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Bunched-Beam Phase Rotation. David Neuffer Fermilab. 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
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Bunched-Beam Phase Rotation David Neuffer Fermilab
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
Adiabatic buncher + Vernier Rotation • Drift (90m) • decay; beam develops correlation • Buncher(60m)(~333200MHz) • 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) !
Longitudinal Motion (1-D simulations) Drift Bunch E rotate Cool System would capture both signs (+, -) !!
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 torf= ~1.5m at end: • Gradually increase rf gradient (linear or quadratic ramp): Example: rf : 0.901.5m
Adiabatic Buncher overview • Adiabatic buncher • Set T0, : • 125 MeV/c, 0.01 • In buncher: • Match torf=1.5m at end: • zero-phase with 1/ at integer intervals of : • Adiabatically increase rf gradient: rf : 0.901.5m
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
“Vernier” Rotation • At end of buncher, choose: • Fixed-energy particle T0 • Second reference bunch TN • Vernier offset • Example: • T0 = 125 MeV • Choose N= 10, =0.1 • T10 starts at 77.28 MeV • Along rotator, keep reference particles at (N + ) rf spacing • 10 = 36° at =0.1 • Bunch centroids change: • Use Erf = 10MV/m; LRt=8.74m • High gradient not needed … • Bunches rotate to ~equal energies. rf : 1.4851.517m in rotation; rf = ct/10 at end (rf 1.532m) Nonlinearities cancel: T(1/) ; Sin()
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;
Key Parameters • General • Muon capture momentum (200MeV/c?) 280MeV/c? • Baseline rf frequency (200MHz) • Drift • Length LD • Buncher– Length (LB) • Gradient, ramp VB (linear OK) • Final Rf frequency (LD + LB) (1/) = RF • Phase Rotator-Length (LR) • Vernier, offset : NR, V • Rf gradient VR • Match into cooling channel, Accelerator
Implementation in ICOOL • Define 2 reference particles: P1, P2 • ACCEL option 10 • N –wavelengths between ref particles • V(z) = A +Bz +Cz2 • Long. Mode • Phase model 0 or 1 • 0 at t1 (partREFP model 3 or 4icle 1) • 1 at (t1 + t2)/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.
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
Palmer Dec. 2003 scenario • Drift –110.7m • Bunch -51m • (1/) =0.0079 • -E Rotate – 52m • P1=280 , P2=154V = 18.032 • Match and cool (100m) • P0 =214 MeV/c • 0.75 m cells, 0.02m LiH
Simulation results • (Palmer, Gallardo, Fernow,… • 0.25 /p in 30 mm acceptance
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)
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
“Latest” short buncher • Drift – 20m • Bunch – 20m • Vrf = 0 to 15 MV/m ( 2/3) • P1 at 205.037, P2=130.94 • N = 5.0 • Rotate – 20m • N = 5.05 • Vrf = 15 MV/m ( 2/3) • Palmer Cooler up to 100m 40m 60m 95m
Simulation results • ICOOL results • 0.12 /p within 0.3 cm acceptance • Bunch train ~12 bunches long (16m) • (but not 8 bunches …)
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
Hardware/Cost (Shelter Island Now) • Rf requirements: • Buncher: ~300~210 MHz; 0.14.8MV/m (60m) (~10 frequencies; ~10MHz intervals) • Rotator: ~210200 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
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 anyneutrino factory … To do: • Optimizations, Best Scenario, cost/performance …
~50 MHz variations Example I (250 MeV) • Uses ~90m drift + 100m 10050 MHz rf (<4MV/m) ~300MV total • Captures 250200 MeV ’s into 250 MeV bunches with ±80 MeV widths Example II (125 MeV) • Uses ~60m drift + 90m 10050 MHz rf (<3MV/m) ~180MV total • Captures 125100 MeV ’s into 125 MeV bunches with ±40 MeV widths
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…
Hardware For Adiabatic Buncher • Transverse focussing (currently) • B=1.25T solenoidal focusing • R=0.30m transport for beam Rf requirements: • Buncher: ~300~210 MHz; 0.14.8MV/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: 210200 MHz; 10MV/m (~10m)
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 …
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 ?
$$ 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$ )