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Pros and Cons of Existing Cooling Schemes David Neuffer Fermilab
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2 Introduction Basic cooling equations/comments Cooling Schemes for neutrino factores Solenoid based Study 2B – IDS baseline –Problems / limitations Variations: gas-filled rf –Quad-channel Newer version-shorter front end –With gas-filled cooler Study 2 –MICE channel –Other possible variants μ + -μ - Collider scenarios –Baseline –spirals, solenoids, 50T –Variants- rings, wiggles, PIC, REMEX, ETC -Beam cooling …
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3 Ionization Cooling Principle Loss of transverse momentum in absorber: Heating by multiple scattering
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4 Longitudinal Cooling Must mix with transverse dimensions to get L cooling Sum of x, y, L cooling rates is invariant P μ > ~200MeV/c required to avoid strong longitudinal heating Most initial cooling scenarios cool only tranversely; Scenarios with some initial longitudinal cooling should help 0 for P μ 0.3 GeV/c Emittance Exchange Δ E straggling
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5 Comments Cooling scenarios actually follow rms cooling equations fairly well Good cooling requires small scattering and straggling Low-Z material, small beam at absorber (small ⊥ ) Large rf Voltage to compensate energy loss and keep beam bunched System cannot cool below equilibrium emittance (~) Simulations usually show losses in initial part of a cooling region Probably from mismatch or aperture restriction Could be reduced by better 6-D phase-space matching (?)
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6 Cooling requirements for ν-Factory Beam from target has ,rms 2 × 10 -2 m-rad; ║,rms 1m Δx=~0.1m ×20 MeV/c; Δz=~1m ×δE = 100MeV; -Storage Ring -Factory Goal is to collect maximum number of + and/or - that fit within -Factory acceptances Acceptance of -Factory is estimated as: A T < 30 (π mm) (was 15 for Study 1 and 2) A L < 15 (π cm) (in 200 MHz rf) Transverse cooling by ~3 is sufficient (?) ,rms cooled from ~0.02 to 0.006 m; Longitudinal constraint met by splitting up bunch into string of bunches: ║,rms 0.06 m-rad/bunch
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7 Baseline Capture Scheme High-frequency Buncher + Rotation Drift (110m) Allows beam to decay; beam develops correlation Buncher (~333 230MHz) Bunching rf with E 0 = 125 MeV, 1 = 0.01 { L 1 =~1.5m at L tot = 150m} V rf increases gradually from 0 to ~6 MV/m Rotation (~233 200MHz) Adiabatic rotation V rf =~12 MV/m (x2/3) Cooler (~80m long) (~200 MHz) fixed frequency transverse cooling system Captures both μ + and μ - !!
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8 Study2B scenario Drift –110.7m (1.75T) Bunch -51m V (1/ ) =0.0079 12 rf freq., 110MV 330 MHz 230MHz -E Rotate – 54m – (416MV total) 15 rf freq. 230 202 MHz P 1 = 280, P 2 = 154 N V = 18.032 Match and cool (80m) 0.75 m cells, 0.02m LiH Captures both μ + and μ - ~0.2 μ/p within reference acceptance at end Rms emittance cooled from ε ⊥ = 0.017 to ε ⊥ = ~0.006m
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9 -Factory Study 2B cooling channel Lattice is weak-focusing B max = 2.5T, solenoidal β ≅ 0.8m Cools transversely from ~0.018 to ~0.008m in ~80m BeforeAfter LiH cooling -0.4m+0.4m
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10 Detailed simulations In new “detailed” simulations, (realistic fields, Be windows, etc. ) obtains ~0.204 μ/p after 60m cooling Be windows (+apertures) reduce t from 0.017 to 0.014 before cooling channel Gain in μ/p is ~.12 to ~.2 from ~60m of cooling Rms emittance still cools Losses match cooling 60m 0m A t < 0.03 A t < 0.015 All μ’s μ/P 24 ε t,rms
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11 Costs of baseline 2B scheme (Palmer-Zisman, Mucool 322) Cooling system is ~20% of total costs Dominated by length and power supply costs (∝ V 2 L) Does not include extra costs of multi-frequency rf (Buncher,Rotator) Transport/L should be ~same for Buncher, Rotator, Cooler RegionLengthTransport +Rf cavities Rf PS Total (P$) Drift110m25 Buncher49m325 8 45 Rotator56m2912 44 85 Cooler 80m751793185 Complete system 934 ST 2 ST 2B
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12 Baseline flaws Rf Cavities are pillbox cavities with high B-field, 15 MV/m in Cooler- B flips 12 MV/m in Rotator B=1.75T Be foils in Rotator cool by ~20% But add ~10% in losses Limit final performance ? Cooling channel at baseline acceptance does not gain after 60m Open cell cavities would have more power costs (by ?)
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13 Variation: -Factory Cooling –H 2 Cooling is limited: LiH absorber, β ≅ 0.8m from ~0.018 to ~0.0076m in ~80m ε eq 0.0056m Could be improved H 2 Absorber (120A) or smaller β ~0.0055 ε eq 0.003m ~20% more in acceptance Less beam in halo BeforeAfter LiH cooling +0.4m After H 2 cooling -0.4m
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14 Study 2 Cooling Channel (≈ MICE) Uses Be-window pill box cavities B changes sign at absorbers B = ~2.8T H 2 absorbers, abs 0.5m Other solenoid cell variations Fernow and Palmer sFOFO 2.75m cells 108 m cooling channel consists of: – 16 2.75m cells + 40 1.65m cells – B max increases from 3 T to 5.5 – Cools from ε t, rms = 11mm to 2mm –More than needed in present design –First 40m cools from 11mm to 5mm – Good for current designs – Needs 18 to 11mm precooler Simulation Results
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15 Use gas-filled rf cavities in Rotator Transverse emittance Acceptance (per 24GeV p) Pressure at 150Atm H 2 eq Rf voltage to 24 MV/m Transverse rms emittance cools 0.019 to ~0.008m Acceptance About equal to Study 2B This has same geometry as baseline Like most cases ~½ of μ’s are outside acceptance ~
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16 Quad cooling channel for front end Use 1.5m long cell – FODO 60º to 90º/cell at P 215MeV/c max = 2.6m; min =0.9 to 0.6m B’ = 4 to 6 T/m Advantages: No large magnetic fields along the axis Quads much cheaper ? No beam angular momentum effects Disadvantages No low * region Relatively weak focusing Limited δP/P H 2 -cooled example as good as Study2B LiH case
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17 Shorter Bunch train Reduce drift, buncher, rotator to get shorter bunch train: Δn: 18 -> 10 217m ⇒ 125m 57m drift, 31m buncher, 36m rotator Rf voltages up to 15MV/m (×2/3) Obtains ~0.26 μ/p 24 in ref. acceptance Slightly better than Study 2B baseline 80+ m bunchtrain reduced to < 50m Better for Collider -3040m 500MeV/c
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18 12.9 m43.5 m31.5 m36 m drift Capture buncher rotator capture Drift Buncher or Rotator MC Front End Layout in G4beamline (Pi+ = Yellow, Mu+=Light Blue) Evaluate in G4BeamLine C. Yoshikawa
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19 Have tracked N=10 with ICOOL and G4BL Results are similar Consistency check Additional simulations will allow more variation and optimization Captures both signs ICOOL G4BeamLine μ+μ+ μ-μ-
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20 Example: N B = 10, H 2 cooling 0 0.1 0.2 μ/p (8GeV) μ/p within acceptance All μ’s Transverse emittance ε t,,N (m) 1.5 ZM
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21 Tilted Solenoid? – Y. Alexhin Tilt solenoids to insert dispersion ~20cm ? Allows wedge absorbers to cool longitudinally If wide aperture, oscillations of both μ + and μ - particles can be within the channel Cooling decrement 0.025/m in x, y, z Not yet simulated in front end 22 x z DxDx DyDy
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22 Summary on ν-Factory Cooling Ionization Cooling increases μ intensity significantly Should be incorporated A grapefruit is easier to fit in a transport than a futball Including some initial longitudinal cooling should be studied Increasing A L from 15 to 20 to 25 mm increases μ/P by 10 to 20% Variations to improve performance/cost should be studied
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23 “ Baseline ” Cooling Scenario for Collider Steps 1,2: Bunching, phase rotation, cooling (= factory) : 10cm 6cm 3,4: 6-D cooling with 200, 400 MHz “Ring Coolers” : 6cm 2.4cm 1.0cm 5: compress to 1 bunch 6, 7: 6-D 200, 400 MHz Coolers : 3cm 1.0cm 8: 800 MHz “Ring Cooler” : 1.0cm 0.3cm 9: up to 50T coolers (H 2, solenoids) : 0.4cm 0.08cm Total length of system ~0.8km “Guggenheim” 6D cooler
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24 Comments on “Baseline” Individual cooling segments have been simulated Not matched from segment to segment Segments could be more efficient if tapered cool could be reduced within segments Adiabatic variation could improve matching Guggenheims based on rings Don’t have to be rings Bunch recombiner needs work Last steps (Low-energy cooling with High-field solenoids) also needs optimization; match into accelerator
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25 Variant Cooling scenarios HCC- Helical Cooling Channel PIC-Parametric-resonance Ionization Cooling Use resonance beam dynamics to intensify focusing REMEX, low-energy emittance exchange Bucked field cooling
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26 Comments on Variants HCC very compact, efficient cooler; suited for multistage systems Integrated longitudinal/transverse cooling BUT Hard to fit rf within magnets Works within relatively narrow parameter range (Balbekov) Field strengths are relatively large (B-fields, rf gradients) 400 MHz RF
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27 More Comments on Variants Bucked-field lattice (superFernow) * = 1cm Small δP acceptance PIC/REMEX Resonant lattice/transport Hard to include large δP Has not been simulated –Should try P μ =300MeV/c Correction fields (sextupole, etc.) have not been used Could improve accept. Solenoids + 6-pole ? Li lens cooler Small * at absorber
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28 Cooling for Beta-beam C. Rubbia et al Nucl. Inst. and Meth. A 568, 475 (2006). D. Neuffer, NIM A 583, p.109 (2008) β-beam source production can use ionization cooling Inject Li at 25 MeV (v/c=0.1, ΣJ i =0.4) nuclear interaction at gas jet target produces 8 Li or 8 B – 6 Li + 3 He 8 B + p Multiturn storage with ionization “cooling” maximizes ion production 6-D cooling requires mixing both x and y with E: ( ΣJ i =0.4) (cooling rate is small) Separation of produced ions from circulating beam is difficult. Very dense, shaped 3 He jet target is needed Has not been accurately simulated Ring dynamics + nuclear interactions Would work better with 3 He beam, 6 Li (waterfall) target Beam and product are separable Li target is easier
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29 Summary
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