Pros and Cons of Existing Cooling Schemes David Neuffer Fermilab

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 …

3 Ionization Cooling Principle Loss of transverse momentum in absorber: Heating by multiple scattering

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

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 (?)

6 Cooling requirements for ν-Factory  Beam from target has  ,rms  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 m;  Longitudinal constraint met by splitting up bunch into string of bunches:  ║,rms  0.06 m-rad/bunch

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 - !!

8 Study2B scenario  Drift –110.7m (1.75T)  Bunch -51m  V  (1/  ) =  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 =  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 ⊥ = to ε ⊥ = ~0.006m

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

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 to 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 < All μ’s μ/P 24 ε t,rms

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 Buncher49m Rotator56m Cooler 80m Complete system 934 ST 2 ST 2B

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 ?)

13 Variation: -Factory Cooling –H 2  Cooling is limited:  LiH absorber, β  ≅ 0.8m   from ~0.018 to ~0.0076m in ~80m  ε eq  m  Could be improved  H 2 Absorber (120A) or smaller β     ~  ε eq  0.003m  ~20% more in acceptance  Less beam in halo BeforeAfter LiH cooling +0.4m After H 2 cooling -0.4m

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: – m cells m 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

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 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  ~

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

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

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

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-

20 Example: N B = 10, H 2 cooling μ/p (8GeV) μ/p within acceptance All μ’s Transverse emittance ε t,,N (m) 1.5 ZM

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 22 x z DxDx DyDy

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

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

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

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

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

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

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

29 Summary