1. Genesis /ALICE Benchmarking Igor Zagorodnov Beam Dynamics Group Meeting 17.03.08

2. Genesis 1.3 (S.Reiche et al) ALICE only 3D 3D Cartesian field solver (ADI) Runge-Kutta integrator Dirichlet boundary conditions transverse motion many other physics parallel (MPI) 1D/2D/3D 3D azimuthal field solver (Neumann) Leap-Frog integrator Perfectly Matched Layer transverse motion simplified model parallel (MPI) tested by me on the examples from the book of SSY (~Saldin et al, 2000 „The Physics …“,)

3. 2.5 MeV

4. Genesis vs. ALICE / Energy Spread (round Gaussian beam, Gaussian energy spread, parallel motion only) ALICE Genesis W = 4 kW SASE 2 parameters

5. How to simulate emmitance with laminar particle motion only? -E. Saldin et al, TESLA-FEL 95-02 (1995); S.Reiche PhD Thesis (1999). - E. Saldin et al, The Physics of Free Electron Lasers (2000) - E. Saldin et al, DESY 05-164 (2005)

6. Genesis vs. ALICE / Emmitance (round Gaussian beam, Gaussian energy spread) ALICE (laminar) Genesis

7. ALICE (laminar) Genesis Field growth rate Genesis vs. ALICE (emittance parameter fit)

8. ALICE (laminar) Genesis Detuning corresponds to maximal growth rate in linear regime Genesis vs. ALICE with laminar motion The transverse motion has to be implemented in ALICE

9. Genesis vs. ALICE with transverse motion P0 = 4 kW 19% Genesis (N=6e4) Genesis (N=3e4) Alice (N=6e4) Alice (N=3e4) The difference in saturation length is 7 %. The difference in power gain is 19 %. The difference does not reduce with changing of the discrete model parameters ?!. I=5KA N ~10 400

10. GINGER/GENESIS results for “0-order” 200- pC case Observations: Again, GENESIS shows slightly longer gain length, 10-m later saturation but 15% higher power Again, GINGER shows deeper post- saturation power oscillation Little sensitivity (2 m, 7%) in GINGER results to 8X particle number increase Possible reasons for differences:  bugs  slight differences in initial e-beam properties (e.g. mismatch)  grid effects (e.g. outer boundary)  ??? William M. Fawley, ICFA 2003 Workshop on Start-to-End Numerical Simulations of X-RAY FEL’s

12. Bridsall C.K., Langdon A.B., Plasma Physics via Computer Simulations, 1991 Dawson J.M, Particle simulation of Plasmas // Reviews of Modern Physics, 1983 About advantages of the „quiet start“ see, for example, in

13. N trans x,%x,% y,%y,%  px, %  py, % Genesis 75001.57.55.15.8 150004.14.74.13.2 ASTRA 75001.64.20.432.3 150000.43.30.621.9 Alice 75000.81.00.8 150000.4 0.5 Properties of the Normal macroparticle distribution

14. N trans RxyRpxpyRxpyRypx Genesis 75008e-32e-25e-38e-3 150008e-31e-21e-33e-3 ASTRA 75004e-37e-35e-3 150005e-34e-36e-34e-3 Alice 75001e-32e-38e-42e-3 150005e-41e-35e-48e-4 Properties of the Normal macroparticle distribution

15. ALICE Genesis clustering Quiet start ? What is the reason? ASTRA

16. The polar form of Box-Muller algorithm (in Genesis) maps the „quiet“ uniform distribution in a clustered normal distribution. Uniform Normal Quiet start ?

17. ALICE Genesis Quiet start ? clustering

18. ALICE Genesis Quiet start ? clustering

19. ASTRA

20. Modified Genesis vs. ALICE with transverse motion P0 = 4000 Watt Genesis (modified) (N=6e4) Alice (N=6e4)

21. The transformation used in ALICE It transforms the uniform distribution X i (0,1) to the normal distribution Y i (  ). This transformation does not destroy the „quiet start“. It uses the straightforward transformation by inverse error function

22. Convergence Genesis Genesis (modified) ALICE Genesis Genesis (modified) ALICE Genesis: Hammersley and Box-Mueller Genesis (modified):Hammersley and the inverse error function ALICE:Sobol and the inverse error function I=5KA N ~10 400 at saturation