1	Context of the Neutrino Factory Neutrino factory (2018) 4MW proton driver p⁺ à p⁺ à m⁺ à e⁺n_en_m Linear e⁺e⁻ collider (2014/5) Leptons at 0.4 to 1TeV Muon collider (2023) p⁺ à p⁺,p⁻ à m⁺,m⁻à Multi-TeV lepton collision and others…
2	Pion Capture and Muon Front-End
3	Muon1 Particle Tracking Code Nonlinear 3-dimensional simulation PARMILA was being used before Uses realistic initial p⁺ distribution Monté-Carlo simulation by Paul Drumm Particle decays with momentum kicks Solenoid end-fields included OPERA-3d field maps used for FFAG-like magnets in chicane (Mike Harold)
4	Decay Channel Lattice 12 parameters Solenoids alternated in field strength and narrowed according to a pattern 137 parameters Varied everything individually
5	Improved Transmission Decay channel: Original design: 3.1% m⁺ out per p⁺ from rod 12-parameter optimisation à 6.5% m⁺/p⁺ 1.88% through chicane 137 parameters à 9.6% m⁺/p⁺ 2.24% through chicane Re-optimised for chicane transmission: Original design got 1.13% 12 parameters à 1.93% 137 parameters à 2.41%
6	Optimised Design for the Decay Channel (137 parameters)
7	Optimiser Architecture How do you optimise in 137-dimensional space? Hard to calculate gradient due to stochastic noise Use genetic algorithm Random designs Mutation Interpolation Crossover How do you run 3`700`000 simulations? Distributed computing Internet-based / FTP ~130 users active in last week >75`000 results sent in Periodically exchange sample results file
8	Why did it make all the solenoid fields have the same sign? Original design had alternating (FODO) solenoids Optimiser independently chose a FOFO lattice Has to do with the stability of off-energy particles
9	Design Optimised for Transmission Through Chicane Nontrivial optimum found Preferred length? Narrowing can only be due to nonlinear end-fields
10	Recent Work on Losses Muon1 modified to count lost particle energies For a 4MW p⁺ beam: 35kW deposited in S1 (r=10cm) Large >1kW amounts deposited up to S5 Added “collimators” to the simulation Decreases losses to 10’s of watts in all but S1 and S2 S1 needs enlarging to accommodate an entire Larmor rotation Consistent target-area layout is needed
11	New Design with Muon Cooling Decay channel (as before) 31.4MHz RF phase rotation Reduces energy spread from 190±70 to ±23MeV Cooling ring (20 turns) Uses H₂(l) or graphite absorbers Cooling in all 3 planes 16% emittance loss per turn?