1. Bunched-Beam Phase Rotation David Neuffer Fermilab

2. 2 Outline  Introduction  “High-frequency” Buncher and  Rotation  Concept  1-D, 3-D simulations  Continuing Studies …  Variations  Matching, Optimization  Study 3  Match to Palmer cooling section  Obtains up to ~0.27  /p  Variations (shorter, …)  cost performance optimum

3. 3 Adiabatic buncher + Vernier  Rotation  Drift (90m)   decay; beam develops  correlation  Buncher (60m) (~333  200MHz)  Forms beam into string of bunches  Rotation (~10m) (~200MHz)  Lines bunches into equal energies  Cooler (~100m long) (~200 MHz)  fixed frequency transverse cooling system Replaces Induction Linacs with medium- frequency rf (~200MHz) !

4. 4 Longitudinal Motion (1-D simulations) DriftBunch  E rotate Cool System would capture both signs (  +,  - ) !!

5. 5 Adiabatic Buncher overview  Want rf phase to be zero for reference energies as beam travels down buncher  Spacing must be N rf  rf increases (rf frequency decreases)  Match to rf = ~1.5m at end:  Gradually increase rf gradient (linear or quadratic ramp): Example: rf : 0.90  1.5m

6. 6 Adiabatic Buncher overview  Adiabatic buncher  Set T 0,  :  125 MeV/c, 0.01  In buncher:  Match to rf =1.5m at end:  zero-phase with 1/  at integer intervals of  :  Adiabatically increase rf gradient: rf : 0.90  1.5m

7. 7  Rotation  At end of buncher, change rf to decelerate high-energy bunches, accelerate low energy bunches  With central reference particle at zero phase, set rf a bit less than bunch spacing (increase rf frequency)  Places low/high energy bunches at accelerating/decelerating phases  Can use fixed frequency (requires fast rotation) or  Change frequency along channel to maintain phasing “Vernier” rotation –A. Van Ginneken

8. 8 “Vernier”  Rotation  At end of buncher, choose:  Fixed-energy particle T 0  Second reference bunch T N  Vernier offset   Example:  T 0 = 125 MeV  Choose N= 10,  =0.1 –T 10 starts at 77.28 MeV  Along rotator, keep reference particles at (N +  ) rf spacing  10 = 36° at  =0.1  Bunch centroids change:  Use E rf = 10MV/m; L Rt =8.74m  High gradient not needed …  Bunches rotate to ~equal energies. rf : 1.485  1.517m in rotation; rf =  ct/10 at end ( rf  1.532m) Nonlinearities cancel: T(1/  ) ; Sin(  )

9. 9 First ICOOL Simulations  ICOOL Simulations  Include Transverse motion + realistic initial distributions  Initial beam – Study II target production  Transverse focusing -  20 T (Target)  1.25T solenoid  1.25 T focusing throughout (  x = 10cm)  Buncher +  E rotation  Use parameters approximating 1-D simulation;  Initial transport into Study 2 Cooling channel  Accepts only  T =0.12 rms; ~40% loss by scraping  Up to ~0.2  obtained  Better with matched cooling ?  T =0.20 rms;

10. 10 ICOOL simulation –Buncher, , Cool

11. 11 Key Parameters  General  Muon capture momentum (200MeV/c?) 280MeV/c?  Baseline rf frequency (200MHz)  Drift  Length L D  Buncher – Length (L B )  Gradient, ramp V B (linear OK)  Final Rf frequency (L D + L B )  (1/  ) = RF  Phase Rotator- Length (L  R )  Vernier, offset : N  R,  V  Rf gradient V  R  Match into cooling channel, Accelerator

12. 12 Implementation in ICOOL  Define 2 reference particles: P 1, P 2  ACCEL option 10  N –wavelengths between ref particles  V(z) = A +Bz +Cz 2  Long. Mode  Phase model 0 or 1 –0 at t 1 (partREFP model 3 or 4icle 1) –1 at (t 1 + t 2 )/2  3 –constant velocity  4 –energy loss + reference energy gain in cavities SREGION ! RF 0.50 1 1e-2 1 0. 0.30 ACCEL 10. 0. 0. 0. 5.05 1. 30. 15 0 0 0. 0. 0. 0. 0 VAC NONE 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

13. 13 New Cooling Channel  Need initial cooling channel  (Cool  T from 0.02m to 0.01m)  Longitudinal cooling ?  Examples  Solenoidal precooler (Palmer)  “Quad-channel” precooler  3-D precooler  Match into precooler  First try was unmatched  Transverse match –B=Const.  B sinusoidal –Gallardo, Fernow & Palmer

14. 14 Palmer Dec. 2003 scenario  Drift –110.7m  Bunch -51m  (1/  ) =0.0079  -E Rotate – 52m  P 1 = 280, P 2 = 154  V = 18.032  Match and cool (100m)  P 0 = 214 MeV/c  0.75 m cells, 0.02m LiH

15. 15 Simulation results  (Palmer, Gallardo, Fernow,…  0.25  /p in 30  mm acceptance

16. 16 How many rf frequencies?  Example has new frequency every rf cavity  Elvira and Keuss explored how many different rf cavities were needed, using Geant4  60 initially  20 OK  10 also OK, but slightly worse performance  Need to go through this exercise for present scenario Only 20 frequencies and voltages. (20 equidistant linacs made of 3 cells)

17. 17 Shorter bunch train (for Ring Cooler ?)  Ring Cooler requires shorter bunch train for single-turn injection – ~30m?  200MHz example  –reduce drift to 20m (from 90)  -reduce buncher to 20m  Rotator is ~12m  ~85% within <~30m  Total rf voltage required is about the same (~200MV)  RFOFO cooler wants 12m bunch train !!! “Long” Bunch “Short” Bunch  2 scale

18. 18 “Latest” short buncher  Drift – 20m  Bunch – 20m  Vrf = 0 to 15 MV/m (  2/3 )  P 1 at 205.037, P 2 = 130.94  N = 5.0  Rotate – 20 m  N = 5.05  Vrf = 15 MV/m (  2/3 )  Palmer Cooler up to 100m 60m 40m 95m

19. 19 Simulation results  ICOOL results  0.12  /p within 0.3  cm acceptance  Bunch train ~12 bunches long (16m)  (but not 8 bunches …)

20. 20 FFAG-influenced variation – 100MHz  100 MHz example  90m drift; 60m buncher, 40m rf rotation  Capture centered at 250 MeV  Higher energy capture means shorter bunch train  Beam at 250MeV ± 200MeV accepted into 100 MHz buncher  Bunch widths < ±100 MeV  Uses ~ 400MV of rf

21. 21 Comment on costs

22. 22 Hardware/Cost (Shelter Island  Now)  Rf requirements:  Buncher: ~300  ~210 MHz; 0.1  4.8MV/m (60m) (~10 frequencies; ~10MHz intervals)  Rotator: ~210  200 MHz; 10MV/m (~10m)  Transverse focussing  160m B=1.25T solenoidal focusing;R=0.30m transport  2002 cost estimate  (Rf =30M$ (Moretti) ; magnets =40M$ (M. Green) ; conv. fac.,misc. 20M $) ( ?? 100M$ )  NOW – Rotator  up to 50m, rf at least 40M$ (?) more  Transverse Focusing at 2T, R =0.25m, 200+ m long Need better/updated cost estimate; cost/performance optimization see Palmer’s talk

23. 23 Summary  High-frequency Buncher and  E Rotator simpler and cheaper (?) than induction linac system  Performance better (?) than study 2, And  System will capture both signs (  +,  - ) ! (Twice as good ?)  Method could be baseline capture and phase-energy rotation for any neutrino factory … To do:  Optimizations, Best Scenario, cost/performance …

24. 24 ~50 MHz variations Example I (250 MeV) oUses ~90m drift + 100m 100  50 MHz rf (<4MV/m) ~300MV total  Captures 250  200 MeV  ’s into 250 MeV bunches with ±80 MeV widths Example II (125 MeV) oUses ~60m drift + 90m 100  50 MHz rf (<3MV/m) ~180MV total  Captures 125  100 MeV  ’s into 125 MeV bunches with ±40 MeV widths

25. 25 Variations/ Optimizations …  Many possible variations and optimizations  But possible variations will be reduced after design/construction  Shorter bunch trains ??  For ring Coolers ?  Other frequencies ??  200 MHz(FNAL)  88 MHz ?? (CERN)  ??? ~44MHz  Cost/performance optima for neutrino factory (Study 3?)  Collider ?? both signs (  +,  - ) !  Graduate students (MSU) (Alexiy Poklonskiy, Pavel Snopok) will study these variations; optimizations; etc…

26. 26 Hardware For Adiabatic Buncher  Transverse focussing ( currently)  B=1.25T solenoidal focusing  R=0.30m transport for beam Rf requirements:  Buncher: ~300  ~210 MHz; 0.1  4.8MV/m (60m) (initially 1 cavity every 1m; reduces frequency in 2-4MHZ steps; 1-D and GEANT4 simulations indicate ~10 frequencies are sufficient (~10MHz intervals)  Rotator: 210  200 MHz; 10MV/m (~10m)

27. 27 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$

28. 28 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 …

29. 29 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$  (D. Summers says he can do Al solenoids for ~10 M$)  Would quad-focusing be cheaper ?

30. 30 $$ 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$ )