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Experience on GA optimization of photoinjector and minimum emittance in rings

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. Outline. Basics of genetic algorithm and multi-objective optimization

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Experience on GA optimization of photoinjector and minimum emittance in rings

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  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 • 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 • 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 • 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 • 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 • 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 • 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) 1011110011001001010111111111110111 (single-point crossover) 0110001111111011101100000110010010 • Mutation: each digit flips at a given rate (0.001) (bitwise mutation) 10111111111110111 11111111111111111 • Selection (NSGA-II) • 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 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

  8. Mathematica implementation of NSGA-II • 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 linuxclusters, TORQUE on multicore workstations/laptops Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 2012

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

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

  11. Outline • 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 • TME --- Theoretical Minimum Emittance lattices • no lattice constraints, figure of merit for damping rings • AME --- Achromatic Minimum Emittance lattices • require achromatic arcs for dispersion-free straight section, injection, rf, etc. • EME --- Effective Minimum Emittance lattices • no lattice constraints, but minimize the effective emittancefor light sources “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. Natural horizontal emittance betatronemittance for uncoupled lattices depending on linear lattice design Dispersion action For isomagnetic rings with conventional dipoles of bending angle q : a remarkable fact known since 1981 “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. Minimum emittance theory (summary) |A|, and c are completely determined by the dipole For uniform dipoles: This cubic equation determines the optimal dispersion for EME “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

  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

  16. Optimal bending profile • 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 bending curvature (B field) bending radius profile TME AME AME EME TME EME AME TME slice number slice number “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. Linearly-ramped bending profile A model sufficiently close to the optimal, yet can be solved analytically TME AME/EME (rmax , L) (r0, L0) S = 0 S = 0 is chosen as a given parameter “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. Theoretical minimum emittance(TME) f1 and f2 are functions of (g,r) F is normalized by the value of reference uniform dipole, i.e., improvement in TME emittance r k k “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

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

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

  21. Basic layout of a normal-conducting rf photoinjector 25 MV/m • Adopted from dc injector as an example, major difference is the cathode field solenoid rf buncher two-cell cavities @ 650MHz gun cavity @ 325MHz

  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 high coh. high flux 4 x bunch charge meet requirements, can be better

  23. Preliminary result of a potential nc rf photoinjector (2) 0.77pc 0.3nc • ASTRA output of bunch information

  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

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