1. Advanced Modeling of a Next Generation Light Source Ji Qiang Lawrence Berkeley National Laboratory Oct. 3, 2013

2. 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

3. 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

4. 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)

5. Final Electron Beam Distribution from a Direct Numerical Simulation Using Real Number of Electrons bunch length coordinate (mm) current (A) Energy deviation (keV) final current profilefinal longitudinal phase space

6. Computational Model

7. 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 1 st principle model Three-Step Photo-Emission Model D. Dowell et al., PRSTAB 2009.

8. A 2 nd Order Numerical Model to Simulate Photo-Emission Process: Significantly Reduces the Number of Emission Steps Current Profile with Different Number of Emission Steps (2 nd order vs. 1 st order emission model) photocathode bunch length coordinate (m) cathode 2 nd order: 750 1 st order: 750 1 st order: 1500 1 st order: 3000

9. 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 Integrated Green’s function is needed for modeling large aspect ratio beams! integrated Green functionstandard Green function R. D. Ryne, ICFA Beam DynamicsMini Workshop on Space Charge Simulation, Trinity College, Oxford, 2003 J. 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(N 2 ))

10. Efficient Shifted Green Function Method to Calculate Image Space-Charge Effects cathode Shifted-green function Analytical solution y oe-e- e+e+ z computational domain contains only the original beam J. Qiang, M. Furman, and R. Ryne, J. Comp. Phys. vol. 198, 278 (2004). (O(N logN))

11. Space-Charge Driven Energy Modulation vs. Distance in a Drift Space analytical model without including transverse effects analytical model with including transverse effects

12. 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). direct summation (O(N 2 )) order of magnitude reduction FFT based (O(Nlog(N)))

13. Efficient Integrated Green Function (IGF) Method to Calculate Longitudinal Coherent Synchrotron Radiation (CSR) Wakefields typical CSR calculation: a)no short-range interaction b)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

14. 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 points Non-IGF 104312 points Limit γ ∞ IGF method obtains the same accuracy as direct integration with a factor of 100 fewer sample points Bend entry (Case A & B) Bend exit (Case C & D) qE z (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 qE z (MeV/m) Limit γ -> ∞ IGF 1024 Non-IGF 104312 C. Mitchell, J. Qiang and R. Ryne, NIMA 715, 119 (2013).

15. 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

16. Resistive Wall Wakefield Effects in Undulator

17. Resistive Wall Impedance with Anomalous Skin Effects (in low temperature superconductor) B. Podobedov, PRST-AB 12, 044401 (2009). 4 K temperature is assumed

18. 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.

19. Energy Loss Across the Electron Beam (low temperature superconductor) Al Cu

20. Energy Loss Across the Electron Beam (room temperature conductor) Al Cu

21. Power Loss vs. Undulator Vacuum Gap loss per unit length final total loss

22. Wakefield Induced RMS Energy Spread vs. Undulator Vacuum Gap energy spread per unit length final total energy spread

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

24. 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

25. Evolution of RMS Emittances, RMS Sizes and Kinetic Energy in a Next Generation Light Source Beam Delivery System rms emittances rms sizes and kinetic energy

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

27. Evolution of 1 nm X-Ray Radiation Power in Undulator with different uncorrelated energy spread from a laser heater

28. Parallel Design Optimization

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

30. 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.

31. Differential Evolution Algorithm for Global Single Objective Parameter Optimization

32. 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 NPmax. 6. If the stopping condition is met, stop. Otherwise, return to Step 3. A New Parallel Multi-Objective Differential Evolution Algorithm with Variable Population Size and External Storage (VPES-PMDE)

33. 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

34. cavity (187 MHz) solenoidcavity (650 MHz) cathode e beam A Real Application: Parallel Multi-Objective Optimization with 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

35. Thank You for Your Attention!

36. head of the beam Electron Beam Current Profile at the Entrance of the Undulator

37. Total Undulator Length vs. Undulator Vacuum Gap