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Bunched-Beam Phase Rotation David Neuffer Fermilab

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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

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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) !

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

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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

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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

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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

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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( )

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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;

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10 ICOOL simulation –Buncher, , Cool

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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

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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.

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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

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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

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

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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)

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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

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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

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

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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

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21 Comment on costs

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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

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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 …

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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

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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…

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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)

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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$

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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 …

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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 ?

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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$ )

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