1. Simulating the RFOFO Ring with Geant Amit Klier University of California, Riverside Muon Collaboration Meeting Riverside, January 2004

2. Jan. 28, 2004Simulating RFOFO with GEANT 2 OUTLINE Basics - geometry and magnetic field Setting the parameters Reference orbit and the clock Single particles in the ring “ Cooling ” with an Ideal Absorber Acceptance and RF parameters Cooling of a beam With/without muon decay Comparing to other results

3. Jan. 28, 2004Simulating RFOFO with GEANT 3 Basic ingredients Simulation software data-driven Geant v3.21 (R. Raja) Geometry from B. Palmer, R. Fernow, V. Balbekov (MC-Note 264) Realistic magnetic field maps – external (R. Godang, S. Bracker: MC-Note 271)

4. Jan. 28, 2004Simulating RFOFO with GEANT 4 The ring geometry 33 m circumference 12 cells (2.75m): LH 2 wedge absorber – opening angle 110°, pointing upwards no windows 6 RF cavities – 28.75 cm long, acceptance radius 25 cm 2 tilted solenoids inner/outer r = 77/88 cm tilt angle ±3° (only for display here)

5. Jan. 28, 2004Simulating RFOFO with GEANT 5 A view of a single cell

6. Jan. 28, 2004Simulating RFOFO with GEANT 6 3-D view of the RFOFO ring

7. Jan. 28, 2004Simulating RFOFO with GEANT 7 Setting the ring parameters The reference orbit Run without RF acceleration or absorbers Find a closed orbit (periodic in cells) Start at the middle of the wedge absorber – symmetry plane  One of 2 point in which p T vanishes (with no RF and absorber)

8. Jan. 28, 2004Simulating RFOFO with GEANT 8 With only magnetic field turned on The ring shows stability for initial p z ’ s in the range ~165 – 260 MeV/c The strategy: Find closed orbits for various initial P z x and y dependence  dispersion functions Set the clock – determine RF cavity entry times (the clock ’ s rotation frequency should be an integer  RF frequency)  Then RF cavities and absorbers can be turned on

9. Jan. 28, 2004Simulating RFOFO with GEANT 9 Closed orbits in a single cell Solid line – the reference orbit 270 MeV 250 MeV 227 MeV E = 200 MeV 200 MeV 227 MeV 250 MeV E = 270 MeV

10. Jan. 28, 2004Simulating RFOFO with GEANT 10 Dispersion functions at the center of the wedge

11. Jan. 28, 2004Simulating RFOFO with GEANT 11 Setting the clock RF frequency: f = 201.25 MHz Set the entry times of the RF cavities p z =200.96 MeV/c (E  227 MeV)  the 25 th harmonic (actually, ~201.26 MHz was the closest I could get)

12. Jan. 28, 2004Simulating RFOFO with GEANT 12 Turn on RF and LH 2 absorber Use an “ ideal ” absorber no multiple scattering, straggling Simplified RF acceleration field: In the cavity volume (cavity coordinates): E x =E y =0, E z =G · sin[  (t-t ent )+  ent ] (G=13.5 MV/m,  ent =-13° for the single-particle simulation) Inject muons at 5 initial points in each phase space coordinate central value, ±1,2  (Gaussian beam from MC-264)

13. Jan. 28, 2004Simulating RFOFO with GEANT 13 Perfect absorber – perfect cooling

14. Jan. 28, 2004Simulating RFOFO with GEANT 14

15. Jan. 28, 2004Simulating RFOFO with GEANT 15 Introducing “ realistic ” absorbers.. Turn on all processes (except muon decay) Looks like a big mess! But only a few particles are shown here! High statistics are needed to simulate cooling – a beam

16. Jan. 28, 2004Simulating RFOFO with GEANT 16 The beam Gaussian distributions (from MC-264):  x =  y = 4.25 cm  p x =  p y = 30 MeV/c  z = 7 cm (  cT = 8 cm in the Note)  p z = 22.5 MeV/c (   E = 20 MeV in the Note) To find the best acceptance: 400 muons, no decay, ideal absorber Count the number of muons after 6 ring turns ( “ stable ” ) For cooling simulation: 1600 muons, w/ & w/o decay, “ realistic ” absorber

17. Jan. 28, 2004Simulating RFOFO with GEANT 17 Finding the best acceptance using ideal absorber  ent ~ -2 o maximum @ ~14 MV/m

18. Jan. 28, 2004Simulating RFOFO with GEANT 18 Simulating beam cooling with a “ realistic ” absorber A Gaussian beam of 1600 muons was generated with all physics processes on The same beam without muon decay – performance cross-check Emittance calculation (similar to ECALC9) Slightly different cuts; No transverse amplitude – momentum correlation (  L calculated only from E-t covariance matrix)

19. Jan. 28, 2004Simulating RFOFO with GEANT 19 The beam in 15 turns (no muon decay)

20. Jan. 28, 2004Simulating RFOFO with GEANT 20 Cooling performance: transmission, 2-D emittances

21. Jan. 28, 2004Simulating RFOFO with GEANT 21 Cooling performance: 6-D emittance, merit factor

22. Jan. 28, 2004Simulating RFOFO with GEANT 22 Performance after 10 turns – comparison to other simulations ICOOL (MC-239) Balbekov (MC-264) Geant (current) Transmission, no decay (%) 617064 Transmission with decay (%) 505651 Merit factor5055~40 Possible reason for lower merit factor: smaller initial beam (longitudinal)

23. Jan. 28, 2004Simulating RFOFO with GEANT 23 Why do we see the jump in longitudinal emittance? (first few turns)

24. Jan. 28, 2004Simulating RFOFO with GEANT 24 Conclusions Geant performance shows good agreement with other simulations (ICOOL, Balbekov) lower merit factor maybe due to different initial beam To be done: Use “ standard ” ECALC9 to calculate emittance More realistic ring – absorber windows, injection, etc. Geant-Simulate other cooling rings (e.g. Kirk-Garren) – with R. Godang, S. Kahn, EE working group MC-Note in preparation, to be published soon …