1	Optimisation of the RAL Muon Front End Design
2	Contents Designs considered Decay channel with chicane Decay channel with phase rotation, cooling Tracking code Optimisation approach Results Future work …and issues still to be solved
3	Design Components Pion to muon decay channel Accepts pions from the target Uses a series of wide-bore solenoids “Phase rotation” systems FFAG-style dipole bending chicane (2001) For short bunch length à 400MeV muon linac 31.4 MHz RF phase rotation (2003) For low energy spread à ionisation cooling ring
4	Pion to Muon Decay Channel Challenge: high emittance of target pions Currently come from a 20cm tantalum rod
5	Pion to Muon Decay Channel Challenge: high emittance of target pions Currently come from a 20cm tantalum rod
6	Pion to Muon Decay Channel Challenge: high emittance of target pions Currently come from a 20cm tantalum rod Solution: superconducting solenoids S/C enables a high focussing field Larger aperture than quadrupoles Basic lattice uses regular ~4T focussing Initial smaller 20T solenoid around target 30m length = 2.5 pion decay times at 200MeV
7	Chicane Phase-Rotation
8	RF Phase-Rotation 31.4MHz RF at 1.6MV/m (2003 design) Reduces the energy spread 180±75MeV to ±23MeV Cavities within solenoidal focussing structure Feeds into cooling ring
9	Muon1 Particle Tracking Code Non-linearised 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)
10	Muon1 Tracking Code Details Typically use 20k-50k particles Tracking is done by 4^th order classical Runge-Kutta on the 6D phase space Currently timestep is fixed at 0.01ns Solenoids fields and end-fields are a 3^rd order power expansion Field maps trilinearly interpolated Particle decays are stochastic, sampled
11	Optimiser Architecture How do you optimise in a very high-dimensional space? Hard to calculate derivatives due to stochastic noise and sheer number of dimensions Can use a genetic algorithm Begins with random designs Improves with mutation, interpolation, crossover… Has been highly successful so far in problems with up to 137 parameters
12	Decay Channel Parameters 12 parameters Solenoids alternated in field strength and narrowed according to a pattern 137 parameters Varied everything individually
13	Phase Rotation Plan Chicane is a fixed field map, not varied Solenoid channels varied as before Both sides of chicane Length up to 0.9m now RF voltages 0-4MV/m Any RF phases ~580 parameters RF phase rotation Similar solenoids, phases (no field map) RF voltages up to 1.6MV/m ~270 parameters
14	Results- 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 9.7% 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%
15	NuFact Intensity Goals “Success” is 10²¹ m⁺/yr in the storage ring
16	Distributed Computing System How do you run 3`900`000 simulations? Distributed computing Internet-based / FTP ~450GHz of processing power ~130 users active, 75`000 results sent in last week Periodically exchange sample results file Can test millions of designs Accelerator design-range specification language Includes “C” interpreter Examples: SolenoidsTo15cm, ChicaneLinacA
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18	Optimised Design for the Decay Channel (137 parameters)
19	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
20	Design Optimised for Transmission Through Chicane Nontrivial optimum found Preferred length? Narrowing can only be due to nonlinear end-fields
21	Future Optimisations Chicane and RF phase rotation designs are starting to be run now Initial results promising Cooling ring later this year
22	RAL Design for Cooling Ring 10-20 turns Uses H₂(l) or graphite absorbers Cooling in all 3 planes 16% emittance loss per turn (probably)
23	Unresolved Issues (to-do) Solenoid field clipping distance Need ‘solid’ solenoids for best accuracy ICOOL has recently added these New target dataset needed for 8GeV Trying to get MARS Possibility of target energy optimisation Code could do with variable timesteps and/or error control
24	Target Area 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