1. August 8, 2007 AAC'07 K. Yonehara 1 Cooling simulations for Muon Collider and 6DMANX Katsuya Yonehara Fermilab APC MCTF

2. August 8, 2007AAC'07 K. Yonehara2 Keys in this talk Feasible study of Helical Cooling Channel (HCC) toward to Muon Colliders –Matching + Cooling Magnets –Incorporate RF cavity 6DMANX

3. August 8, 2007AAC'07 K. Yonehara3 Design practical helical cooling magnet Siberian snake (conventional) type magnet Coil diameter: 1.0 m Maximum b field: 10 T Helical solenoid coil Coil diameter: 0.5 m Maximum b field: 6 T See M. Lamm’s talk for more detail Design HCC Magnet

4. Matching + Helical Cooling Magnets August 8, 2007AAC'07 K. Yonehara4 Helix period = 1.2 m Number of coils per period = 20 Coil length = 0.05 m Gap between coils = 0.01 m Current = 430.0 A/mm 2 Increase gap between coils from 10 to 40 mm HCC Downstream Matching Upstream Matching Design HCC Magnet Gap between coils = 0.04 m Current = 1075.0 A/mm 2

5. Ideas of including RF cavities in HCC August 8, 2007AAC’07 K. Yonehara5 Type 1: Inside coil Type 3: Isolate from HCC Type 2: In between coils Coil RF cavity HCC section RF section Incorporate RF cavity in HCC In progress

6. August 8, 2007AAC'07 K. Yonehara6 Design parameter in type 1 channel parameters  Bzbdbqbsf Inner d of coil Expected Maximum bE RF phase unitm TTT/mT/m2GHzcmTMV/mdegree 1st HCC1.61.0-4.31.0-0.20.50.450.06.016.4140.0 2nd HCC1.0 -6.81.5-0.31.40.830.08.016.4140.0 3rd HCC0.51.0-13.63.1-0.63.81.615.017.016.4140.0 Use a pillbox cavity (but no window this time). RF frequency is determined by the size of helical solenoid coil.  Diameter of 400 MHz cavity = 50 cm  Diameter of 800 MHz cavity = 25 cm  Diameter of 1600 MHz cavity = 12.5 cm The pressure of gaseous hydrogen is 200 atm at room temp to adjust the RF field gradient to be a practical value.  The field gradient can be increased if the breakdown would be well suppressed by the high pressurized hydrogen gas. Thermal isolation between coils and cavities must be addressed as an engineering issue. Incorporate RF cavity in HCC Helical solenoid coil RF cavity Window GH2 RF is completely inside the coil.

7. August 8, 2007AAC'07 K. Yonehara7 Simulation result in type 1 channel Acceptance strongly depends on the RF frequency. Three HCCs can be connected and make one large HCC section. In this case, transmission efficiency in a whole channel is 50 % because of the mismatching between HCCs. This can be improved by making longer HCCs or incorporating more frequencies. Incorporate RF cavity in HCC

8. Simulation result in type 2 channel August 8, 2007AAC'07 K. Yonehara8 Helical period = 1.0 m Number of coils = 20 Coil length = 0.01 m RF length = 0.04 m Coil diameter = 0.32 m RF diameter = 0.5 m RF frequency = 400 MHz Field gradient = 20 MV/m GH2 pressure = 200 atm at room temp 20 RF cavities per 1 m period in each design RF Occupation = Total RF cavity length/Helical period Increasing RF occupation allows larger longitudinal acceptance but distorts b field quality (see red vs blue lines). RF is not limited by size of HCC (100 % RF occupation is type 1 design). Most Feasible design!! Thermal isolation can be addressed as an engineering issue. Incorporate RF cavity in HCC Helical solenoid coil RF cavity Window GH2 Best parameters (red) RF is in between coils.

9. August 8, 2007AAC'07 K. Yonehara9 Concept of 6DMANX Demonstration –Six dimensional helical cooling theory Demonstrate 6D cooling, Continuous emittance exchange, Exceptional cooling performance… –Test simulation tool 6DMANX

10. August 8, 2007AAC'07 K. Yonehara10 Highlights of 6DMANX design No RF cavity inside HCC –Save R&D time & money Use liquid helium (LHe) as absorber –No big safety issue –Thin windows at both ends of channel Momentum dependent (z-dependent) field map –Maximum field must be less than 6 T 6DMANX

11. August 8, 2007AAC'07 K. Yonehara11 Overview of MANX channel Use Liquid He absorber No RF cavity Length of cooling channel: 3.2 m Length of matching section: 2.4 m Helical pitch  : 1.0 Helical orbit radius: 25 cm Helical period: 1.6 m Transverse cooling: ~1.3 Longitudinal cooling: ~1.3 6D cooling: ~2 6DMANX

12. August 8, 2007AAC'07 K. Yonehara12 6DMANX Simulation study 6DMANX Initial beam size (rms) = ± 60 mm  p/p (rms) = ± 40/300 MeV/c x’ and y’ (rms) = ± 0.4 6D cooling factor = 2.0 Transmission efficiency ≥ 30 % Need to make a correction of unstable Phase space.

13. Summary We now have convincingly shown in simulations that HCC provides significant 6D cooling needed for Muon Colliders. Matching + HCC magnets can be built by using helical solenoid coils. Three options to include RF cavity in HCC are shown in this talk. –Currently two are shown to be feasible in simulations. –Remaining issues can be addressed as engineering exercises. We need to demonstrate the HCC theory and validate simulation results. –6DMANX is designed to investigate for these requirements. August 8, 2007AAC'07 K. Yonehara13