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Ionization Cooling for a     Collider

Ionization Cooling for a     Collider. David Neuffer Fermilab 7/15/06. Outline. Collider Parameters Cooling Requirements Ionization Cooling Cooling description Heating – Longitudinal Cooling Emittance Exchange- Partition Number Helical wiggler-PIC-REMEX Low-Energy “Cooling”

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Ionization Cooling for a     Collider

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

  2. Outline • Collider Parameters • Cooling Requirements • 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 • R Palmer 4:00 PM Talk: Curia II

  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.  ColliderOverview

  5.  Collider Parameters

  6. 1.5 TeV  Collider Parameters

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

  8.  Collider cooling requirements • Collider requires cooling of bunches to minimal beam sizes, and minimal number of bunches • approximate parameters: ~21011 s / bunch, ,rms  0.25 to 0.025×10-4m-rad; ║,rms  0.04 m-rad • Beam from target has ,rms  210-2 m-rad; ║,rms  1 m-rad •  6-D  - cooling by ~ 107 to 109 is required

  9. Cooling Summary

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

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

  12. Combining Cooling and Heating: • Low-Z absorbers (H2, 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. Transverse cooling limits • Transverse Cooling – equilibrium emittance equilibrium scattering angle • Want materials with small multiple scattering (large LR), but relatively large dE/ds, density () • Want small  at absorbers => strong focusing • - equilibrium emittances (/) smallest for low-Z materials

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

  15. Longitudinal “Cooling” • Energy cooling occursifthe derivative : (dE/ds)/E= gL(dp/ds)/p > 0 • gL(E) is negative for E < ~ 0.2 GeV and only weaklypositive for E > ~ 0.2 GeV • Ionization cooling does not effectively cool longitudinally Energy straggling increases energy spread

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

  18. Cooling + Energy straggling ... Energy spread (sE) cooling equation: Equilibrium σp: Longitudinal Emittance Cooling equation: • Longitudinal Cooling requires: • Positive gL(η, “wedge”), Strong bunching (βcτsmall) • Large Vrf, small λrf Energy loss/recovery Before decay requires:

  19. μ Cooling Regimes • Efficient cooling requires: • Frictional Cooling (<1MeV/c) Σg=~3 • Ionization Cooling (~0.3GeV/c) Σg=~2 • Radiative Cooling (>1TeV/c) Σg=~4 • Low-εt cooling Σg=~2β2 (longitudinal heating)

  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. More complete coupled cooling equations: Wang and Kim, (MuCOOL 240) have developed coupled cooling equations including dispersion, wedges, solenoids, and symmetric focussing (βx = βy = βT) Scattering terms θD,θWare dispersion, wedge angles

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

  23. RF Problem: cavity gradient in magnetic field is limited? • Rf breakdown field decreases in magnetic fields? • Solenoidal focussing gives large B at cavities • But gas in cavity suppresses breakdown Muons, Inc. results: 50+ MV/m no change with B Vacuum Cavities 800 MHz results: 40MV/m→13MV/m 10% of liquid H2

  24. Study 2 Cooling Channel (for MICE) • Cell contains • Rf for acceleration/bunching • H2 absorbers • Solenoidal magnets 108 m cooling channel consists of: 16 2.75m cells + 40 1.65m cells Focusing increases along channel: Bmax increases from 3 T to 5.5 T sFOFO 2.75m cells Simulation Results

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

  26. Helical 6-D Cooler (Derbenev) • Magnetic field is solenoid B0+ dipole + quad + … • System is filled with H2 gas, includes rf cavities • Cools 6-D (large E means longer path length) Key parameters: a, k=2π/λ, solenoid field B0, transverse field b(a)

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

  28. +- Collider Cooling Scenarios • +- Collider requires energy cooling and emittance exchange (and anti-exchange) to obtain small L, εx, εy 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 …

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

  30. PIC-Parametric-resonance Ionization Cooling (JLab, Slava 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’

  31. PIC ,eff: 6cm  0.1cm Transverse + longitudinal cooling Reverse emittance exchange to reduce transverse emittance (“REMEX”) Chromaticity correction a problem PIC/REMEX cooling (Derbenev)

  32. PIC/REMEX examples (Bogacz, Beard, Newsham, Derbenev) • Solenoids + quads + dipoles+rf • 2m cells • β= 1.4cm, ηx= 0.0m • Problems: • Large σp/p • Large σθ • Short absorber • Solution approach: • Use simulations to tune this as a resonant beam line

  33. Low-Energy “Cooling” • At Pμ = 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/β2 • βt scales as β • Solenoid βt  p/B • εN,rms  Pμ2 ??? • Decrease εN,transverse while εlong increases • “wedgeless” emittance exchange • εN,rms × 1/30, εlong ×300 ???

  34. 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 =0.004m (40 MeV/c, 8000 T/m)

  35. Low-Energy “cooling”-emittance exchange • dPμ/dsvaries as ~1/β3 • “Cooling” distance becomes very short: for H at Pμ=10MeV/c • Focusing can get quite strong: • Solenoid: • β=0.002m at 30T, 10MeV/c • εN,eq= 1.5×10-4 cm at 10MeV/c • Small enough for “low-emittance” collider 100 cm Lcool 0.1 cm 10 200 MeV/c Pµ

  36. Emittance exchange: solenoid focusing • Solenoid focusing(30T) •  0.002m • Momentum (30→10 MeV/c) • L ≈ 5cm • R < 1cm • Liquid Hydrogen (or gas) Lcool • εN,eq= 1.5×10-4 cm at 10MeV/c 0.1cm Use gas H2 if cooling length too short -Will need rf to change p toz 10 200 MeV/c Pµ

  37. Summary • Significant progress in cooling is required • Ingredients needed in Collider cooling scenario include: • Longitudinal cooling by large factors … • Transverse cooling by very large factors • Final beam compression with reverse emittance exchange • Reacceleration and bunching from low energy

  38. Linac-area MuCool Test Area • Test area for bench test and beam-test of Liquid H2 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)

  39. MTA experimental program • Rf: 805, 201 MHz, gas-filled • 201MHz just reached 16 MV/m • H2 absorbers

  40. 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)

  41. 10% cooling of 200 MeV muons requires ~ 20 MV of RF single particle measurements =>D ( e out/e in ) = 10-3 CouplingCoils1&2 Spectrometer solenoid 1 Matching coils 1&2 Matching coils 1&2 Spectrometer solenoid 2 Focus coils 1 Focus coils 2 Focus coils 3 m Beam PID TOF 0 Cherenkov TOF 1 RF cavities 1 RF cavities 2 Downstream particle ID: TOF 2 Cherenkov Calorimeter Diffusers 1&2 Liquid Hydrogen absorbers 1,2,3 Incoming muon beam Trackers 1 & 2 measurement of emittance in and out

  42. MICE Experiment

  43. Constraints: beam-beam  • Significant Constraint is Beam-Beam Tune shift in Collider • At Nµ=2×1011, rµ=1.37×10-17m, N=2.5×10-6m • Could be larger? •  could be up to ~0.2 ?? • Beam-beam compensation? M. Furman simulation =0.1

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