. Bunched-Beam Phase Rotation for a Neutrino Factory David Neuffer, Andreas Van Ginneken, Daniel Elvira Fermilab

2. 2 Outline  Study I – II -Factory – feasible but too expensive  Remove Induction Linac  Replace with High-Frequency Buncher and phase-energy rotation:  Capture beam in high-frequency buckets  Reduce energy spread with high-frequency  E rotation  Inject into fixed-frequency cooling  Simulation and Optimization  Simucool – adds transverse motion + some optimization  DPGeant – fully realistic simulation; match into realistic cooling  Discussion  Cost estimates ???  Future development

3. 3 Study 2 Costs ….  “Cost” reduced by ~25% from Study I

4. 4 Induction Linac Technology Study II scenario uses ~ 250m long induction linac to capture muons. Cost is prohibitive Technology is difficult

5. 5 System Overview  Drift (100m) – decay and drift  Buncher (60m) 300  187MHz, V  4.8 (z/L) 2 MV  Trap beam into string of ~200 MHz bunches  E Rotator(8.4m) 187MHz, V = 10 MV/m  rotate string of bunches to ~ equal energies  Cooler (100m) 183MHz – ionization cooling

6. 6 Longitudinal Motion Through System Drift Bunch  E rotate Cool

7. 7 SIMUCOOL Beam at end of buncher

8. 8 Simucool-optimized buncher and fixed frequency  E rotation  Obtains ~0.28  /p at end of buncher

9. 9 Simucool optimizations (AvG)  Large statistics tracking code ( SIMUCOOL ) can be used to reoptimize Buncher +  E Rotation  Reoptimize baseline adiabatic buncher and fixed frequency  E rotation (track rms bunches in each band)  – Obtains ~0.3  /p (up from 0.25)  Change fixed-frequency to “vernier”; sets phase to N-1/2 wavelengths from first to last ref. bunch; maximizes  E rotation - obtains ~0.35  /p  Retrack with ICOOL – similar results are obtained

10. 10 “Vernier”-optimized  E rotation  Obtains ~0.34  /p at end of buncher

11. 11 Latest Optimizations  A van Ginneken has completed a new set of optimizations; changes some parameters  Drift – reduced to ~76m  Buncher parameters changed:  Reference energies: 64 MeV; 186MeV  20 bunches between reference energies 384  233 MHz  Linear ramp in voltage 0 to 6.5MV/m  Still 60m long  Rotator changed  “vernier” frequency (20 +  ) wavelengths between reference bunches (234  220 MHz), 10MV/m  Optimize on longitudinal bunch densities  Best case has   0.16  Longer Rotator (~30m)

12. 12 System Components (new version)  Drift (80m)  Buncher (60m) 380  230 MHz, V  6.5 (z/L) MV/m  E Rotator(30m) 230  220 MHz, V = 10 MV/m  Cooler (100m) ~220 MHz

13. 13 Bunching and  Rotation Beam after drift plus adiabatic buncher – Beam is formed into string of ~ 200MHz bunches Beam after ~200MHz rf rotation; Beam is formed into string of equal-energy bunches; matched to cooling rf acceptance

14. 14 DPGeant simulations (D. Elvira)  Fully “realistic” transverse and longitudinal fields  Magnetic fields formed by current coils  Rf fields from pillbox cavities (within solenoidal coils  Studied varying number of different rf cavities in Buncher  (60 (1/m) to 20 to 10) … 20 was “better”, 10 only a bit worse  Simulations of  -E rotation  Will extend simulations + optimization through cooling channel

15. 15 Beam at end of drift

16. 16 Beam at end of Buncher 64.9 % of the particles survive at the end of the buncher

17. 17 DP Geant results – rf rotation  First rf rotation with DPGeant

18. 18 Hardware For Adiabatic Buncher  Transverse focussing ( currently)  B=1.25T solenoidal focusing  R=0.30m transport for beam Rf requirements:  Buncher: ~300  ~200 MHz; 0.1  4.8MV/m (60m) (initially 1 cavity every 1m; reduces frequency in 2-4MHZ steps; 1-D and other early simulations indicate ~10 frequencies are sufficient (~10MHz intervals)  Rotator: 230  220 MHz; 10MV/m (~10m)

19. 19 RF requirements for High-frequency buncher and phase rotation Rf frequencyVoltage (Quadratic to Linear ramp) 300 MHz0.075 - 1 MV - 6m 290 MHz0.675 - 4 MV - 6m 280 MHz1.875 - 7 MV - 6m 270 MHz3.675 - 10 MV - 6m 260 MHz6.08 - 13 MV - 6m 250 MHz9.08 - 16 MV - 6m 240 MHz12.7 - 19 MV - 6m 230 MHz16.9 - 22 MV - 6m 220 MHz21.7 - 25 MV - 6m 210 MHz Buncher: 28 MV - 6m ( Total rf voltage: 101 to 145 MV) 200 MHz100 MV (10m) - Rotator

20. 20 Rf Cost Estimate (Moretti) FrequencyCavity lengthCavity CostRf PowerTotal 300MHz0.5 m225 k$ 450k$ 2901450350800 28029007001600 270290010001900 260290010001900 250290010001900 240290010001900 2303120015002700 2204140015002900 2105180020003800 20010380042008000 33.5m133751447527850k$

21. 21 Transport requirements  Baseline example has 1.25 T solenoid for entire transport (drift + buncher + rf rotation) (~170m)  Uncooled  -beam requires 30cm radius transport (100m drift with 30cm IR – 1.25T)  In simulations, solenoid coils are wrapped outside rf cavities.  (~70m 1.25T magnet with 65cm IR)  FODO (quad) transport could also be used …

22. 22 Cost of Solenoid (PDG handbook)  Stored Energy:  Cost:  Combine 2 solenoids: 3.5 + 7.9 = 11.4 M$  Multiply by ~2  ~20 M$ ?  (D. Summers can do Al solenoids for ~10 M$)

23. 23 Cost of magnets (M. Green)  100m drift: 11.9 M$ (based on study 2)  Buncher and phase rotation: 26 M$ (study 2)  Cryosystem: 1.5M$; Power supplies 0.5M$  Total Magnet System : 40M$

24. 24 $$ Cost Savings ??  High Frequency  -  E Rotation replaces Study 2:  Decay length (20m, 5M$)  Induction Linacs + minicool (350m, 320M$)  Buncher (50m, 70M$)  Replaces with:  Drift (100m)  Buncher (60m)  Rf Rotator (10m)  Rf cost =30M$; magnet cost =40M$ Conv. Fac. 10M$ Misc. 10M$ ……  Back of the envelope: (400M$  ?? 100M$ )

25. 25 Summary  High-frequency Buncher and  E Rotation simpler and cheaper than induction linac system  Performance probably not as good as study 2, But  System will capture both signs (  +,  - )  To do:  Complete simulations with match into cooling channel!  Optimizations  Scenario reoptimization

26. 26 Energy projection