MICE Step IV Lattice Design Based on Genetic Algorithm Optimizations Ao Liu on behalf of the MICE collaboration Fermilab

MICE optics review – Ao Liu, FNAL Outline Motivation Introduction to the simulation setup and the genetic algorithm optimizations Optimization-guided MICE Step IV lattices and their performance Conclusions and Q&A 1/14/16 MICE optics review – Ao Liu, FNAL

MICE optics review – Ao Liu, FNAL Motivation MICE Step IV goals – demonstrate material physics properties Measurement of the muon Multiple Coulomb Scattering (MCS) and energy loss in the materials; Measurement of the transverse normalized emittance (ε⊥) reduction In the absence of M1 coil downstream (M1D) Lack of optics matching power; Measurement of the MCS and energy loss are largely unaffected; Can we still demonstrate ε⊥ reduction? Need: New lattice designs for all the run modes, which should have: Decent transmission (good acceptance) Maximized ε⊥ reduction between the reference planes with minimum ε⊥ growth, especially in the SSD. 1/14/16 MICE optics review – Ao Liu, FNAL

Introduction to the simulation setup MICE Analysis User Software (MAUS) Powerful tool developed by MICE to do tracking, analysis, reconstruction, etc. Has multiple detectors built-in, detailed construction of the geometry and tracking in materials based on Geant4 G4Beamline 2.16 Simulation of MICE Step IV readily available (P. Snopok); Comparison with MAUS was done previously. Fast, parallelized and has been tested by many cases within the muon community; Available on NERSC 1/14/16 MICE optics review – Ao Liu, FNAL

Simulation setup – G4Beamline G4BL GUI multi-event display Current geometry of MICE channel Materials in channel to match MAUS as accurately as possible: SciFi tracker planes (2 mm Polystyrene each), 65 mm LiH absorber; TOF2 at the end of the channel (+4200 mm from the absorber); Beam pipe to kill particles hitting it (r=258 mm); Monte Carlo initial particle ensemble matched to the solenoid longitudinal field Bz Beam starts at z=-3000 mm from the absorber (upstream tracker). 1/14/16 MICE optics review – Ao Liu, FNAL

Simulation setup – G4Beamline (cont’d) Bz ε4D Nominal 200 MeV/c flip mode; Transmission = 98% with δp/p in ± 5% 4.9% emit. Reduction between ref. planes G4BL is consistent with MAUS results – both Geant4 based 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization setup – G4Beamline (cont’d) Additional G4BL simulation details: In counting the good muons/transmission, the active area of the TOF2 (30-by-30 cm) was used as the requirement to have a “survived/measurable” muon; and, particles that fall out of the active area (r≤15 cm) at any one of the tracker station are considered lost; The max. step size = 5 mm minimizes the simulation time, while not introducing any significant tracking errors; 65 mm LiH used in the following optimization studies; stochastic processes are enabled; 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization setup – GA Single Objective Genetic Algorithm (SOGA): Searches the parameter space thoroughly and finds the global optimum; The more variables, the more powerful; Objective function: T : Transmission. T2 guarantees a good transmission and avoids bias from scraping particles with strong MCS εref,u , εref,d : Transverse normalized emittance at the reference planes (±1800 mm from the absorber). The first term is what we measure; εbound,u , εbound,d : Transverse normalized emittance at the boundaries of the upstream and downstream tracker (± 3000 mm). The second term guarantees a regulated emittance in the trackers (especially downstream). 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization setup – GA (for our case) Set up G4Beamline, generate the initial beam Select the best individuals, make the offspring. A child generation is constructed Track the muons, calculate the objective function 6 parameters controlling coil currents; (reviewed later) All parameters within current magnet operation limit. GA starts, first generation: A group of random configurations A scan of 10 different values for each parameter is 1 MILLION runs! Then 6 run modes? When the maximum generation number is reached, or the population stops improving,stop the algorithm 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization setup – GA (for our case) A few more details: Optimization variables (and their ranges) and the corresponding coil current: Investigated both flip and solenoid modes at all three momentum: 140, 200 and 240 MeV/c 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization result – GA on NERSC GA was set up on NERSC to run ~ 30 generations to converge in each optimization: Fast! Each generation has 120 individuals Efficient optimization with GA Easy to apply more constraints, or Re-optimize based on a new environment (changed variable limits, input optics parameters, etc.) Use the “good” muons only in analyzing results 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization result – 200 MeV/c Flip Ref. plane downstream 4 % reduction in ε⊥ Transmission: 93% Ref. plane upstream Sol 2.8 % reduction in ε⊥ Transmission: 92% 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization result – 140 MeV/c flip T=93% ε⊥ reduction: 7.7% 140 MeV/c Sol T=91% ε⊥ reduction: 2.2% Left: flip mode; right: solenoid mode 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization result – 240 MeV/c flip T=90% ε⊥ reduction: 2.2% 240 MeV/c Sol T=90% ε⊥ reduction: 2.1% Left: flip mode; right: solenoid mode 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization result - Continued Variable values corresponding to the previous results: In each run mode, we are able to deliver an ensemble of particles that can be cooled in the MICE Step IV lattice, with at least 90% transmission to the TOF2 without M1D. In most of them, the normalized transverse emit. reduction is more than 3%; Are we introducing bias to the emit. measurement in muon loss? 1/14/16 MICE optics review – Ao Liu, FNAL

200 MeV/c flip mode – from the above-shown optimization result Check the phase space density at the two ref. planes: =2(Jx+Jy) Number of muons in the acceptance A ratio that is larger than 1 shows cooling in that acceptance; J. Scott Berg, BNL Loss taken into account – not fooled by losing only muons with more MCS to reduce RMS normalized emit. 1/14/16 MICE optics review – Ao Liu, FNAL

200 MeV/c flip mode – Interpretation of the particle loss The beam loss is not dominated by the large scattering in the absorber: The majority of the lost muons do not encounter a big jump in its emittance; Instead, they form islands which continue to build up in the downstream channel – eventually leave the aperture and are lost Good muons Before abs. Good muons After abs. Lost muons Before abs. Lost muons After abs. 1/14/16 MICE optics review – Ao Liu, FNAL

MICE optics review – Ao Liu, FNAL Conclusions GA was applied to optimize the Step IV lattice for each run mode without M1D. Emittance reduction can be obtained with good transmission, within the magnet operation limits Optimizations can be re-done efficiently to adopt new running environment or constraints. Demonstration of emittance reduction will not be biased by the lost particles; Step IV will be a necessary step to compare experimental data with simulation models, and understand the beam optics in the cooling channel. 1/14/16 MICE optics review – Ao Liu, FNAL

MICE optics review – Ao Liu, FNAL Questions? yes or no, thanks! 1/14/16 MICE optics review – Ao Liu, FNAL

My only backup slide – as requested 1/14/16 MICE optics review – Ao Liu, FNAL

Optimization result – Bz and emit. evolution (no M1D nor M2D) Flip mode (left), 140 and 240 MeV/c (upper and lower), T=72% and 74% Solenoid mode (right), 140 and 240 MeV/c (upper and lower), T=73% and 82% It is possible but more difficult to pursue Step IV with M2D off Challenges are data collection inefficiency and understanding the outcome from the big loss 1/14/16 MICE optics review – Ao Liu, FNAL