1. Experience on GA optimization of photoinjector and minimum emittance in rings Chun-xi Wang Advanced Photon Source (APS) Argonne National Laboratory (ANL) wangcx@aps.anl.gov

2. Outline 2  Basics of genetic algorithm and multi-objective optimization  Optimization of bending profile for minimum emittance  Optimization of high-brightness photoinjector Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

3. Multi-objective optimization 3  Multiple objectives (conflicting interests)  Pareto optimal solutions (Pareto front)  Many algorithms for searching Pareto front (e.g. NSGA-II) Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

4. Multi-objective optimization 4  Early usage in accelerator field Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

5. Multi-objective optimization 5  Recent popularity Availability of computer clusters for parallel computation Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

6. Genetic Algorithm 6  An empirical/heuristic technique for searching a solution  Mimic the process of natural evolution for optimization  Inheritance (chromosome, crossover), mutation, selection  Basic procedure  Evaluation of fitness functions usually is very time consuming and parallel computation is often necessary  Elitist selection is often important for performance Chromosome: a string that encodes a candidate solution Crossover: genetic operator used to reproduce from parents Mutation: genetic operator used to maintain genetic diversity Selection: a fitness-based process to select parents for new generation Choose the initial population, i.e., a set of chromosomes Select the best-fits for reproduction Breed new chromosomes through crossover/mutation Evaluate the fitness of new breeds Select the best-fits as the new generation, and continue evolution Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

7. Genetic Algorithm 7  Chromosome: a string that encodes a candidate solution (binary-coded) {1,0,0,1,1,0,1,0; …; …; total number of parameters} parameter accuracy  Inheritance: chromosome recombination/crossover at a rate (0.7) 10111100110010010 10111111111110111 (single-point crossover) 01100011111110111 01100000110010010  Mutation: each digit flips at a given rate (0.001) (bitwise mutation) 10111111111110111 11111111111111111  Selection (NSGA-II) http://www.ai-junkie.com/ga/intro/gat1.html Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 Sorting according to fitness: fast non-dominated sort Elitist: always retain the best individuals in the next new generation Maintain diversity to cover the whole front: crowding distance Constraint handling: binary tournament selection

8. Mathematica implementation of NSGA-II Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 8 A basic implementation is available from a Mathematica demonstration Mathematica is fast enough to handle the optimization It is easy to use for managing parallel computation of fitness functions Options for parallel computation GridMathematica: no extra coding, platform independent, limited by license Using Mathemtica as a script language to invoke system job managers: SGE on linux clusters, TORQUE on multicore workstations/laptops

9. Testing of non-constrained NSGA-II Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 9 SCHKUR

10. Testing of constrained NSGA-II Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 10 CONSTRTNK

11. Outline 11  Basics of genetic algorithm and multi-objective optimization  Optimization of bending profile for minimum emittance  Optimization of high-brightness photoinjector Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

12. Common storage ring lattice types “Theoretical minimum emittance in storage rings”, C.-x. Wang, presented at ICFA Beam Dynamics Mini Workshop on Low Emittance Rings, Heraklion, Greece, 3-5 Oct. 2011 12 1.TME --- Theoretical Minimum Emittance lattices no lattice constraints, figure of merit for damping rings 2.AME --- Achromatic Minimum Emittance lattices require achromatic arcs for dispersion-free straight section, injection, rf, etc. 3.EME --- Effective Minimum Emittance lattices no lattice constraints, but minimize the effective emittance for light sources

13. Natural horizontal emittance “Theoretical minimum emittance in storage rings”, C.-x. Wang, presented at ICFA Beam Dynamics Mini Workshop on Low Emittance Rings, Heraklion, Greece, 3-5 Oct. 2011 13 betatron emittance for uncoupled lattices Dispersion action depending on linear lattice design For isomagnetic rings with conventional dipoles of bending angle  : a remarkable fact known since 1981

14. Minimum emittance theory ( summary ) “Theoretical minimum emittance in storage rings”, C.-x. Wang, presented at ICFA Beam Dynamics Mini Workshop on Low Emittance Rings, Heraklion, Greece, 3-5 Oct. 2011 14 |A|, and c are completely determined by the dipole For uniform dipoles: This cubic equation determines the optimal dispersion for EME

15. Optimization of bending profile Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 15

16. Optimal bending profile “Theoretical minimum emittance in storage rings”, C.-x. Wang, presented at ICFA Beam Dynamics Mini Workshop on Low Emittance Rings, Heraklion, Greece, 3-5 Oct. 2011 16 TMEAME TME EME AME bending curvature (B field) bending radius profile slice number  dipole of a given length and bending angle is sliced into many slices  each slice has arbitrary strength (up to a maximum, no polarity change)  two different optimizers are used to optimize the emittance, etc.  optimization was done for 3 different peak field (2, 4, and 6 times stronger) TME slice number TME AMEEME

17. Linearly-ramped bending profile “Theoretical minimum emittance in storage rings”, C.-x. Wang, presented at ICFA Beam Dynamics Mini Workshop on Low Emittance Rings, Heraklion, Greece, 3-5 Oct. 2011 17 A model sufficiently close to the optimal, yet can be solved analytically TMEAME/EME is chosen as a given parameter S = 0 (  0, L 0 ) (  max, L)

18. Theoretical minimum emittance (TME) “Theoretical minimum emittance in storage rings”, C.-x. Wang, presented at ICFA Beam Dynamics Mini Workshop on Low Emittance Rings, Heraklion, Greece, 3-5 Oct. 2011 18 F is normalized by the value of reference uniform dipole, i.e., f 1 and f 2 are functions of (g,r)   improvement in TME emittance r

19. Outline 19  Basics of genetic algorithm and multi-objective optimization  Optimization of bending profile for minimum emittance  Optimization of high-brightness photoinjector Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 Design study of a high-brightness cw injector for ERL Optimization of APS injector & linac

20. C.-x. Wang: Scheme for ERL-based x-ray light sources (ERL09) 20 Low-frequency normal-conducting rf gun cavity Design for a CW, VHF Photogun Vacuum pumps in plenum Cathode Beam exit aperture Vacuum pumping slots Cathode insertion & withdrawal channel (mechanism not shown) HIGH BUNCH RATE, ACCOMODATES VARIED CATHODE MATERIALS Fernando Sannibale John Staples Russ Wells LBNL VHF photogun cavity (Corlett talk, Oct. 2008) Used a 350MHz cavity from J. Staple for simulation 187 MHz, 20 MW/m at cathode, 10^-11 Torr

21. C.-x. Wang: Scheme for ERL-based x-ray light sources (ERL09) 21 Basic layout of a normal-conducting rf photoinjector Adopted from dc injector as an example, major difference is the cathode field gun cavity @ 325MHz solenoid rf buncher two-cell cavities @ 650MHz 25 MV/m

22. C.-x. Wang: Scheme for ERL-based x-ray light sources (ERL09) 22 Preliminary result of a potential nc rf photoinjector (1) Optimized using ASTRA and the genetic optimizer in SDDS-toolkit (using non-dominated sorting, similar to NSGA-II) Only beer-can laser pulse is used, assuming thermal emittance from GaAs Needs to push through mergers meet requirements, can be better 4 x bunch charge high coh.high flux

23. C.-x. Wang: Scheme for ERL-based x-ray light sources (ERL09) 23 Preliminary result of a potential nc rf photoinjector (2) ASTRA output of bunch information 0.3nc 0.77pc

24. APS injector optimization study Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012 24