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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

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

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

21. 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