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Study of Helical Cooling Channel

Muons, Inc. Study of Helical Cooling Channel. Katsuya Yonehara APC, Fermilab. Agenda for HCC session. HCC simulation effort, K. Yonehara Test HCC theory Optimize HCC parameter by using numerical simulation HCC magnet design effort, V. Kashikhin Magnet design status Demonstration test

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Study of Helical Cooling Channel

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  1. Muons, Inc. Study of Helical Cooling Channel Katsuya Yonehara APC, Fermilab

  2. Agenda for HCC session • HCC simulation effort, K. Yonehara • Test HCC theory • Optimize HCC parameter by using numerical simulation • HCC magnet design effort, V. Kashikhin • Magnet design status • Demonstration test • etc • HCC RF study, M. Neubauer • Design dielectric loaded RF cavity • etc MC Design workshop @BNL K. Yonehara

  3. New Fernow-Neuffer plot Goal phase space ν = 0.325 GHz λ = 1.0 – 0.8 m ν = 0.65 GHz λ = 0.5 – 0.3 m 100 % @ z = 0 m Study2a 97 % @ z = 40 m 91 % @ z = 49 m REMEX 89 % @ z = 129 m ν = 1.3 GHz λ = 0.3 m 84 % @ z = 129 m 84 % @ z = 303 m PIC • GH2 pressure = 160 atm • 60 μm Be RF window • E ~ 27 MV/m • Detailed parameter will be given in later slide (slide 15)

  4. Helical Cooling Channel (HCC)

  5. Stability condition in transverse phase space Stability condition is, therefore with Stability condition can be represented by g (field index) and q (= kc/k-1) and MC Design workshop @BNL, K. Yonehara

  6. Test cooling decrement Fdrag : drag force Λ±= Λγ = 0.047 /meter MC Design workshop @BNL, K. Yonehara

  7. Benefit of cryogenic operation • Low resistivity RF cavity • High RF Q value • Thin skin depth • Low gas pressure • Thin pressure window MC Design workshop @BNL, K. Yonehara

  8. Design RF window in HCC HCC is entirely filled with GH2 Here is some advantage: • Any hydrogen safety window may not be required in beam path • Only RF window is needed to generate ideal E field • GH2 works on RF window as a coolant • RF power deposition into RF window won’t be issued Ex) Thickness of RF window in 200 MHz vacuum cavity is designed 380 μm made of Beryllium to avoid frequency shift caused by RF power deposition in RF window MC Design workshop @BNL, K. Yonehara

  9. What is the minimum RF window thickness? Skin depth Aluminum window (ρ = 2.82×10-8 Ω/m @ room temp, ν = 325 MHz) m Beryllium window(ρ = 18.5×10-8 Ω/m @ room temp, ν = 325 MHz) m The modeled RF window in simulation is five times thicker than δ (ex. 60 μm Be window) • This assumption will be premature • For instance, the Lorentz force on the window is not involved • More mechanical analysis will be needed MC Design workshop @BNL, K. Yonehara

  10. RF window effect • Compare transmission efficiency in HCC with three different • window materials (no material, Aluminum, Beryllium) • Window thickness is 0.1 mm εNo window = 100 % εBe window = 89 % εAl window = 67 % MC Design workshop @BNL, K. Yonehara

  11. Consider pressure end plate • End plate is not involved in simulation, yet • More mechanical analysis is needed to determine thickness • of entrance/exit pressure windows Here is some estimation based on past mechanical analysis Past result: Required window thickness = 1” (Inconel 718) with 500 mmΦ with GH2 pressure = 50 atm (= 200 atm at 300) Now, GH2 pressure is 40 atm, assume window has a curve shape that makes 3 times stronger than flat plate, and window size is 320 mmΦ Present design: Required window thickness = 5 mm (Inconel 718) Estimated Δp in entrance window ∼ 10 MeV/c Thickness of exit window will be much thinner than 5 mm since beam size is approximately 16 times smaller than initial beam size MC Design workshop @BNL, K. Yonehara

  12. Correction non-linear dE/ds effect dE/ds [GeV/m] Make some correction in dispersion function 160 atm GH2 where D’ can be determined from dp/ds μ Momentum [GeV/c] Dispersion = 0.13 m (Close to isochronous condition) Dispersion = 0.35 m (path length is overestimated) Dispersion = 0.28 m (dE/ds correction) Long path at hi p Short path at lo p MC Design workshop @BNL, K. Yonehara

  13. RF bucket dependence v = 400 MHz, κ=1.0, λ=1.0 m GH2 pressure = 200 atm (at room temp) Old design New design E = 31.4 MV/m, ψ=160˚, Lrf = 100 mm E = 16.0 MV/m, ψ=140˚, Lrf = 50 mm ΔE [GeV] ΔE [GeV] MC Design workshop @BNL, K. Yonehara

  14. Past studies by Balbekov • HCC has been simulated with totally independent simulation code by Balbekov • The simulation results are reproduced in two different simulation codes • He also pointed out that there is strong frequency dependence on the longitudinal • acceptance • The admittance of HCC is given in PRSTAB paper MC Design workshop @BNL, K. Yonehara

  15. Emittance evolution in HCC Let us revisit new Fernow Neuffer plot on slide 3 εLongitudinal [mm] ν = 0.325 to 0.65 GHz Beam phase space is self-adjusted ν = 0.65 to 1.3 GHz MC Design workshop @BNL, K. Yonehara εTransverse [mm rad]

  16. Parameter list MC Design workshop @BNL, K. Yonehara

  17. Beam parameter Beta tune Q+ = 0.918 Beta tune Q- = 0.730 Beta function = 0.27 m at λ= 1.0 m 0.09 m at λ = 0.3 m Momentum slip factor η = 0.661 Dispersion D = 0.28 m Cooling decrement Λ/3 = 0.0184 /m MC Design workshop @BNL, K. Yonehara

  18. Transmission efficiency and beam size 1 2 3 4 5 6 7 8 ν = 0.325 to 0.65 GHz ν = 0.65 to 1.3 GHz 1 ν = 0.325 to 0.65 GHz 2 3 ν = 0.65 to 1.3 GHz 5 6 4 8 7 Δp/p and beam size are taken full width of distribution MC Design workshop @BNL, K. Yonehara

  19. Emittance evolution 1 ν = 0.325 to 0.65 GHz 2 ν = 0.65 to 1.3 GHz 3 5 4 6 8 7 Merit factor = ε6D,init/ε6D,final × Transmission ε MC Design workshop @BNL, K. Yonehara

  20. Remaining challenge issue • Mechanical design of HCC • Need HCC RF cavity and HCC magnet studies • Some study has been done (see Mike & Vladimir) • Is it possible to generate E = 27 MV/m? • Need cryogenic study • Need mechanical analysis • Pressure vessel, Support, etc • Investigate hydrogen safety • High pressurizing GH2 filled RF cavity test • Design 6D demo experiment • Including with the study of phase space matching MC Design workshop @BNL, K. Yonehara

  21. Any more simulation effort? I can reproduce these simulation results in real HCC if we can generate… • E = 27 MV/m • Maximum B = 14 Tesla • Solve matching issue If E = 16 MV/m, then • Merit factor ~2 103 (tested with short channel) MC Design workshop @BNL, K. Yonehara

  22. Summary • First full HCC simulation has been done • Merit factor > 105 in z = 300 meters • See individual beam element study, HCC RF and magnet in following speakers • All simulations have been done in g4bl-v1.16 (Thanks Tom!) MC Design workshop @BNL, K. Yonehara

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