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

2. 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 Motivation Introduction to the simulation setup and the genetic algorithm optimizations Optimization-guided MICE Step IV lattices and their performance Conclusions and Q&A MICE optics review – Ao Liu, FNAL 1/14/161

3. Motivations 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. 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. MICE optics review – Ao Liu, FNAL 1/14/162

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 –Requires more computing power and currently unavailable at NERSC G4Beamline 2.16 –Simulation of MICE Step IV readily available (P. Snopok); Comparison with MAUS was previously done. –Fast, parallelized and has been tested by many cases within the muon community; Available on NERSC 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 –Requires more computing power and currently unavailable at NERSC G4Beamline 2.16 –Simulation of MICE Step IV readily available (P. Snopok); Comparison with MAUS was previously done. –Fast, parallelized and has been tested by many cases within the muon community; Available on NERSC MICE optics review – Ao Liu, FNAL 1/14/163

5. Simulation setup – G4Beamline MICE coils and currents – both SS and FC, geometry ID 70 Materials in channel to match MAUS as accurately as possible: –SciFi tracker planes (2 mm Polystyrene each), 6.5 cm LiH absorber; –TOF2 added at the end of the channel (+4200 mm from the absorber); –Added beam pipe to kill particles hitting it (r=258 mm); –No PRY; vacuum in beam pipes Use initial beam generated by constant solenoid mode covariance matrix, which matches the B z at the starting point. –Beam starts at z=-3000 mm from the absorber (tracker0). MICE coils and currents – both SS and FC, geometry ID 70 Materials in channel to match MAUS as accurately as possible: –SciFi tracker planes (2 mm Polystyrene each), 6.5 cm LiH absorber; –TOF2 added at the end of the channel (+4200 mm from the absorber); –Added beam pipe to kill particles hitting it (r=258 mm); –No PRY; vacuum in beam pipes Use initial beam generated by constant solenoid mode covariance matrix, which matches the B z at the starting point. –Beam starts at z=-3000 mm from the absorber (tracker0). Modified from Pavel’s original G4BL input, with new geometry and detectors implemented MICE optics review – Ao Liu, FNAL 1/14/164

6. Simulation setup – G4Beamline (cont’d) Comparing p=200 MeV/c nominal baseline setting (from MAUS simulations, by T. Carlisle): Apply the MAUS parameters in G4BL to reproduce the results, where No δp/p, 6 mm, start with p=207 MeV/c; LH2 absorber; No scintillating fibers included; Included stochastic processes but no decay; Transmission from tracker 0 to 1 is ~100% 4.5% emit. reduction consistent with MAUS result MICE optics review – Ao Liu, FNAL 1/14/165

7. Simulation setup – G4Beamline (cont’d) MICE optics review – Ao Liu, FNAL Adding δp/p and and SciFi materials in G4BL - Provide a more realistic model.  Reduces the trans. to 98%, while emit reduction with such a symmetric, mild-varying optics is stable. PzPz β ε 4D 1/14/166

8. Optimization setup – G4Beamline (cont’d) A few more 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; –In the tracking, particles that fall out of the active area (r≤15 cm) at any one of the tracker station are considered lost; –The step size of the tracking has been adjusted to require minimum computing time, while not introducing any significant errors; –65 mm LiH used in the following optimization studies; decay is enabled; A few more 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; –In the tracking, particles that fall out of the active area (r≤15 cm) at any one of the tracker station are considered lost; –The step size of the tracking has been adjusted to require minimum computing time, while not introducing any significant errors; –65 mm LiH used in the following optimization studies; decay is enabled; MICE optics review – Ao Liu, FNAL 1/14/167

9. Optimization setup – GA Genetic Algorithm is –Heuristic: approaches the optimum solution by trials and errors; –Efficient: the more variables, the more powerful; –Thorough: performs a nice search in the parameter space; Single Objective GA (SOGA): –The transmission to TOF2 (T) squared, multiplies the emittance reduction between ref. planes (±1800 mm) and start and end of the trackers (± 3000 mm) – Optimization objective above guarantees a good transmission and minimizes the possible emit. growth in the TKD. Genetic Algorithm is –Heuristic: approaches the optimum solution by trials and errors; –Efficient: the more variables, the more powerful; –Thorough: performs a nice search in the parameter space; Single Objective GA (SOGA): –The transmission to TOF2 (T) squared, multiplies the emittance reduction between ref. planes (±1800 mm) and start and end of the trackers (± 3000 mm) – Optimization objective above guarantees a good transmission and minimizes the possible emit. growth in the TKD. 1/14/168 MICE optics review – Ao Liu, FNAL

10. Optimization setup – GA (for our case) A scan of 10 different values for each parameter is 1 MILLION runs! 6 parameters controlling coil currents; (reviewed later) All parameters within current magnet operation limit. Set up G4Beamline using the currents, calculate the Bz at -3000 mm, generate the initial beam Select the best individuals, make the offspring. A child generation is generated Track the muons from -3000 mm to TOF2 (4196 mm). Select the good muons, calculate the emittance at the trackers When the maximum generation number is reached, or the population stops improving,stop the algorithm GA starts, use a number of random individual current settings produced as the first generation MICE optics review – Ao Liu, FNAL 1/14/169

11. 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 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 MICE optics review – Ao Liu, FNAL 1/14/1610

12. Optimization result – GA on NERSC GA was set up on NERSC to run –120 individuals in each generation –80 generations maximum –32 core-hours to run each generation; –~ 30 generations to converge in each optimization. Efficient optimization with GA –Easy to apply more constraints, or –Re-optimize based on a new environment (changed variable limits, input beam parameters, etc.) Use the “good” muons only in analyzing results GA was set up on NERSC to run –120 individuals in each generation –80 generations maximum –32 core-hours to run each generation; –~ 30 generations to converge in each optimization. Efficient optimization with GA –Easy to apply more constraints, or –Re-optimize based on a new environment (changed variable limits, input beam parameters, etc.) Use the “good” muons only in analyzing results MICE optics review – Ao Liu, FNAL 1/14/1611

13. Optimization result – B z and emit. evolution MICE optics review – Ao Liu, FNAL 1/14/1612 140 MeV/c T=93% 200 MeV/c T=93% 240 MeV/c T=90% 140 MeV/c T=91% 200 MeV/c T=92% 240 MeV/c T=90% Left: flip mode; right: solenoid mode

14. Optimization result - Continued Some more details: –Variable values corresponding to the previous results: –Some of the configurations have ~ 2 T in the trackers: Tracker resolution improves with higher B z ; Next, investigate how the optimizations perform with a high B z limit on Trackers both upstream and downstream? Some more details: –Variable values corresponding to the previous results: –Some of the configurations have ~ 2 T in the trackers: Tracker resolution improves with higher B z ; Next, investigate how the optimizations perform with a high B z limit on Trackers both upstream and downstream? 1/14/1613 MICE optics review – Ao Liu, FNAL

15. Optimization result – B z and emit. evolution (high B z requirement) MICE optics review – Ao Liu, FNAL 1/14/1614 140 MeV/c T=92% 200 MeV/c T=92% 240 MeV/c T=90% 140 MeV/c T=91% 200 MeV/c T=92% 240 MeV/c T=90% Left: flip mode; right: solenoid mode

16. Optimization result – Continued discussion Some more details: –Variable values corresponding to the previous results: –At lower momentum, the instability of emittance reduction (growth after the ref. plane downstream) becomes more obvious because increase in δp/p is more obvious by passing through materials. Some more details: –Variable values corresponding to the previous results: –At lower momentum, the instability of emittance reduction (growth after the ref. plane downstream) becomes more obvious because increase in δp/p is more obvious by passing through materials. 1/14/1615 MICE optics review – Ao Liu, FNAL

17. Conclusions from the optimizations In each operation scenario, 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. In most of them, the normalized transverse emit. reduction is more than 3%; The GA application in the lattice design was successfully demonstrated. Upon any new environment, e.g. new current limits, geometry, input beam, optimizations can be run timely to obtain the optimized configuration. In each operation scenario, 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. In most of them, the normalized transverse emit. reduction is more than 3%; The GA application in the lattice design was successfully demonstrated. Upon any new environment, e.g. new current limits, geometry, input beam, optimizations can be run timely to obtain the optimized configuration. 1/14/1616 MICE optics review – Ao Liu, FNAL

18. Conclusions from the optimizations – Cont’d Doing Step IV is necessary and will be fruitful for the optics study purposes: –Enables a comparison with the simulation model; Refining the simulation setup based on the measured particle data –Understanding the loss pattern in the above configurations will greatly help us understand and handle imperfections, such as optics mismatch, misalignment, solenoid errors, etc. What resulted in the loss? –Take 200 MeV/c flip mode as an example Doing Step IV is necessary and will be fruitful for the optics study purposes: –Enables a comparison with the simulation model; Refining the simulation setup based on the measured particle data –Understanding the loss pattern in the above configurations will greatly help us understand and handle imperfections, such as optics mismatch, misalignment, solenoid errors, etc. What resulted in the loss? –Take 200 MeV/c flip mode as an example 1/14/1617 MICE optics review – Ao Liu, FNAL

19. 200 MeV/c flip mode – from the above- shown optimization result Check the phase space density at the two ref. planes: 1/14/1618 MICE optics review – Ao Liu, FNAL J. Scott Berg, BNL =2(J x +J y ) Number of muons in the acceptance A ratio that is larger than 1 shows cooling in that acceptance; Loss taken into account – not fooled by losing only muons with more MCS and reducing RMS normalized emit.

20. 200 MeV/c flip mode – from the above- shown optimization result – Cont’d Is the demonstration of emit. reduction biased by the lost particles? –Another study: look at the phase space evolution of good and bad muons: Is the demonstration of emit. reduction biased by the lost particles? –Another study: look at the phase space evolution of good and bad muons: 1/14/1619 MICE optics review – Ao Liu, FNAL Good muons x-x’ (mm - rad) Lost muons x-x’ (mm - rad)

21. 200 MeV/c flip mode – from the above- shown optimization result – Cont’d Is the demonstration of emit. reduction biased by the lost particles? –Another study: look at the phase space evolution of good and bad muons: Is the demonstration of emit. reduction biased by the lost particles? –Another study: look at the phase space evolution of good and bad muons: 1/14/1620 MICE optics review – Ao Liu, FNAL Two beams overlapping together looks like:

22. Just a backup – in case the previous gif animations don’t work Is the demonstration of emit. reduction biased by the lost particles? –Another study: look at the phase space evolution of good and bad muons: Is the demonstration of emit. reduction biased by the lost particles? –Another study: look at the phase space evolution of good and bad muons: 1/14/1621 MICE optics review – Ao Liu, FNAL

23. 200 MeV/c flip mode – Interpretation of the particle loss Implication from the phase space evolution of lost muons: –Not a direct result from MCS (e.g. a big jump into large angles): the emit. reduction was NOT from scraping off muons with large MCS angles; –Separatrix and filamentation were generated – emittance growth and eventually particle loss For a standard accelerator lattice, particle loss is encountered for certain phase advance (tune), momentum, or action; For a lattice with energy loss during transportation, nonlinear effects accumulate stochastically! The measurement at MICE Step IV is able to demonstrate the cooling without bias from the lost muons. Implication from the phase space evolution of lost muons: –Not a direct result from MCS (e.g. a big jump into large angles): the emit. reduction was NOT from scraping off muons with large MCS angles; –Separatrix and filamentation were generated – emittance growth and eventually particle loss For a standard accelerator lattice, particle loss is encountered for certain phase advance (tune), momentum, or action; For a lattice with energy loss during transportation, nonlinear effects accumulate stochastically! The measurement at MICE Step IV is able to demonstrate the cooling without bias from the lost muons. 1/14/1622 MICE optics review – Ao Liu, FNAL

24. Conclusions G4Beamline simulation of the MICE Step IV is consistent with MAUS results; GA was applied to optimize the Step IV lattice for each run mode. Emittance reduction can be obtained with good transmission, within the magnet operation limits; Demonstration of emittance reduction will not be biased by the lost particles; Optimizations can be re-done to adopt new running environment. Step IV will be a necessary step to compare experimental data with simulation models, and understand the beam optics in the cooling channel. G4Beamline simulation of the MICE Step IV is consistent with MAUS results; GA was applied to optimize the Step IV lattice for each run mode. Emittance reduction can be obtained with good transmission, within the magnet operation limits; Demonstration of emittance reduction will not be biased by the lost particles; Optimizations can be re-done to adopt new running environment. Step IV will be a necessary step to compare experimental data with simulation models, and understand the beam optics in the cooling channel. MICE optics review – Ao Liu, FNAL 1/14/1623

25. YES OR NO, THANKS! Questions? MICE optics review – Ao Liu, FNAL 1/14/16 24

26. Backup slides 1/14/16 25 MICE optics review – Ao Liu, FNAL

27. Optimization result – B z and emit. evolution (low B z requirement but no M1D nor M2D) 1/14/1626 MICE optics review – Ao Liu, FNAL 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

28. Flip mode, 200 MeV/c Optical beta functions for flip mode, 200 MeV/c (left), and phase space evolution for lost muons within different initial momentum ranges: 1/14/1627 MICE optics review – Ao Liu, FNAL 190 to 195 MeV/c195 to 200 MeV/c 200 to 205 MeV/c205 to 210 MeV/c

29. Flip mode, 200 MeV/c The time-momentum phase space of good and bad muons: 1/14/1628 MICE optics review – Ao Liu, FNAL ns MeV/c

30. Flip mode, 200 MeV/c – phase space density 1/14/1629 MICE optics review – Ao Liu, FNAL Density increases for small amplitudes and decreases for larger amplitudes – consistent with filamentation