1. Geant Simulation of Muon Cooling Rings
Amit Klier
University of California Riverside

2. A. Klier - Geant simulation
Outline
A short reminder from Nufact03
The RFOFO ring
Geometry
Software improvements
Simulation results
The small dipole ring
Some Results
June
A. Klier - Geant simulation

3. A. Klier - Geant simulation
Muc_Geant
Modified, data-driven Geant3 application for simulating muon cooling
Electric fields added
Runge-Kutta changed to include changing electric fields (eg RF cavities)
Realistic magnetic fields can be read from external field maps
June
A. Klier - Geant simulation

4. From Nuact03 Tetra ring simulated Rajendran Raja – Nufact 03
June
A. Klier - Geant simulation

5. A. Klier - Geant simulation
The RFOFO ring
A few code changes w.r.t. Tetra
Realistic magnetic field maps read-in (R. Godang, S. Bracker – MC-Note 271)
June
A. Klier - Geant simulation

6. A. Klier - Geant simulation
The RFOFO ring
Full Geant simulation: A. Klier – MC-Note 298
June
A. Klier - Geant simulation

7. A. Klier - Geant simulation
The ring geometry
33 m circumference
12 cells (2.75m):
A wedge absorber
opening angle 110°,
pointing ’upwards’
6 RF cavities
28.75 cm long,
iris radius 25 cm
flat E field in z direction
2 tilted solenoids
inner/outer r = 77/88 cm
tilt angle ±3°
Only for display here
June
A. Klier - Geant simulation

8. Closed orbits in a single cell
Solid line – the reference orbit
200 MeV
270 MeV
227 MeV
250 MeV
227 MeV
250 MeV
E = 200 MeV
E = 270 MeV
June
A. Klier - Geant simulation

9. Software improvements
ICOOL input/output format used, ecalc9 can be used to calculate emittance
Use initial time of particle at entry
Use virtual detectors
June
A. Klier - Geant simulation

10. A. Klier - Geant simulation
Cooling of a muon beam
June
A. Klier - Geant simulation

11. A. Klier - Geant simulation
Comparison with ICOOL
Transmission
6-D emittance
June
A. Klier - Geant simulation

12. A. Klier - Geant simulation
More comparisons
Results after 10 turns:
Merit factor
Trans.
W/O decay
With decay
Merit
Factor
Balbekov
(MC-264)
70%
56% 55
ICOOL
(Fernow) --
58% 66
Geant
72%
57% 70
June
A. Klier - Geant simulation

13. Change beam entry angle
June
A. Klier - Geant simulation

14. A. Klier - Geant simulation
The small dipole ring
“Weak” (edge) focusing
(ideally) scaling
Filled with
~10 Atm.
hydrogen
77K
Dipole field ~ 2 T
For P~200 MeV/c, the radius should be ~60 cm
June
A. Klier - Geant simulation

15. A. Klier - Geant simulation
Field map (from S. Kahn)
By in a single quadrant
By at R=60 cm
Return yoke
June
A. Klier - Geant simulation

16. A. Klier - Geant simulation
Reference orbit
Scale B down to 90%
closed orbit:
P= MeV/c
Rmin=56.32 cm
(x=0 in virtual detectors)
Rmin
Virtual detector plane
RF cavity (active region)
June
A. Klier - Geant simulation

17. A. Klier - Geant simulation
Ellipses
Stable up to y~13 cm
Y plane symmetry imposed
June
A. Klier - Geant simulation

18. A. Klier - Geant simulation
Acceptance of the ring
“A blob”
Py=~19 MeV/c
y=~8.5 cm
Px=~34 MeV/c
More “natural” decrease
with no x-z plane symmetry
x=~6.5 cm
June
A. Klier - Geant simulation

19. “Cooling” with no scattering
Xinitial=6 cm
Yinitial=8 cm
tinitial= –1.5 ns
Xcentral=0.04 cm
Ycentral=0 cm
tcentral=0 ns
PXinitial=30 MeV/c
PYinitial=17.5 MeV/c
Einitial=213 MeV
PXcentral=0.12 MeV/c
PYcentral=0 MeV/c
Ecentral=201.8 MeV
June
A. Klier - Geant simulation

20. Software improvements
More flexibility – less “hard-coding”, more external parameters
Field map reading code used to be RFOFO-specific, now more general
More RF parameters
Cavities in small dipole ring are off-center
So far, only perfect pillbox (or flat field..) cavity are simulated
Flexibility: different frequencies, gradients, types can be used in the same channel
June
A. Klier - Geant simulation

21. A. Klier - Geant simulation
To do
Simulate the small dipole ring with a beam
Introduce more realistic features:
Injection
Detectors
June
A. Klier - Geant simulation

22. A. Klier - Geant simulation
June
A. Klier - Geant simulation

23. A. Klier - Geant simulation
Additional Slides
June
A. Klier - Geant simulation

24. A. Klier - Geant simulation
Comparison with ICOOL
Transverse emittance
Longitudinal emittance
June
A. Klier - Geant simulation