1. 2/29/20121 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. 2/29/20122

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. 2/29/20123

4. 4 Domination and the Pareto set

5. The NSGA-II algorithm NSGA (non-dominated sorting genetic algorithm) -II 2/29/20125 K. Deb, IEEE Transtions On Evolutionary Computation Vol 6, No 2,April 2002 Selection (of parents) Crossover Mutation

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. 2/29/20126 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? 2/29/20127

8. Taper Models Considered 2/29/20128 Adding phase shift variables to the above models. So far we only varied the first few phase shifts after exponential growth. Focusing scheme Basic 8 variables Cubic 9 variables Quartic 8 variables For

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 2/29/20129

10. The basic 8 variable model (0118) 2/29/201210 param eterlowhighdeltabest a0.010.30.0010.1043 z010400.213.1 b1.13.30.012.0359 K020400.134.4 r1-0.0050.0050.000050.0018 z120800.280.0 r2-0.010.010.000050.0061 z2-z10700.228.9 (a, z0)(b, K 0 )(r1, z1)(r2, z2-z1)

11. The basic 8 variable model with 7 phase shifts (0115b) 2/29/201211 (a, z0) (b, K 0 ) Introduce phase shifts in gaps following undulators 5 to 11. (r1, z1)(r2, z2-z1) param eterlowhighdeltabest a0.010.30.0010.114 z010400.216.8 b1.13.30.012.072 K020400.134.9 r1-0.0050.0050.000050.0008 z120800.274.3 r2-0.010.010.000050.0022 z2-z10700.29.3

12. The cubic model (9 variables) (0119) 2/29/201212 (z0, a1)(a2, a3) (K0, r1)(z1,r2) parame terLowhighdeltabest z010400.218.8 a1-0.10.10.0010.0118 a20.0010.30.0010.0551 a3-0.10.10.0010.0538 K020400.127.9 r1-0.010.010.0005-0.005 z120800.238.1 r2-0.010.010.0005-0.009 z2-z10700.266.8

13. The quadratic and quartic model (0112) 2/29/201213 (a, z0)(b, K 0 ) (r1, z1)(r2, z2-z1)

14. Summary of time-independent results 2/29/201214 caseNvargenerationpopulationmax Power inc in 10 gen emittance (um)taper ratio capture ratio ##TW%um% "01182012"basic 81036001.7600.20%0.07530.07543.0%1+a x^b "01152012b "8+71006001.8300.27%0.07900.081641.1%from random "01152012b" no phase 1.563 0.081635.1% "01212012"phase 71096001.8050.00%0.07510.076243.4% based on 01182012 @ gen 47, 1.753 TW "01192012"cubic 91006001.7430.00%0.07020.072244.3%1+a x+b x^2+c x^3 "01202012"9+71156001.8420.31%0.07940.080442.0% "01202012" no phase 1.521 0.080434.7% "01122012"quartic 81046001.7990.00%0.07570.078342.1%1+a x^2 + b x^4

15. Effects of phase shift variables 2/29/201215 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 2/29/201216 Taper profile slightly shifted (detuned to maximize for average power for the slices) to maintain high power (but not optimized) The three model attain similar power. More study is needed to understand the results.

17. Time dependent simulation with phase shifts 2/29/201217 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 2/29/201218