Experience on GA optimization of photoinjector and minimum emittance in rings Chun-xi Wang Advanced Photon Source (APS) Argonne National Laboratory (ANL)

Experience on GA optimization of photoinjector and minimum emittance in

rings

Chun-xi WangAdvanced Photon Source (APS)

Argonne National Laboratory (ANL)[email protected]

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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

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Multi-objective optimization

Multiple objectives (conflicting interests) Pareto optimal solutions (Pareto front) Many algorithms for searching Pareto front (e.g. NSGA-II)


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Early usage in accelerator field


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Recent popularity

Availability of computer clusters for parallel computation


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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


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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) 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.htmlExperience 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


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 linux clusters, TORQUE on multicore workstations/laptops


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Testing of non-constrained NSGA-II

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SCH KUR


Testing of constrained NSGA-II

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CONSTR TNK

Outline

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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

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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

Natural horizontal emittance


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betatron emittance for uncoupled lattices

Dispersion action

depending on linear lattice design

For isomagnetic rings with conventional dipoles of bending angle q :

a remarkable fact known since 1981

Minimum emittance theory (summary)


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|A|, and c are completely determined by the dipole

For uniform dipoles:

This cubic equation determines the optimal dispersion for EME


Optimization of bending profile

Optimal bending profile


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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

TMEAME EME

Linearly-ramped bending profile


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A model sufficiently close to the optimal, yet can be solved analytically

TME AME/EME

is chosen as a given parameter

S = 0 S = 0(r 0, L0)

(r max , L)

Theoretical minimum emittance (TME)


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F is normalized by the value of reference uniform dipole, i.e.,

f1 and f2 are functions of (g,r)

k

k

improvement in TME emittance

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Outline

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• Design study of a high-brightness cw injector for ERL

• Optimization of APS injector & linac

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 SannibaleJohn StaplesRuss 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


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


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


Preliminary result of a potential nc rf photoinjector (2)

ASTRA output of bunch information

0.3nc 0.77pc


APS injector optimization study

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Documents

Experience on GA optimization of photoinjector and minimum emittance in rings Chun-xi Wang Advanced Photon Source (APS) Argonne National Laboratory (ANL)