1. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 1 Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory Cary Yoshikawa Chuck Ankenbrandt Dave Neuffer Katsuya Yonehara

2. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 2 Evolution of the QIHC (2 snapshots) Configuration in the Phase II proposal, which was awarded and is funding current studies. Current configuration Outline Motivation Design upstream of HCC for increased acceptance Design downstream of HCC for bunch merging Design upstream of HCC for increased acceptance Design downstream of HCC for bunch merging Summary & Future

3. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 3 Upstream of an HCC optimized for cooling: Affords a larger RF bucket size when operating near transition for purpose of capture and bunching after the tapered solenoid. Having control over both γ T and energy of synchronous particle should enlarge phase space available for particles to be captured. The Quasi-Isochronous HC should match naturally into an HCC that is maximized for cooling (equal cooling decrements). The Quasi-Isochronous HC aims to shorten the length of the front end of a muon collider/neutrino factory by exploiting the tunable slip factor: in the following ways: Motivation Downstream of the HCC optimized for cooling : Allows recombination of bunches over a potentially shorter distance compared to other studies by utilizing a large slip factor after inducing different energies across the bunches:

4. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 4 Configuration in the Phase II Proposal z(m)SubsystemPurpose 0.0 to 4.5Capture/Tapered SolenoidEnhance pion/muon capture 4.5 to 24.5First straight RF Buncher in vacuum1.Initial capture of π’s & μ’s into RF buckets. 2.Allow lower momenta π’s to decay into μ’s. 24.5 to 44.5Second straight RF Buncher in 100 atm H2 w/ variably thick Be windows. 1.H2 gas allows higher RF gradient. 2.Be causes higher momenta π’s to interact, enhancing useful μ’s. 3.Transverse cooling. 44.5 to 50.0Match into HCC1.To match between straight solenoid into HCC. 2.Enhance μ capture by manipulating RF bucket size. 50.0 to 350HCC(Multi-Bunch)To cool string of multiple bunches of muons in 6D phase space. 350 to 360Bunch Combiner Preparation (BCP)To transform string of bunches at same energy into string at different energies with head bunches at higher energies than trailing bunches. 360 to 393Bunch Combiner (BC) To combine the multiple bunches in a single one via free drift in large | η | channel. 393 to 693HCC(Single-Bunch)To cool single bunch of muons in 6D phase space.

5. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 5 The rate of muons created across the transition from vacuum into the Be/H2 has increased by: ~21% (728  882) Birth of Mu-’s 2m before H2/Be 35 MV/m region P vs. z Birth of Mu-’s 2m into H2/Be 35 MV/m region P vs. z PhaseII Upstream HCC: Justification for adding H 2 /Be (z=24.5m)

6. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 6 Initial design was based on a reference with constant momentum (237 MeV/c) and γ T extracted in matching section via earliest arrivals over incremental longitudinal sections. Note that because κ goes from 0 to 1, the reference sees more material as it traverses the matching section and thus |sin(φs)| must increase to compensate energy loss, forcing the bucket area to decrease along z. Phase II HCC Upstream: Matching Section

7. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 7 (204.5, 236.3) Phase II HCC Upstream: Matching Section z = 50.0 m (End of Match) P (MeV/c) t (nsec) ~9000 μ – /100k POT

8. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 8 In principle, it is possible to achieve monotonic RF bucket growth by manipulating the phase φ s, γ T (via ), and field gradient. Phase II HCC Upstream: Matching Section

9. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 9 Phase II HCC Downstream: Bunch Recombiner Preparation Before bunches out of the HCC can be combined, the string of mono-energetic bunches must be transformed into one whose head bunches (early arrivals) are at higher energies than the tail (late arrivals), since we operate above transition. This can be achieved by using an RF at off frequency. In this case, 204.08MHz for bunches with 200 MHz spacing. ε L =0.002m/bunch cτ(m) KE(MeV) -4 20 f=204.08 MHz V’ = 15 MV/m 9.6m in QIHC η = 0.05 0 300

10. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 10 Phase II HCC Downstream: Bunch Recombiner -4 20 0 cτ(m) KE(MeV) -4 20 300 Drift 32.5 m in QIHCC w/ η= 0.43 Note that these simulations are 1-D only. 3-D using g4beamline is shown later. Total length:9.6+32.5=~43m. Compare to 340m* * R. Fernow, “Estimate of Front-End Magnetic Requirements,” NFMCC Tech. Note 529 (2008) 20-4 After synchrotron oscillations within a 200 MHz rf bucket. ~95% of the initial beam is captured within that bucket. V’ = 12 MV/m η = 0.05

11. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 11 Current HCC Upstream: End of 2 nd Straight Section 1.081E4 1.061E4 9.159E3 9.496E3 Pi– & Mu– Mu– Pi+ & Mu+ Mu+

12. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 12 Emittances out of second straight: ε T =11 mm-rad x ε || = 378 mm-rad HCC(cooling optimized) acceptance: ε T =20 mm-rad x ε || = 40 mm-rad Need to transform a cigar shaped ε T xε ║ (11 x 378) into a football shaped one (20 x 40). p t 450 MeV/c … Current HCC Upstream: Match Want a low κ HCC that’ll have large momentum acceptance (150 MeV/c < p <450 MeV/c) that cools longitudinally. Since we will need to operate with a nearly straight solenoid, we will need to operate below transition. Desire a low κ HCC with a ptransition ~≥ 450 MeV/c. P(MeV/c) t(nsec) Pref = 225 MeV/c free drift for 45.2 m B z (on z-axis) = 2.4 T Bz(on ref) = 2.3 T B φ (on z-axis) = 0.62200 T db φ /dρ (on z-axis) = -1.33809 T

13. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 13 Maxing out use of wedge (60 atm case) increases longitudinal acceptance by 19% over the case without any wedge. Perhaps the matching scheme should incorporate ~30m of κ = 0.25 QIHCC with Be wedges in H2 gas at 60 atm, followed by removal of the Be wedges to achieve the lowest equilibrium emittances. H2:200 atmH2:100 atm H2:60 atm εlong (m-rad) at z = 0 m0.133000.148100.15820 εlong (m-rad) at z = 30 m0.096190.098430.09901 εtrans (m-rad) at z = 0 m0.035130.034260.03374 εtrans (m-rad) at z = 30 m0.017870.019140.01915 ε6D (m^3) at z = 0 m1.42800E-041.50800E-041.53100E-04 ε6D (m^3) at z = 30 m2.30000E-052.85800E-052.78500E-05 Lowest emittance (~equilibrium) at z=30m. Highest emittance (acceptance) at z=0. Current HCC Upstream: Wedge in Match To enhance longitudinal cooling, we studied effect of adding a cylindrical wedge. 1.H2:200 atm: No wedge, only H 2 at 200 atm at 293 K. 2.H2:100 atm: Be wedge ~1mm at reference to loose same energy as 100 atm H 2. 3.H2: 60 atm: Max Be wedge ~1.48 mm w/ H 2 at knee of breakdown. E max = 32 MV/m φ s ~14º P ref = 225 MeV/c f = 201.25 MHz Bz(z-axis) = 2.4T Bz(on ref) = 2.3T

14. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 14 G4beamline simulation of phase rotation of bunches with 200 MHz spacing with off frequency 405 MHz. t(ns) p(GeV/c) 14 Current HCC Downstream Katsuya Yonehara bunch 1 bunch 7 bunch 13 bunch 1 bunch 7 bunch 13 f=405 MHz V’ = 10 MV/m 2.5 m in QIHC η = 0.04

15. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 15 Phase II HCC Downstream: Bunch Recombiner p(GeV/c t(ns) Drift 46.5 m in QIHCC w/ η= 0.72 f=200 MHz V’ = 5 MV/m in QIHC η = 0.04 5 nsec Initial phase rotation in G4BL result in energy spreads that are larger than 1D simulation. These large energy spreads translate into large time spreads at the end of the drift region. bunch 1 bunch 7 bunch 13 t(ns) p(GeV/c

16. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 16 Conclusions and Future (upstream of HCC) Maxing out use of wedge (60 atm case) increases longitudinal acceptance by 19% over the case without any wedge. Perhaps the matching scheme should incorporate ~30m of κ = 0.25 QIHCC with Be wedges in H2 gas at 60 atm, followed by removal of the Be wedges to achieve the lowest equilibrium emittances. Consider use of higher RF frequencies upstream of the matching section to lower its ε L acceptance requirement. 201.25  325 MHz? Perhaps the matching section is better suited to follow one that has the overall longitudinal emittance be spread across several bunches with smaller emittances, ie. Dave’s baseline FE with phase rotation. Throughout 0 < κ < 1 match, design for continual RF bucket growth by manipulating the phase φs, γ T (via ), and field gradient.

17. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 17 Initial 1D studies show promising results with 95% capture of muons merged into a single bunch over ~43 m. Initial 3D studies in G4BL have phase rotation resulting in energy spreads that are larger than 1D simulation, translating into larger time spreads at the end of the drift region. Phase rotation parameters to optimize: Off frequency, V’max Drift parameters to optimize: η, λ Can also consider effect of adding RF manipulation into both phase rotation (harmonics) and drift regions. Conclusions and Future (downstream of HCC)

18. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 18 Back up

19. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 19 Configuration in the Phase II Proposal z(m)SubsystemPurposePhysical DimensionsFields 0.0 to 4.5Capture/Tapered SolenoidEnhance pion/muon captureL = 4.5 m R = 7.5 cm  35 cm Bsol = 20 T  4.2 T 4.5 to 24.5First straight RF Buncher in vacuum 1.Initial capture of π’s & μ’s into RF buckets. 2.Allow lower momenta π’s to decay into μ’s. L = 20 m R = 35 cm Bsol = 4.2 T 160 RF Cavities: V’max = 5 MV/m, f= 162.5 MHz φs=186°: P(μ−)=150  162 MeV/c 24.5 to 44.5 Second straight RF Buncher in 100 atm H2 w/ variably thick Be windows. 1.H2 gas allows higher RF gradient. 2.Be causes higher momenta π’s to interact, enhancing useful μ’s. 3.Transverse cooling. L = 20 m R = 35 cm Bsol = 4.2 T 160 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz φs=208  194°, P(μ−)=162  237 MeV/c 44.5 to 50.0 Match into HCC1.To match between straight solenoid into HCC. 2.Enhance μ capture due to transition occurring in match. L = 5.5 m (5.5 λ’s) R = 35 cm Bsol = 6.3 T  4.2 T 44 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz φs varied to maintain P(μ−)=237 MeV/c 50.0 to 350 HCC(Multi-Bunch)To cool string of multiple bunches of muons in 6D phase space. L = 300 m λ=1m R = 35 cm Bsol = 4.2 T V’max = 16 MV/m, f= 200,400,800 MHz 350 to 360Bunch Combiner Preparation (BCP) To transform string of bunches at same energy into string at different energies with head bunches at higher energies than trailing bunches. L = 10 m λ=1m R = 35 cm Bsol = 4.2 T V’max = 15 MV/m f= 204.08 MHz for 201.25 MHz spacing. 360 to 393Bunch Combiner (BC)To combine the multiple bunches in a single one via free drift in large | η | channel. L = 33 m λ=1m R = 35 cm Bsol = 4.2 T V’max = 0 393 to 693HCC(Single-Bunch)To cool single bunch of muons in 6D phase space.L = 300 m λ=1m R = 35 cm Bsol = 4.2 T V’max = 16 MV/m, f= 200,400,800 MHz

20. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 20 5 MV/m Vacuum 35 MV/m H2 100 atm @ 273K Σ{variable Be windows} = λ I (π)/2

21. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 21 Mu+ P vs t Pi+ P vs t Mu- P vs t Pi- P vs t (204.5, 236.3) Phase II HCC Upstream: Matching Section z = 50.0 m (End of Match)

22. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 22 H 2, 35 MV/m Vacuum, 5 MV/m ε T (acceptance) < 20 mm 162.5 MHz Current HCC Upstream: Two Straights

23. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 23 H 2, 35 MV/m Vacuum, 5 MV/m 162.5 MHz ε L (acceptance) < 40 mm Current HCC Upstream Emittances out of second straight are 11 mm-rad transverse by 378 mm-rad longitudinal. oTransverse is fine. oLongitudinal is ~10x’s too large. Need to transform a cigar shaped ε T xε ║ (11 x 378) into a football shaped one (20 x 40).

24. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 24 To transform a cigar ε T xε ║ into a football, we strive to have emittance exchange from longitudinal to transverse at a rate that can be cooled transversely, netting zero emittance growth transversely and cooling longitudinally. So, we look into the following for different cooling decrement schemes in the HCC at various kappa, with particular attention to low kappa values. Transverse stability Transverse equilibrium emittance Momentum acceptance Linear extrapolation Note at low kappa, we expect less transverse/longitudinal coupling, so the hope is that the momentum acceptance mostly applies to the transverse component and the RF holds onto the muons hot longitudinally. Current HCC Upstream

25. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 25 Transverse stability requires: 0 < G < R 2 or equivalently 0 < G/R 2 < 1 where Current HCC Upstream

26. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 26 Current HCC Upstream Emittances out of second straight: ε T =11 mm-rad x ε || = 378 mm-rad HCC(cooling optimized) acceptance: ε T =20 mm-rad x ε || = 40 mm-rad Need to transform a cigar shaped ε T xε ║ (11 x 378) into a football shaped one (20 x 40). Look into cooling at low κ. stable unstable

27. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 27 Equal Cooling κ = 0.1 Transverse Only Cooling κ = 0.1 Equal Cooling κ = 0.2 Equal Cooling κ = 0.3 Transverse Only Cooling κ = 0.2 Transverse Only Cooling κ = 0.3

28. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 28 Neither equal cooling decrements nor transverse only cooling provides the desired acceptance. Prior experience with Quasi Iso HCC work suggests the following possibilities to increase acceptance. 1.Enlarging R ref as well as R aperture. Will use R ref = R aperture = 30 cm (front end baseline). Previously, used R ref = 16 cm & R aperture = 35 cm (HCC baseline). 2.Increasing B fields. Equal cooling and transverse only fix B fields, which turn out to be rather low. Quasi-Iso allows Bsol to be a degree of freedom. 3.Try to simultaneously design for p transition ≥ 450 MeV/c and p ref = 225 MeV/c. This attempt is not totally consistent. The pseudo-p transition mentioned on slides going forward effectively defines the dispersion for a muon with p=p transition on the reference orbit. But, only a muon with p=p ref will be on the reference orbit. Despite the skewed accounting scheme for the dispersion, the exercise proved useful. Recall:

29. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 29 P ~transition = 750 MeV/c B sol = 2 T P ~transition = 850 MeV/c B sol = 2 T P ~transition = 450 MeV/c B sol = 2 T P ~transition = 850 MeV/c B sol = 2.3 T G/R 2 = 0.224 G/R 2 = 0.322

30. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 30 Ptransition (MeV/c)κ Bsol (T)Ď-1bd (T)bq (T/m)b2 (T)G/R2 Plow – PhighPEarliest Arrival (MeV/c) 4500.2521.126 0.19778 0.838970.125850.412100-300271 5500.2521.6530.270540.360160.054020.507100-345300 6500.2522.2850.35786-0.21441-0.032160.539100-402338 7500.2523.0230.45972-0.88475-0.132710.462100-455395 8500.2523.8660.57613-1.65084-0.247630.224100-326> 326 8500.252.33.8660.58700-1.26141-0.189210.322100-504406 8750.252.44.0930.62200-1.33809-0.200710.294100-521424 9000.252.54.3270.65790-1.42075-0.213110.269100-539445 9500.252.74.8140.73245-1.60403-0.240610.225100-572431 10500.253.25.8680.89607-1.91261-0.286890.159100-600~500; ~isochronous >400 P ~transition = 875 MeV/c B sol = 2.4 T P ~transition = 1050 MeV/c B sol = 3.2 T

31. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 31 To enhance longitudinal cooling, we investigated effect of adding a wedge: 1.Baseline is the 200 atm of H2 at 293 K as studied before. (200 atm) 2.Channel contains 100 atm of H2 at 293 K plus a cylindrical Be wedge 1.051 mm thick at the reference (r=30cm) between RF cavities 10 cm apart. (100 atm) Wedge has zero thickness on the z-axis and twice as thick at r=60 cm. Energy loss in Be equals that in H2. 3.Channel contains 60 atm of H2 at 293 K plus a cylindrical Be wedge 1.481 mm thick at the reference (r=30cm) between RF cavities 10 cm apart. (60 atm) Wedge has zero thickness on the z-axis and twice as thick at r=60 cm. Total energy loss is same as in both cases above. H2 density is at knee of breakdown curve. Current HCC Upstream: Wedge in Match

32. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 32 HCC Current HCC Upstream: Wedge in Match

33. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 33 HCC Current HCC Upstream: Wedge in Match

34. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 34 Current HCC Upstream: Wedge in Match

35. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 35 bunched beam Phase rotationToF(ns) P(GeV) Test with 3 bunches (ToF = -30, 0, 30 ns) ν = 0.405 GHz, E = 10 MV/m ¼ synchrotron oscillation at z = 2.5λ 35 Current HCC Downstream Katsuya Yonehara bunch 1 bunch 7 bunch 13 bunch 1 bunch 7 bunch 13

36. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 36 Phase slipping in HS magnet η = 0.72 Particles are aligned in timing at z = 49λ Note that Δt is too large to be in 200 MHz RF bucket 36 Current HCC Downstream bunched beam cont. Katsuya Yonehara bunch 1 bunch 7 bunch 13 bunch 1 bunch 7 bunch 13

37. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 37 Merging in isochronous HS magnet ν =0.2 GHz, E=5 MV/m η =0.04 37 Current HCC Downstream bunched beam cont. Katsuya Yonehara bunch 1 bunch 7 bunch 13 bunch 1 bunch 7 bunch 13 5 nsec

38. Muons, Inc. 3/1/2011MAP Winter Meeting at JLAB Cary Y. Yoshikawa 38 single particle ν =0.408 GHz, E=5 MV/m η =0.04 ¼ of synchrotron oscillation at z=4.2 λ Phase rotation in HS magnetPhase rotation in Bessel field magnet η = 0.72 Particles are aligned in timing at z = 33λ 8/20/1038MI, Friday meeting Current HCC Downstream Katsuya Yonehara