experience on ga optimization of photoinjector and minimum emittance in rings chun-xi wang advanced...
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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)
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
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
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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
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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
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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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
Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 20128
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
Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 20129
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Testing of non-constrained NSGA-II
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SCH KUR
Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 201210
Testing of constrained NSGA-II
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CONSTR TNK
Outline
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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
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
“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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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)
“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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|A|, and c are completely determined by the dipole
For uniform dipoles:
This cubic equation determines the optimal dispersion for EME
Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 201215
Optimization of bending profile
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
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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
“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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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)
“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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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
r
Outline
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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
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
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
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
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
Experience on GA optimization of photoinjector and minimum emittance in rings, C.-x. Wang, Mini-workshop at Indiana University, Mar. 14-16, 201224
APS injector optimization study
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