1. Ionization Cooling for a ν-Factory or     Collider David Neuffer Fermilab 7/15/06

2. 2 Outline  Cooling Requirements  ν-Factory     Collider  Ionization Cooling  Cooling description  Heating – Longitudinal Cooling  Emittance Exchange- Partition Number  Helical wiggler-PIC-REMEX  Low-Energy “Cooling”  Emittance exchange  Li lens  Solenoid  Cooling Scenarios

3. 3 References  A. N. Skrinsky and V.V. Parkhomchuk, Sov. J. Nucl. Physics 12, 3(1981).  D. Neuffer, Particle Accelerators 14, 75 (1983)  D. Neuffer, “  +  - Colliders”, CERN report 99-12 (1999).  D. Neuffer, “Introduction to Muon Cooling, NIM A532,p. 26 (2004).  C. X. Wang and K. J. Kim, “Linear Theory of 6-D Ionization Cooling”, (PRL) MuCOOL Note 240, April 2002. (also COOL03), NIM A532, p. 260 (2004)  Y. Derbenev and R. Johnson, Phys. Rev. ST Accel. Beams 8, E041002 (2005); COOL05 proc.  Simulation tools  R. Fernow, ICOOL http://pubweb.bnl.gov/users/fernow/www/icool/readme.html  T. Roberts, G4BeamLine (Muons, Inc.) http://www.muonsinc.com/

4.     Collider Overview

5. 5     Collider Parameters

6. 6 Overview of -Factory  Proton Driver (1-4 MW) – proton bunches on target produce  s  Front-end:  decay   + collect and cool  s: (phase rotation + ionization cooling)  Accelerator - to full energy ( linac + RLAs to 20—50 GeV)  - Storage ring Store  ’s until decay (~300 B turns)  e +   e * decays produce neutrino beams directed toward:  Long base line neutrino detector (2000—8000 km away …)  10 20 to 10 21 ( e,  *) /SS/year

7. 7 Producing and Capturing   Collaboration baseline:  10GeV p-beam on  Target (Hg-jet) immersed in  20  1.75 T solenoid, taking  ~300 MeV/c  μ -Collider: Rf: ~200 MHz, Capture string of ~20 bunches- Recombine after cooling ν -Factory: Rf: ~200 MHz, 12 MV/m Capture in string Of ~50 bunches

8. 8 Cooling Requirements  Beam from target has  ,rms  2 × 10 -2 m-rad;  ║,rms  1m  -Storage Ring -Factory  Goal is to collect maximum number of  + and/or  - that fit within accelerator / storage ring acceptances  Transverse cooling by ~10  is sufficient  ,rms  0.2 to 0.8×10 -2 m-rad;  ║,rms  0.06 m-rad/bunch     Collider  Goal is maximal cooling of maximum number of both  + AND  - ; high luminosity needed.  Cooling by > ~100  in each of  x,  y,  z is required  ,rms  0.5 to 0.025×10 -4 m-rad;  ║,rms  0.04 m-rad

9. 9 Cooling Summary

10. 10 Transverse cooling:  Particle loses momentum P(   and  ) in material  Particle regains P  (only) in RF  Multiple Scattering in material increases rms emittance: Muon Cooling-general principle

11. 11 Ionization Cooling Principle Loss of transverse momentum in absorber: Heating by multiple scattering

12. 12 Combining Cooling and Heating:  Low-Z absorbers (H 2, Li, Be, …) to reduce multiple scattering  High Gradient RF  To cool before  -decay (2.2   s)  To keep beam bunched  Strong-Focusing at absorbers  To keep multiple scattering  less than beam divergence …  Quad focusing ?  Li lens focusing ?  Solenoid focusing?

13. 13 Transverse cooling limits  Transverse Cooling – equilibrium emittance equilibrium scattering angle  Want materials with small multiple scattering (large L R ), but relatively large dE/ds, density (  )  Want small   at absorbers => strong focusing  - equilibrium emittances (/   ) smallest for low-Z materials

14. 14 Ionization Cooling problems  Must focus to very small β   β  : 1m → ~1mm  Intrinsic scattering of beam is large  θ rms > ~0.1 radians  Intrinsic momentum spread is large  σ P /P > ~0.03  Cooling must occur within muon lifetime   = 2.2γ  s or L  = 660 βγ m pathlength  Does not (directly) cool longitudinally

15. 15 Longitudinal “Cooling”  Energy cooling occurs if the derivative :  (dE/ds)/  E= g L (dp/ds)/p > 0  g L (E) is negative for E < ~ 0.2 GeV and only weakly positive for E > ~ 0.2 GeV  Ionization cooling does not effectively cool longitudinally Energy straggling increases energy spread

16. 16 “Emittance exchange” enables longitudinal cooling:  Cooling derivative is changed by use of dispersion + wedge (Dependence of energy loss on energy can be increased) (if due to path length)

17. 17 Partition Numbers, δE-δt cooling With emittance exchange the longitudinal partition number g L changes: But the transverse cooling partition number decreases: The sum of the cooling partition numbers (at P = P  ) remains constant: Σ g > 0

18. 18 Cooling + Energy straggling... Energy spread   E  cooling equation: Longitudinal Emittance Cooling equation : Longitudinal Cooling requires:  Positive g L (η, “wedge”), Strong bunching (β cτ small)  Large V rf, small λ rf Energy loss/recovery Before decay requires: Equilibrium σ p :

19. 19 μ Cooling Regimes  Efficient cooling requires:  Frictional Cooling (<1MeV/c) Σ g =~3  Ionization Cooling (~0.3GeV/c) Σ g =~2  Radiative Cooling (>1TeV/c) Σ g =~4  Low-ε t cooling Σ g =~2β 2 (longitudinal heating)

20. 20 Focusing for Cooling  Strong focussing needed – magnetic quads, solenoids, Li lens ?  Solenoids have been used in most (recent) studies  Focus horizontally and vertically  Focus both  + and  -  Strong focussing possible:  β  = 0.13m for B=10T, p  = 200 MeV/c  β  = 0.0027m for B=50T, p  = 20 MeV/c  But:  Solenoid introduces angular motion  L damped by cooling + field flips  No chromatic correction (yet)  B within rf cavities ?    (   )

21. 21 Solenoidal Focusing and Angular Momentum  Angular motion with focusing complicates cooling  Energy loss in absorbers reduces P , including P  Orbits cool to Larmor centers, not r = 0 Solution: Flip magnetic fields; new Larmor center is near r=0

22. 22 More complete coupled cooling equations: θ D, θ W are dispersion, wedge angles Scattering terms Wang and Kim, (MuCOOL 240) have developed coupled cooling equations including dispersion, wedges, solenoids, and symmetric focussing (β x = β y = β T )

23. 23 Cooling with   exchange and solenoids (Wang and Kim) Example: rms Cooling equations with dispersion and wedges (at  =  =  ) in x-plane: The additional correlation and heating terms are “small” in “well-designed” systems.

24. 24 Study 2 Cooling Channel (for MICE)  Cell contains  Rf for acceleration/bunching  H 2 absorbers  Solenoidal magnets sFOFO 2.75m cells 108 m cooling channel consists of: 16 2.75m cells + 40 1.65m cells Focusing increases along channel: B max increases from 3 T to 5.5 T Simulation Results

25. 25 Study2 cooling channel  Focusing function at absorbers: 0.5m→0.2m  Total length of channel 100+m  Cools to  ~0.002m

26. 26 Study 2A cooling channel  Lattice is weak-focusing  B max = 2.5T, solenoidal  β  ≅ 0.8m  Cools transversely   from ~0.018 to ~0.007m  in ~70m Before After cooling -0.4m+0.4m

27. 27 RFOFO ring cooler performance  Example cools longitudinally more than transversely  Can be adjusted for more transverse cooling E-ct before and after Transverse before and after

28. 28 RF Problem: cavity gradient in magnetic field is limited? Vacuum Cavities 800 MHz results: 40MV/m →13MV/m Muons, Inc. results: 50+ MV/m no change with B  Rf breakdown field decreases in magnetic fields?  Solenoidal focussing gives large B at cavities  But gas in cavity suppresses breakdown 10% of liquid H 2

29. 29 Helical 6-D Cooler (Derbenev)  Magnetic field is solenoid B 0 + dipole + quad + …  System is filled with H 2 gas, includes rf cavities  Cools 6-D (large E means longer path length) Key parameters: a, k=2π/λ, solenoid field B 0, transverse field b(a)

30. 30 Comments on Helical Wiggler parameters  1/  T 2 ≅ 0.67 for equal cooling at ∑ g =2  Energy loss at liquid H 2 density is ~30MV/m (800atm-e gas)  Typical simulations have used ~ 15MV/m energy loss  Need more rf gradient: ~22MV/m  (could use less if needed…) PP 200 MeV/c (0.67T-m) λ1.0m a0.16m  =ka= P  /P z 1 B5.5T (Bρ/B=0.12m) b(a)1.28T (Bρ/b=0.52m) b ' (a)-0.46T/m D(a)- dispersion 0.29m Δ g =1/  T 2 0.9 Typical case

31. 31 Helical Wiggler 3-D Cooling (P µ =250MeV/c) l=1.0 l=0.8 l=0.6 l=0.4 Cooling factor ~ 50,000 × Yonehara, et al.

32. 32 Helical wiggler R&D  Need Magnet design  Solenoid, dipole + quad  Displaced solenoid coils can provide needed field  Matching in/out

33. 33  + -   Collider Cooling Scenarios  + -   Collider requires energy cooling and emittance exchange (and anti-exchange) to obtain small  L, ε x, ε y emittances required for high-luminosity  Start with large beam from target, compress and cool, going to stronger focussing and bunching as the beam gets smaller …

34. 34 Updated Scenario (Palmer-5-1-06) PIC? Low Emttance Muon Collider REMEX? “Guggenheim” 6D cooler 800 MHz 6D cooler

35. 35 Palmer scenario to do:  Matching from section to section  Buncher/Wiggler – 3D dynamics  Reoptimization  Phase rotation buncher is ν-Factory case (not Collider optimum)  Tapered Guggenheims  Final cooler  Matching in/out  Rf match in/out  “realistic” field models  Reacceleration scenario from low-emittance  Lower frequency rf + buncher  Can PIC/REMEX or … get us to smaller emittance?

36. PIC-Parametric-resonance Ionization Cooling (JLab, Y. Derbenev) (also Balbekov, 1997) Excite ½ integer parametric resonance (in Linac or ring)  Similar to vertical rigid pendulum or ½-integer extraction  Elliptical phase space motion becomes hyperbolic  Use xx’=const to reduce x, increase x'  Use Ionization Cooling to reduce x' Detuning issues being addressed (chromatic and spherical aberrations, space-charge tune spread). Simulations underway. First: Then: IC reduces x’

37. 37 PIC/REMEX cooling (Derbenev)  PIC  ,eff : 0.6cm  0.1cm  Transverse + longitudinal cooling  Reverse emittance exchange to reduce transverse emittance  (“REMEX”)  Chromaticity correction a problem  Depth of focus a problem  L absorber < ~ β   No “realistic” simulations

38. 38 PIC/REMEX examples (Bogacz, Beard, Newsham, Derbenev) Example:  Solenoids + quads + dipoles+rf  2m cells  β  = 1.4cm, η x = 0.0m  Problems:  Large σ p /p (~3%)  Large σ θ (>0.1)  Short absorber –1cm Be = 3MeV  Solution approach:  Use simulations to tune this as a resonant beam line

39. 39 Cooling scenario (~Muons, Inc.)

40. 40 Low-Energy “Cooling”=REMEX without wedges  At P μ = 10 to 200 MeV/c, energy loss heats the beam longitudinally  Transverse cooling can occur  emittance exchange  Equilibrium transverse emittance decreases  dE/ds scales as 1/β 2  β t scales as β –Solenoid β t  p/B  ε N,rms  P μ 2 ???  Decrease ε N,transverse while ε long increases  “wedgeless” emittance exchange  ε N,rms × 1/30, ε long ×300 ???

41. 41 Low-Energy “cooling”-emittance exchange  dP μ /ds varies as ~1/β 3  “Cooling” distance becomes very short: for H at P μ = 10MeV/c  Focusing can get quite strong:  Solenoid:  β  =0.002m at 30T, 10MeV/c  ε N,eq = 1.5×10 -4 cm at 10MeV/c  Small enough for “low-emittance” collider PµPµ L cool 200 MeV/c 10 0.1 cm 100 cm

42. 42 Emittance exchange: solenoid focusing  Solenoid focusing(30T)    0.002m  Momentum (30→10 MeV/c)  L ≈ 5cm  R < 1cm  Liquid Hydrogen (or gas) PµPµ L cool 200 MeV/c 10 0.1cm Use gas H 2 if cooling length too short  ε N,eq = 1.5×10 -4 cm at 10MeV/c -Will need rf to change  p to  z

43. 43 Li-lens cooling  Lithium Lens provides strong- focusing and low-Z absorber in same device  Liquid Li-lens may be needed for highest-field, high rep. rate lens  BINP (Silvestrov) was testing prototype liquid Li lens for FNAL  But FNAL support was stopped - and prototypes were not successful... β  =0.026m (200 MeV/c, 1000 T/m) β  =0.004m (40 MeV/c, 8000 T/m)

44. 44 Summary  Cooling for neutrino factory is practical  Collider cooling scenario needs considerable development:  Longitudinal cooling by large factors …  Transverse cooling by very large factors  Final beam compression with reverse emittance exchange  Reacceleration and bunching from low energy

45. 45 Linac-area MuCool Test Area  Test area for bench test and beam-test of Liquid H 2 absorbers  Enclosure complete in ~October 2003  Can test 200 and 805 MHz rf for MuCOOL and also for Fermilab  Assemble and beam test cooling modules  (absorber + rf cavity + solenoid)

46. 46 MTA experimental program  Rf: 805, 201 MHz, gas-filled  201MHz just reached 16 MV/m  805 MHz 3T, gas-cavity test  H 2 absorbers 

47. 47 MICE beam line (Drumm, ISS)  MICE (International Muon Ionization Cooling Experiment)  To verify ionization cooling (for a neutrino factory) with a test of a complete cooling module in a muon beam  Muon beam line and test area in RAL-ISIS (Oxford)  Installation Jan. – Oct. 1 2007  Experiment occurs in ~2007-2009 time frame MICE beam line and experimental area (RAL) TTargetSheffield APion CaptureISIS BDecay SolenoidEID CMuon Transport Channel Liverpool ? DDiffuserOxford

48. 48  Incoming muon beam Diffusers 1&2 Beam PID TOF 0 Cherenkov TOF 1 Trackers 1 & 2 measurement of emittance in and out Liquid Hydrogen absorbers 1,2,3 Downstream particle ID: TOF 2 Cherenkov Calorimeter RF cavities 1RF cavities 2 Spectrometer solenoid 1 Matching coils 1&2 Focus coils 1 Spectrometer solenoid 2 Coupling Coils 1&2 Focus coils 2Focus coils 3 Matching coils 1&2 10% cooling of 200 MeV muons requires ~ 20 MV of RF single particle measurements =>  out /  in ) = 10 -3

49. 49 MICE Experiment

50. 50 Last Slide

51. 51 Postdoc availability – Front end Optimization