Accelerator Physics Group November 11, 2010 Introduction Brookhaven National Laboratory.1 (21)
1 Introduction Introduction.2 (21)
1 Introduction Introduction 2.2 (21)
1 Introduction Introduction 2 3.2 (21)
Introduction Introduction Energy Current Emittance Circumference Cell Straight 3 GeV 500 ma ɛ x = 0.6nm, ɛ y = 8 pm 792 m 30 DBA/15 fold sym. 6.6 m and 9.3 m.3 (21)
Dynamic Aperture Requirement 1 At least 15 mm required from injection group 2 DA at δ = 2.5% helps Touschek lifetime. 3 (take a look at δ = 3.0% when having more RF) Overview and status Before Aug. 2009, DA optimization with nonlinear driving terms are carried out, and continued to ξ x, ξ y = (0, 0), (2, 2), (4.6, 4.6) Weiming Guo (elegant), Johan Bengtsson (Tracy-II), Stephen Kramer... Complementary: Direct tracking, combined with low order nonlinear driving terms are done for similar chromaticities settings. Fanglei Lin (elegant), (elegant/tesla). Introduction.4 (21)
Tracking with elegant and tesla Early stage, elegant (M. Borland etc.) was used for the particle tracking, DA calculation in x y plane and the nonlinear driving terms. New tracking code called tesla was later developed: Linear lattice (nolinear driving terms). Tracking with symplectic integrator. Compact and fast. Good efficiency in searching DA boundary. In the form of library, and linked with optimizer. Irregular DA : maximum survival area in δ x plane. DA at δ = 0, 0.025 and 0.025 was tracked. Introduction.5 (21)
Parallel Multiobjective Optimization A parallel NSGA-II optimizer (K. Deb 2001, Multi-objective optimization using Evolutionary Algorithms). Multi-Objective Genetic Algo. 1: Initialize population. 2: repeat Introduction 7: until should stop 1 Initialize: the very first generation (random). 100 200 CPUs are used for DA optimization..6 (21)
Parallel Multiobjective Optimization A parallel NSGA-II optimizer (K. Deb 2001, Multi-objective optimization using Evolutionary Algorithms). Multi-Objective Genetic Algo. 1: Initialize population. 2: repeat 3: crossover: 2 2 Introduction 7: until should stop 1 Initialize: the very first generation (random). 2 Crossover: generate children from parents. 100 200 CPUs are used for DA optimization..6 (21)
Parallel Multiobjective Optimization A parallel NSGA-II optimizer (K. Deb 2001, Multi-objective optimization using Evolutionary Algorithms). Multi-Objective Genetic Algo. 1: Initialize population. 2: repeat 3: crossover: 2 2 4: mutation: change children. Introduction 7: until should stop 1 Initialize: the very first generation (random). 2 Crossover: generate children from parents. 3 Mutation: change the children slightly. 100 200 CPUs are used for DA optimization..6 (21)
Parallel Multiobjective Optimization A parallel NSGA-II optimizer (K. Deb 2001, Multi-objective optimization using Evolutionary Algorithms). Multi-Objective Genetic Algo. 1: Initialize population. 2: repeat 3: crossover: 2 2 4: mutation: change children. 5: calculate obj. func. f m 6: natural selection: sorting 7: until should stop Introduction 1 Initialize: the very first generation (random). 2 Crossover: generate children from parents. 3 Mutation: change the children slightly. 4 Natural selection: keep population fixed from generation to generation. 100 200 CPUs are used for DA optimization..6 (21)
DA Larger DA area may not necessary provide a better solution,... Introduction Unless it covers an ellipse fully. For δ = 0, 0.025, 0.025, three constraints, three objective functions. Different δ can use same/different ellipse. But, can not avoid small aperture for δ between [ 0.025, 0] and [0, 0.025]. Will solve this later..7 (21)
in x y plane Using elegant with 7 lines mode: Introduction Constraint ellipse A x = 18 mm and A y = 2 mm.8 (21)
DA in δ x Plane Max survival area in δ x plane is more direct: Introduction Large area at y 1um indicates reasonable good at larger y..9 (21)
DA Area and Driving Terms The second strategy uses as objective functions f 1 the sum of the on and off momentum DA and f 2 the geometric sum of tune shifts with amplitude: f 1 = δ S(δ, y = 1µm) ( ) 2 ( ) 2 ( ) 2 νx νx νy (1) f 2 = + + J x J y J y Introduction Tunes with amplitude are chosen. Other driving terms h abcde are not used. Not required but may helps. The multi-objective feature makes the final results not sensitive on how we choose driving terms..10 (21)
Optimize with Sextupole Strength Introduction 6 geometric sextupoles 3 chromatic sextupoles, two for Chromaticity, e.g. (0, 0), (4, 4). Linear lattice is already set and provided by Weiming Guo..11 (21)
Objective Functions of Final Generation Introduction with elegant (M.Borland etc. APS) simulation..12 (21)
Optimize in x y Plane with 6 Sextupoles Tune with amplitude and foot print are shown: Introduction The linear lattice is fixed. Chromaticity is fixed. Only 6 geometric sextupoles are used for optimization. Optimizing in x y plane..13 (21)
Introduction Frequency map of one solution at working point (33.43, 16.35). 3 damping wiggler included. Multipole errors, misalignment and rotation errors are also considered..14 (21)
Optimize in δ x Plane with 9 Sextupoles 6 geometric sextupoles, 2 chromatic for fixed chromaticity and 1 free chromatic sextupole. Introduction.15 (21)
Introduction Frequency map for working point (ν x = 33.15, ν y = 16.27), and chromaticity (ξ x = 4, ξ y = 4). Multipole errors, misalignment and rotation errors are included..16 (21)
Linear Lattice Can be Part of the Optimization Introduction Tune can be varied by β x,y in straight only..17 (21)
Linear Lattice Can be Part of the Optimization Introduction Tune can be varied by β x,y in straight only. High and low beta region can be tuned independently. DW region is fixed..17 (21)
Linear Lattice Can be Part of the Optimization Introduction Tune can be varied by β x,y in straight only. High and low beta region can be tuned independently. DW region is fixed. 9 Sextupoles and 6 quadrupoles are tuned in optimizer..17 (21)
Optimize with Tune Introduction Frequency map of a candidate lattice with tunes (33.28, 16.35) and fitted chromaticity (4.83, 4.80). The rectangle with green dashed line is the constraints. A vertical resonance line, 2ν x + 2ν y = 99, exists around δ = 1% in read and yellow colors..18 (21)
Optimize with Tune Introduction.18 (21)
Driving Terms: Necessary but not Sufficient Do a data mining on the first example, i.e. optimizing DA in x y plane without using driving terms. (Yongjun Li) Introduction σ is sum of normalized driving terms, here are only tunes with amplitude. Normalized by the average of the whole population..19 (21)
High-Low (Low-Low,*) Low-High Fanglei Lin started new HL-beta lattice. Linear and nonlinear optimization. Tunes are (37.18,16.22). Introduction.20 (21)
High-Low (Low-Low,*) Low-High Fanglei Lin started new HL-beta lattice. Linear and nonlinear optimization. Tunes are (37.18,16.22). Optimized with multiobjective optimzer. Introduction Frequency Map and Tune Footprint For standard vacuum vertical gap 25mm Errors: In (x, δ) space 0.5 mrad rms role angle for both quads and sextupoles 0.3 µm rms offset for quads 30 µm rms offset for sextupoles Courtesy of --- Multi-objective optimization for dynamic aperture.20 (21)
High-Low (Low-Low,*) Low-High Fanglei Lin started new HL-beta lattice. Linear and nonlinear optimization. Tunes are (37.18,16.22). Optimized with multiobjective optimzer. Adding DW and physical aperture. (F. Lin) Introduction Frequency Map and Tune Footprint With Physical Aperture.20 (21)
High-Low (Low-Low,*) Low-High Fanglei Lin started new HL-beta lattice. Linear and nonlinear optimization. Tunes are (37.18,16.22). Optimized with multiobjective optimzer. Adding DW and physical aperture. (F. Lin) Introduction Frequency Map and Tune Footprint With Physical Aperture.20 (21)
1 Multi-Objective optimization was done for DA at. 2 Several cases under different chromaticities are studied. 3 Optimized DA is not sensitive to linear tune/lattice. 4 The correlation between DA and driving terms shows that small DT is necessary but not sufficient condition for good DA. 5 High-Low beta lattice optimization is carried out with F. Lin and it is promising. Introduction.21 (21)