Zgoubi tracking study of the decay ring David Kelliher ASTeC/STFC/RAL
Racetrack storage ring Consists of a production straight, matching section and an arc. Ring circumference 1608.8 m. Neutrino production efficiency of 37.3 % Diagram by Marco Apollonio
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
MAD-X and Zgoubi comparison Tunes Zgoubi MAD-X Qx 8.52149586 8.52149162 Qy 8.21158198 8.21158192 Centre of production straight Zgoubi MAD-X x [m] 152.97 153.00 y [m] 103.0514 103.0518
function comparison
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
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.
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
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
Debunching rate MAD-X gives transition gamma 14.5325 Phase slip = 4.7 x 10-3 , assume 7% total momentum spread sbunch= 0.525 m per turn Track in Zgoubi 78 turns - ~1 mean decay time
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)
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.
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.
Future work Add fringe fields to magnets Study decays and trajectories of resulting electrons/positrons Model muon spin precession