1. Zgoubi tracking study of the decay ring
David Kelliher
ASTeC/STFC/RAL

2. Racetrack storage ring
Consists of a production straight, matching section and an arc.
Ring circumference m.
Neutrino production efficiency of 37.3 %
Diagram by Marco Apollonio

3. Zgoubi lattice description
MULTIPOL magnets used to describe all magnets in the racetrack
Rectangular magnets with straight magnetic field lines.
Fringe fields not included
Sharp edge field model i.e. Wedge angle vertical first order focusing effect

4. MAD-X and Zgoubi comparison
Tunes
Zgoubi
MAD-X Qx Qy
Centre of production straight
Zgoubi
MAD-X
x [m]
152.97
153.00
y [m]

5.  function comparison

6. Beam envelope Single particle tracking at 30  mm normalised emittance
Beam size in production straight magnets ~ 30cm
in arc magnets ~ 12 cm
Horizontal aperture requirement in matching section slightly larger than in the production straight

7. Transverse phase space
Single particle tracking, p/p = 0
Particle with 30  mm normalised emittance in both planes tracked successfully 1000 turns
Some smearing in vertical phase space.

8. Amplitude detuning
Calculate tune at various particle amplitudes by finding the peak in the Fourier of the turn-by-turn coordinates.
Vertical tune increases with amplitude, horizontal remains constant
Source of smearing in vertical phase space yet to be determined

9. Debunching study Start at centre of long straight
30 Pi mm normalised emittance in both transverse planes
2% rms momentum spread to accommodate most of beam from the FFAG
2.5ns rms bunch length given by rf period.
Uniform distributions assumed
No rf cavity

10. Debunching rate MAD-X gives transition gamma 14.5325
Phase slip  = 4.7 x , assume 7% total momentum spread
sbunch= m per turn
Track in Zgoubi 78 turns - ~1 mean decay time

11. Bunch train merging 120 m 180 m 120 m
5 bunch trains in ring with 600 ns separation (180m)
Bunches merge in 343 turns
4.4 e-folding times (98.8% muons decayed)

12. Bunch train merging
What is the minimum gap between bunch trains that the detector can live with?
ISS report stipulated a minimum of 100 ns. At this point 2.5% of the beam has yet to decay.

13. Conclusions Racetrack decay ring modelled in Zgoubi
Optics agree well with MAD-X
Debunching rate agrees with MAD-X, i.e. momentum compaction factor in agreement
With 5 bunch trains in ring, trains will merge in 4.4 e-folding decay times.

14. Future work Add fringe fields to magnets
Study decays and trajectories of resulting electrons/positrons
Model muon spin precession