Advanced Modeling of a Next Generation Light Source

Ji Qiang

Lawrence Berkeley National Laboratory

Oct. 3, 2013Oct. 3, 2013

Outline

Introduction Computational model Wakefield effects in undulator Simulation of microbunching instability Start-to-end simulation using a real number of electrons Parallel design optimization

Advanced Multi-Physics Modeling of Accelerators is Needed for Future Light Source Designs that Can't be Modeled with Existing Tools

• FELs and other future light sources are very sensitive to phase space perturbation from processes such as the shot-noise microbunching instability, which significantly

degrades the x-ray performance.• New seeding schemes (e.g. ECHO) demand production and transport of very fine

beam structure not present in high energy physics colliders.• Advanced modeling is needed to accurately model initial shot noise, resolve fine

structure, and avoid numerical artifacts.

The longitudinal phase space of a beam at the exit of a linac shows microbunching instability

Longitudinal phase space at the entrance of an ECHO seeded FEL

Modeling the Development of the Microbunching Instability from the Shot Noise Using about Two Billion Electrons

bench length coordinate (mm) (head)

From the exit of BC1 through BC2 in an FEL driver.

(tail)

Final Electron Beam Distribution from a Direct Numerical Simulation Using Real Number of Electrons

bunch length coordinate (mm)bunch length coordinate (mm)

curr

ent (

A)

Ene

rgy

devi

atio

n (k

eV)

final current profile final longitudinal phase space

Computational Model

Modeling Photo-Electron Emission Using the Three Step Model(Includes both Material and External Schottky Work Function Effects)

• The photo-electron beam quality born out of the photo-cathode sets the limit of the final beam brightness for next generation light source• We now generate the initial particle momentum distribution from a 1st principle model

Three-Step Photo-Emission ModelD. Dowell et al., PRSTAB 2009.

A 2nd Order Numerical Model to Simulate Photo-Emission Process:Significantly Reduces the Number of Emission Steps

Current Profile with Different Number of Emission Steps(2nd order vs. 1st order emission model)

photocathode

bunch length coordinate (m)

t

cathode

2nd order: 750

1st order: 750

1st order: 1500

1st order: 3000

Space-Charge Calculation Based on Integrated Green Function (IGF) for Large Aspect Ratio Beams

Comparison between the IG and SG for a beam with aspect ratio of 30

)(/1),,( 222 zyxzyxGs

Integrated Green’s function is needed for modeling large

aspect ratio beams!

integrated Green function standard Green function

R. D. Ryne, ICFA Beam DynamicsMini Workshop on Space Charge Simulation, Trinity College, Oxford, 2003J. Qiang, S. Lidia, R. D. Ryne, and C. Limborg-Deprey, Phys. Rev. ST Accel. Beams, vol 9, 044204 (2006).

FFT (O(N log N)) With integrated Green’s function

direct summation (O(N2))

Efficient Shifted Green Function Method to Calculate Image Space-Charge Effects

cathodeShifted-green function

Analytical solution

y

o e-e+

z

computational domain contains only the original beam

J. Qiang, M. Furman, and R. Ryne, J. Comp. Phys. vol. 198, 278 (2004).J. Qiang, M. Furman, and R. Ryne, J. Comp. Phys. vol. 198, 278 (2004).

(O(N logN))

Space-Charge Driven Energy Modulation vs. Distance in a Drift Space

analytical model without including transverse effects

analytical model with including transverse effects

Efficient Method to Calculate Longitudinal and Transverse Wakefields

Operations comparison using the direct summation and the FFT based method

J. Qiang, R. D. Ryne, M. Venturini, A. A. Zholents, I. V. Pogorelov, Phys. Rev. ST Accel. Beams, 12, 100702 (2009).J. Qiang, R. D. Ryne, M. Venturini, A. A. Zholents, I. V. Pogorelov, Phys. Rev. ST Accel. Beams, 12, 100702 (2009).

direct summation (O(N2))

order of magnitude reduction

FFT based (O(Nlog(N)))

Efficient Integrated Green Function (IGF) Method to Calculate Longitudinal Coherent Synchrotron Radiation (CSR) Wakefields

)()()( ''2

1'

iciiiic zzzrEN

i

')',()',( drrrwrr si

typical CSR calculation:a)no short-range interactionb)with numerical filtering

new IGF based method :

New method with integrated Green’s function method :

J.B. Murphy et al., Particle Accelerators 57 (1997) 9. E.L. Saldin et al., NIMA 398 (1997) 373.

R. D. Ryne, et al., arXiv:1202.2409 (2012).J. Qiang, et. al, NIMA 682, 49 (2012).

less than 1 um

IGF Significantly Reduces the Numerical Grid Points Needed:A Comparison in 1-D models with Transient Effects

1nC, 50 μm Gaussian bunch at 150 MeV; bend with radius R = 1.5 m*

*G. Stupakov and P. Emma, Proc. EPAC 2002, Paris, France, 1479 (2002).

IGF 1024 pointsNon-IGF 104312 pointsLimit γ ∞

IGF method obtains the same accuracyas direct integration with a factor of 100fewer sample points

Bend entry(Case A & B)

Bend exit(Case C & D)

qEz (

MeV

/m)

z/σ

0.14 m into a 0.5 m bend 0.05 m into a drift that follows a 0.1 m bend

qEz (

MeV

/m)

Limit γ ->∞

IGF 1024

Non-IGF 104312

C. Mitchell, J. Qiang and R. Ryne, NIMA 715, 119 (2013).

Parallel Performance Matters: Particle-Field Decomposition vs. Domain Decomposition

J. Qiang and X. Li, Comput. Phys. Comm., 181, 2024, (2010).

Particle-field decomposition out-performs the conventional domain decomposition

Resistive Wall Wakefield Effects in Undulator

Resistive Wall Impedance with Anomalous Skin Effects(in low temperature superconductor)

B. Podobedov, PRST-AB 12, 044401 (2009).

4 K temperature is assumed

Resistive Wall AC Impedance (in room temperature conductor)

K.L.F. Bane, “Resistive Wall Wakefield in the LCLS Undulator Beam Pipe,” SLAC-PUB-10707, Revised October 2004.

Energy Loss Across the Electron Beam(low temperature superconductor)

AlCu

Energy Loss Across the Electron Beam(room temperature conductor)

AlCu

Power Loss vs. Undulator Vacuum Gap

loss per unit length

final total loss

Wakefield Induced RMS Energy Spread vs. Undulator Vacuum Gap

energy spread per unit length

final total energy spread

Fraction of Electrons Inside the Rho vs. Undulator Vacuum Gap(low temperature superconductor)

Start-to-End Simulation of X-Ray Radiation Using about Two Billion Real Number of Electrons

•The start-to-end multi-physics simulation includes: - self-consistent 3D space-charge effects, - 1D CSR effects, ISR effects, structure wakefields, - self-consistent 3D electron and x-ray radiation interaction

Evolution of RMS Emittances, RMS Sizes and Kinetic Energyin a Next Generation Light Source Beam Delivery System

rms emittances

rms sizes and kinetic energy

Current Profile, Slice Emittances and Longituinal Phase Space at the Entrance of Undulator (~2 billion macropaticles)

Evolution of 1 nm X-Ray Radiation Power in Undulatorwith different uncorrelated energy spread from a laser heater

Parallel Design Optimization

Multi-Level Parallel Differential Evolution Algorithm for Multi-Objective Function Optimization

• Stochastic, population-based evolutionary optimization algorithm • Easy to implement and to extend to multi-processor • DE has been shown to be effective on a large range of classic optimization problems• In a comparison by Storn and Price in 1997 DE was more efficient than simulated annealing and genetic algorithms• Ali and Torn (2004) found that DE was both more accurate and more efficient than controlled random search• In 2004 Lampinen and Storn demonstrated that DE was more accurate than several other optimization methods including four genetic algorithms, simulated annealing and evolutionary programming

Differential Evolution (DE) Algorithm

Ref: R. Storn and K. Price, Journal of Global Optimization 1a1:341-359, (1997)M. M. Ali and A. Torn, Computers and Operations Research, Elsevier, no. 31, p. 1703, 2004.K. Price, R. Storn, and J. Lampinen, Differential Evolution- A Practical Approach to Global Optimization, Springer, Berlin, 2005.

Differential Evolution Algorithm for Global Single Objective Parameter Optimization

1. Define the minimum size, NPmin and the maximum size, NPmax of parent population. Define the maximum size of the external storage, NPext. 2. An initial population of NPini parameter vectors is chosen randomly to uniformly cover the entire solution space.3. Generate offspring population using the differential evolutionary algorithm.4. Check new population against boundary conditions and constraints.5. Combine the new population with the existing parent population from the external storage. Non-dominated solutions (Ndom) are found from this group of solutions and min(Ndom, NPext) of solutions are put back into the external storage. Pruning is used if Ndom>NPext. NP parent solutions are selected from this group of solutions for next generation production. If NPmin <= Ndom<=NPmax, NP = Ndom. Otherwise, NP=NPmin if Ndom<NPmin and NP=NPmax if Ndom > NPmax. 6 . If the stopping condition is met, stop. Otherwise, return to Step 3.

A New Parallel Multi-Objective Differential Evolution Algorithmwith Variable Population Size and External Storage (VPES-PMDE)

Benchmark with an Analytical Example: VPES-PMDE Shows Faster Convergence than a Popular Genetic Algorithm

Ref: K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, IEEE Trans. Evol. Comp, Vol. 6, p. 182, (2002)

VPES-PMDE

NSGA-II

cavity(187 MHz)solenoid cavity (650 MHz) cavity (650 MHz)

cathode

e beam

A Real Application: Parallel Multi-Objective Optimizationwith Parallel Beam Dynamics Simulation of a Photo-Injector

Control Parameters (10):

Initial laser transverse size and pulse length (2)Gun cavity phase (1)Solenoid strength and position (2)RF module starting position (1)Cavity 1 phase and amplitude (2)Cavity 2 phase and amplitude (2)

VPES-PMDE shows much faster convergence than the popular genetic algorithm NSGA-II with 800 function evaluations!

VPES-PMDE

NSGA-II

Thank You for Your Attention!

head of the beam

Electron Beam Current Profile at the Entrance of the Undulator

Total Undulator Length vs. Undulator Vacuum Gap