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Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory

Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory Cary Yoshikawa Chuck Ankenbrandt Dave Neuffer Katsuya Yonehara. Design upstream of HCC for increased acceptance Design downstream of HCC for bunch merging.

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Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory

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  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 MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  2. 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 Outline • Motivation • Evolution of the QIHC (2 snapshots) • Configuration in the Phase II proposal, which was awarded and is funding current studies. • Current configuration • Summary & Future MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  3. Motivation 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: • 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 γT 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). • 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: MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  4. Configuration in the Phase II Proposal MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

  6. Phase II HCC Upstream:Matching Section Initial design was based on a reference with constant momentum (237 MeV/c) and γT 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. MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

  8. Phase II HCC Upstream:Matching Section In principle, it is possible to achieve monotonic RF bucket growth by manipulating the phase φs,γT (via ), and field gradient . MAP 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. KE(MeV) 300 f=204.08 MHz V’ = 15 MV/m 9.6m in QIHC η = 0.05 εL=0.002m/bunch 0 -4 -4 20 20 cτ(m) MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  10. Phase II HCC Downstream:Bunch Recombiner Drift 32.5 m in QIHCC w/ η= 0.43 KE(MeV) 300 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 0 20 -4 20 -4 cτ(m) 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) -4 20 MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

  12. Current HCC Upstream: Match … p P(MeV/c) 450 MeV/c Bz(on z-axis) = 2.4 T Bz(on ref) = 2.3 T Bφ(on z-axis) = 0.62200 T dbφ/dρ (on z-axis) = -1.33809 T Pref = 225 MeV/c free drift for 45.2 m t t(nsec) • Emittances out of second straight: • εT=11 mm-rad x ε||= 378 mm-rad • HCC(cooling optimized) acceptance: • εT=20 mm-rad x ε||= 40 mm-rad • Need to transform a cigar shaped εTxε║ (11 x 378) into a football shaped one (20 x 40). 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. MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  13. Current HCC Upstream: Wedge in Match • To enhance longitudinal cooling, we studied effect of adding a cylindrical wedge. • H2:200 atm: No wedge, only H2 at 200 atm at 293 K. • H2:100 atm: Be wedge ~1mm at reference to loose same energy as 100 atm H2. • H2: 60 atm: Max Be wedge ~1.48 mm w/ H2 at knee of breakdown. Emax = 32 MV/m φs~14º Pref = 225 MeV/c f = 201.25 MHz Bz(z-axis) = 2.4T Bz(on ref) = 2.3T Lowest emittance (~equilibrium) at z=30m. Highest emittance (acceptance) at z=0. • 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. MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

  15. Phase II HCC Downstream:Bunch Recombiner t(ns) bunch 1 bunch 7 bunch 13 Drift 46.5 m in QIHCC w/ η= 0.72 t(ns) p(GeV/c f=200 MHz V’ = 5 MV/m in QIHC η = 0.04 5 nsec p(GeV/c • 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. MAP 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 εL 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, γT (via ), and field gradient . MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  17. Conclusions and Future (downstream of HCC) • 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. MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  18. Back up MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  19. Configuration in the Phase II Proposal MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  20. 35 MV/m H2 100 atm @ 273K Σ{variable Be windows} = λI(π)/2 5 MV/m Vacuum MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

  22. Current HCC Upstream: Two Straights εT(acceptance) < 20 mm 162.5 MHz H2, 35 MV/m Vacuum, 5 MV/m MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  23. Current HCC Upstream 162.5 MHz Vacuum, 5 MV/m H2, 35 MV/m εL(acceptance) < 40 mm • Emittances out of second straight are 11 mm-rad transverse by 378 mm-rad longitudinal. • Transverse is fine. • Longitudinal is ~10x’s too large. • Need to transform a cigar shaped εTxε║ (11 x 378) into a football shaped one (20 x 40). MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  24. Current HCC Upstream • To transform a cigar εTxε║ 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. MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  25. Current HCC Upstream Transverse stability requires: 0 < G < R2 or equivalently 0 < G/R2 < 1 where MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

  27. Transverse Only Cooling κ = 0.1 Equal Cooling κ = 0.1 Transverse Only Cooling κ = 0.2 Equal Cooling κ = 0.2 Transverse Only Cooling κ = 0.3 Equal Cooling κ = 0.3 MAP 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. • Enlarging Rref as well as Raperture. • Will use Rref = Raperture = 30 cm (front end baseline). Previously, used Rref = 16 cm & Raperture = 35 cm (HCC baseline). • 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. • Try to simultaneously design for ptransition≥ 450 MeV/c and pref = 225 MeV/c. • This attempt is not totally consistent. The pseudo-ptransition mentioned on slides going forward effectively defines the dispersion for a muon with p=ptransition on the reference orbit. But, only a muon with p=pref will be on the reference orbit. Despite the skewed accounting scheme for the dispersion, the exercise proved useful. Recall: MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  29. P~transition = 450 MeV/c Bsol = 2 T P~transition = 750 MeV/c Bsol = 2 T P~transition = 850 MeV/c Bsol = 2 T P~transition = 850 MeV/c Bsol = 2.3 T G/R2 = 0.322 G/R2 = 0.224 MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  30. P~transition = 1050 MeV/c Bsol = 3.2 T P~transition = 875 MeV/c Bsol = 2.4 T MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  31. Current HCC Upstream: Wedge in Match • To enhance longitudinal cooling, we investigated effect of adding a wedge: • Baseline is the 200 atm of H2 at 293 K as studied before. (200 atm) • 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. • 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. MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  32. Current HCC Upstream: Wedge in Match HCC MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  33. Current HCC Upstream: Wedge in Match HCC MAP Winter Meeting at JLAB Cary Y. Yoshikawa

  34. Current HCC Upstream: Wedge in Match MAP Winter Meeting at JLAB Cary Y. Yoshikawa

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

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

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

  38. single particle Current HCC Downstream Katsuya Yonehara ν =0.408 GHz, E=5 MV/m η =0.04 ¼ of synchrotron oscillation at z=4.2 λ η = 0.72 Particles are aligned in timing at z = 33λ Phase rotation in HS magnet Phase rotation in Bessel field magnet MAP Winter Meeting at JLAB Cary Y. Yoshikawa 8/20/10 MI, Friday meeting 38

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