1. Helical Cooling Channel Simulation with ICOOL and G4BL K. Yonehara Muon collider meeting, Miami Dec. 13, 2004 Slide 1

2. Contents Introduction Simulation results –ICOOL and G4BL Present interesting –Beam dynamics –Low momentum problem –Design RF cavity Summary/Next to do Muon collider meeting, Miami Dec. 13, 2004 Slide 2

3. Introduction Muon collider meeting, Miami Dec. 13, 2004 Slide 3 Analytical six-dimensional cooling demonstration in the helical cooling channel (HCC) with the high pressure gaseous hydrogen absorber has been done ( MuCoolNote0284 ). We need to verify the new idea by a numerical method. ICOOL and G4BL

4. Introduction Muon collider meeting, Miami Dec. 13, 2004 Slide 4 Now we can analyze the beam dynamics in the simulations and develop the channel for applying to a muon collider.

5. Collaborators D. M. Kaplan Illinois Institute of Technology, Chicago, IL Muon collider meeting, Miami Dec. 13, 2004 Slide 5 M. Alsharo’a, R. P. Johnson, P. Hanlet, K. Paul, T. J. Roberts Muons, Inc., Batavia, IL K. Beard, A. Bogacz, Y. S. Derbenev JLab, Newport News, VA

6. ICOOL and G4BL Specifications ICOOL –Fortran –Based on Geant3 –Tested many times by many people –Easy to learn G4BL –C++ –Based on Geant4 –Flexible –Easy to develop Muon collider meeting, Miami Dec. 13, 2004 Slide 6

7. ICOOL and G4BL Helix coil Muon collider meeting, Miami Dec. 13, 2004 Slide 7 Spin rotator coil

8. ICOOL and G4BL Helical orbit Muon collider meeting, Miami Dec. 13, 2004 Slide 8

9. G4BL ICOOL and G4BL Layout of HCC Muon collider meeting, Miami Dec. 13, 2004 Slide 9 Reference orbit Particle orbit x y ICOOL HCC Length: 10 m Period: 1 m Radius: 0.65 m z

10. ICOOL and G4BL Simulation parameters Muon collider meeting, Miami Dec. 13, 2004 Slide 10 Parameters Value in simulation for  + Unit Beam momentum, p 200 MeV/c Solenoid field -5.45 T Helix period 1.00 m Helical magnet inner radius 0.65 m Transverse field at beam center1.24 T Helix quadrupole gradient-0.206 T/m Helix orbit radius, a 0.159 m Dispersion factor, D1.706 Accelerating RF field amplitude 33.0 (32.7 in G4BL) MV/m Frequency 0.201 GHz Absorber gas pressure 400 atm Absorber energy loss rate 14.9 MeV/m

11. Muon collider meeting, Miami Dec. 13, 2004 Slide 11 These plots include all particles. ICOOL and G4BL First result

12. Muon collider meeting, Miami Dec. 13, 2004 Slide 12 ICOOL and G4BL Summary We first observed the cooling effect of HCC in the simulations which is predicted by the analytical method. The simulation result in ICOOL shows a good agreement (discrepancy <10 %) with G4BL. This could be a proof test for both codes.

13. Beam dynamics No absorber Muon collider meeting, Miami Dec. 13, 2004 Slide 13 dr vs p r z vs dr Reference orbit Start point

14. Beam dynamics With GH2 absorber z vs p r z vs dr Muon collider meeting, Miami Dec. 13, 2004 Slide 14 z, dt vs dE Particle direction

15. Beam dynamics Summary We just start considering this study. We will see more analysis results soon. We observe a strong coupling between transverse and longitudinal motions. Muon collider meeting, Miami Dec. 13, 2004 Slide 15

16. Low momentum problem Introduction The design of helical cooling channel for a lower momentum muon is practical since it can significantly reduce the strength of helix and solenoid fields. However, we never succeed to see a nice cooling result in a lower momentum region. We noticed that the dispersion factor should be modified to take into account the correction of the energy loss process. This correction should be larger for a lower momentum particle since the energy loss rate of it is larger than that of a higher momentum particle. Muon collider meeting, Miami Dec. 13, 2004 Slide 16

17. Low momentum problem Effective dispersion factor D eff = D lattice + D eloss D lattice = D eloss = a p dp da dE/ds p dp d(dE/ds) Muon collider meeting, Miami Dec. 13, 2004 Slide 17

18. p (MeV/c) 150-0.483 200-0.265 250-0.138 3740.0 D eloss Low momentum problem Estimate D eloss Muon collider meeting, Miami Dec. 13, 2004 Slide 18

19. Low momentum problem Analysis of simulation results Use quadratic function for curve fitting: Easy to extract the peak position Muon collider meeting, Miami Dec. 13, 2004 Slide 19 Merit factor = cooling facter Transmission efficiency +

20. Low momentum problem Analyzed result p (MeV/c) Peak position (fitting curve) Distance from 374 MeV/c Dispersion factor by energy loss Fraction between columns 4 & 5 3740.2290.0 2500.0697-0.160-0.1380.86 200-0.0962-0.326-0.2650.81 150-0.321-0.550-0.4830.88 Muon collider meeting, Miami Dec. 13, 2004 Slide 20

21. Low momentum problem Summary (1) The additional dispersion factor caused by the energy loss effect well reproduces the peak position in the merit factor curve. However, we still see a small fraction in the effective dispersion factor. This could be caused by another dispersion effect. Muon collider meeting, Miami Dec. 13, 2004 Slide 21

22. Low momentum problem Evolution of emittances Muon collider meeting, Miami Dec. 13, 2004 Slide 22

23. Low momentum problem Acceptance and Equilibrium emittance p (MeV/c) Initial/Final  tran (mm rad) Initial/Final  long (mm) Initial/Final  6D (mm 3 )  p/p 37427.8/3.3671.0/7.6848900/57.4120/374 25022.5/1.9673.9/2.7232000/6.6260/250 20018.3/1.9166.4/2.4717500/5.1555/200 15014.3/2.9848.3/5.868660/20.045/150 Muon collider meeting, Miami Dec. 13, 2004 Slide 23

24. Low momentum problem Summary (2) The acceptance of higher momentum beam is larger but the cooling decrement is smaller while the cooling decrement in lower momentum beam is larger but the acceptance is smaller. So the optimum beam momentum seems to be 200 ~ 250 MeV/c. The optimum beam momentum can be changed by the absorber density (pressure). Muon collider meeting, Miami Dec. 13, 2004 Slide 24

25. Design RF cavity Install bessel function type RF cavities in the simulation –Frequency > 200, 400, 800, and 1600 MHz. –Location > We tested two types of location of the center of RF cavities; one is on an HCC axis (no offset) and the other is on a reference orbit (with offset). –Shape > We design a unique shape of RF cavities. We will discuss them in future. Muon collider meeting, Miami Dec. 13, 2004 Slide 25

26. Design RF cavity Offset RF Muon collider meeting, Miami Dec. 13, 2004 Slide 26 No offset With offset + + 1 2 3 4 5 1 2 3 4 5

27. Muon collider meeting, Miami Dec. 13, 2004 Slide 27 Design RF cavity Evolution of emittance frequency = 0.2 GHz Cavity radius ~ 0.6 m

28. Design RF cavity Simulation result p (MeV/c) Initial/Final  tran (mm rad) Initial/Final  long (mm) Initial/Final  6D (mm 3 ) Uniform E z 18.3/1.8864.0/2.4217200/4.83 With offset18.9/1.5774.1/4.5420100/6.46 No offset16.2/5.4664.0/3.8512800/41.1 Muon collider meeting, Miami Dec. 13, 2004 Slide 28

29. The RF cavities with offset works well. However, we observe a less reduction of the longitudinal emittance by using the offset type RF cavities. We need to improve the propagation of longitudinal beam cooling in HCC. Design RF cavity Summary Muon collider meeting, Miami Dec. 13, 2004 Slide 29

30. Summary/Next to do The two simulations work pretty well. We study beam dynamics in HCC. We found the effective dispersion factor. We design several type of RF cavities. We figure out the matching problem. Muon collider meeting, Miami Dec. 13, 2004 Slide 30