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Optimizing LCLS2 taper profile with genetic algorithms: preliminary results

Optimizing LCLS2 taper profile with genetic algorithms: preliminary results. X. Huang, J. Wu, T. Raubenhaimer , Y. Jiao, S. Spampinati, A. Mandlekar, G. Yu 2/29/2012. An Overview of Multi-Objective Genetic Algorithms . Multi-objective optimization Goal: to find the Pareto optimal set

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Optimizing LCLS2 taper profile with genetic algorithms: preliminary results

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  1. Optimizing LCLS2 taper profile with genetic algorithms: preliminary results X. Huang, J. Wu, T. Raubenhaimer, Y. Jiao, S. Spampinati, A. Mandlekar, G. Yu 2/29/2012

  2. An Overview of Multi-Objective Genetic Algorithms • Multi-objective optimization • Goal: to find the Pareto optimal set • Traditional approach: Weighted sum of objectives and its variants. • Evolutionary approach: converge to the Pareto front in one run. • Genetic algorithms • Manipulate a set of solutions (a population) toward the optimal front with operations that simulate biological evolution. • Three operators • Selection – apply the evolution pressure toward the optimal front • Crossover – create new solution (child) by combining two solutions (parents) • Mutation – alters an existing solution to create a new one.

  3. Pros and Cons • Obtain global optimum (more likely) despite complexity of the problem. • Optimize multiple objectives simultaneously. • Easy to apply constraints. • But it can be much slower than gradient-based methods.

  4. Domination and the Pareto set

  5. The NSGA-II algorithm • NSGA (non-dominated sorting genetic algorithm) -II Selection (of parents) Crossover Mutation K. Deb, IEEE Transtions On Evolutionary Computation Vol 6, No 2,April 2002

  6. NSGA-II with parallel computation • Use Matlab script for control and processing • The algorithm is implemented in matlab • Post-processing is in matlab • Parallel computation via submitting multiple jobs to a cluster • Use file input/output as communication between external program (Genesis) and matlab. • I/O time limits the average number of nodes in use when computation time is short. 35 min per generation with up to 60 processors, or 4.5 s per evaluation, up from 20 s for individual evaluation. However the speed gain from parallel computing will be much higher for time-dependent runs.

  7. LCLS2 Taper Optimization • Undulator tapering is required for LCLS2 to reach TW power because of SASE saturation. • Taper profile optimization is critical to capture as many electrons as possible in coherent emission. • Exploration of profile models is necessary. • Should phase between undulator segments be included in optimization?

  8. Taper Models Considered For Basic 8 variables Cubic 9 variables Quartic 8 variables Focusing scheme Adding phase shift variables to the above models. So far we only varied the first few phase shifts after exponential growth.

  9. GA setup • Objectives: 2 • Power • “Emittance”: beam size x divergence at the exit, a convenient way to introduce diversity • Population: 600 • Termination condition: about 100 generations or converged. • Evolving mutation and crossover probability

  10. The basic 8 variable model (0118) (a, z0) (b, K0) (r1, z1) (r2, z2-z1)

  11. The basic 8 variable model with 7 phase shifts (0115b) Introduce phase shifts in gaps following undulators 5 to 11. (b, K0) (r1, z1) (r2, z2-z1) (a, z0)

  12. The cubic model (9 variables) (0119) (z0, a1) (a2, a3) (K0, r1) (z1,r2)

  13. The quadratic and quartic model (0112) (a, z0) (b, K0) (r1, z1) (r2, z2-z1)

  14. Summary of time-independent results

  15. Effects of phase shift variables Based on case 0118. Inside undulators, phase rotation and energy loss both change. In the gaps, the two can be decoupled. Can this improve the performance?

  16. Time dependent results with the taper profiles The three model attain similar power. More study is needed to understand the results. Taper profile slightly shifted (detuned to maximize for average power for the slices) to maintain high power (but not optimized)

  17. Time dependent simulation with phase shifts The effects of phase shifts are not conclusive from results we got so far.

  18. Summary • All cases without phase shifts converge to solutions with similar beam power and taper ratio, with a capture ratio of about 43%. • Phase shifts only slightly increase beam power. But they can considerably change capture ratio (e.g., from 35% to 41%). • We will continue the exploration • Other taper profile models • Introduce other objective functions • More time dependent studies

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