Context of the Neutrino Factory Neutrino factory (2018) –4MW proton driver –p +   +   +  e + e  Linear e + e − collider (2014/5) –Leptons at 0.4 to 1TeV Muon collider (2023) –p +   +,  −   +,  −  –Multi-TeV lepton collision and others… Next-generation accelerators, currently in R&D:

Pion Capture and Muon Front-End (or rods) RAL design by Grahame Rees (…or liquid mercury jet, rotating levitating band, granular water-cooled target, etc…)

Muon1 Particle Tracking Code Nonlinear 3-dimensional simulation –PARMILA was being used before Uses realistic initial  + 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) View animation »»

Decay Channel Lattice Drifts Length (m) D [0.5,1] D2+0.5 [0.5,1] Solenoids Field (T)Radius (m)Length (m) S1 20 [0,20] 0.1 [fixed] [0.2,0.45] S2-4 −3.3, 4, −3.3 [-5,5] 0.3 [0.1,0.4] 0.4 [0.2,0.6] S5-S24 ±3.3 (alternating) [-4,4] S [0.1,0.4] Final (S34)0.15 [fixed] 12 parameters –Solenoids alternated in field strength and narrowed according to a pattern 137 parameters –Varied everything individually Tantalum Rod Length (m)0.2 [fixed] Radius (m)0.01 [fixed] Angle (radians)0.1 [0,0.5] Z displacement (m) from S1 start (S1 centred) [0,0.45] Original parameters / Optimisation ranges

Improved Transmission Decay channel: –Original design: 3.1%  + out per  + from rod –12-parameter optimisation  6.5%  + /  % through chicane –137 parameters  9.6%  + /  % through chicane Re-optimised for chicane transmission: –Original design got 1.13% –12 parameters  1.93% –137 parameters  2.41% 3`700`000 runs so far 1`900`000 runs 330`000 runs

Optimised Design for the Decay Channel (137 parameters) Maximum Length Minimum Drift Maximum Aperture Maximum Field (not before S6) (mostly) (except near ends) (except S4, S6)

Optimiser Architecture How do you optimise in 137-dimensional space?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 / FTPInternet-based –~130 users active in last week >75`000 results sent in –Periodically exchange sample results file

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 FODO lattice FOFO lattice

Design Optimised for Transmission Through Chicane Nontrivial optimum found Preferred length? Narrowing can only be due to nonlinear end-fields

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

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 H 2 (l) or graphite absorbers –Cooling in all 3 planes –16% emittance loss per turn? RAL Cooling Ring (2003) by Grahame Rees