1. An overview of TREDI & CSR test cases L. Giannessi – M. Quattromini Presented at “Coherent Synchrotron and its impact on the beam dynamics of high brightness electron beams” January 14-18, 2002 at DESY-Zeuthen (Berlin, GERMANY)

2. TREDI … … is a multi-purpose macroparticle 3D Monte Carlo, devoted to the simulation of electron beams through Rf-guns Linacs (TW & SW) Solenoids Bendings Undulators  Quads’  … where Self Fields are accounted for by means of Lienard-Wiechert retarded potentials

3. SELF FIELDS R(t’) Target Source

4. Motivations  Three dimensional effects in photo-injectors Inhomogeneities of cathode quantum efficiency Laser misalignments Multipolar terms in accelerating fields  “3-D” injector for high aspect ratio beam production …. on the way …  … Study of coherent radiation emission in bendings and interaction with beam emittance and energy spread

5. History 1992-1995 - Start: EU Network on RF-Injectors* Fortran / DOS(PC-386 – 20MHz) Procs: “VII J.D'Etude Sur la Photoem. a Fort Courant” Grenoble 20-22 Septembre 1995 1996-1997 - Covariant smoothing of SC Fields Ported to C/Linux (PC-Pentium – 133MHz) FEL 1996 - NIM A393, p.434 (1997) - Procs. of 2nd Melfi works. 2000 - Aracne ed.(2000) 1998-1999 - Simulation of bunching in low energy FEL** Added Devices (SW Linac – Solenoid - UM) (PC-Pentium – 266MHz) FEL 1998 - NIM A436, p.443 (1999) (not proceedings …) 2001-2002 - Italian initiative for Short FEL Today: Many upgrades - First tests of CSR in new version *Contributions from A. Marranca ** Contributions from P. Musumeci

6. FEL lasing (1998)

7. Major upgrade to: Accomodate more devices (Bends, Linacs, Solenoids …) Load field profiles from files Point2point or Point2grid SC Fields evaluation (NxN  NxM) Allowed piecewise simulations Graphical User Interface for Input File preparation (TCL/Tk) Graphical Post Processor for Mathematica / MathCad / IDL Porting to MPI for Parallel Simulations Fix Data / Code architectural dependence SDDS support for data exchange with FEL codes ? Smoothing of acceleration fields (still more work required) Radiative energy loss 5000 lines  12.000+ lines of code + pre/post processors

8. TREDI FlowChart Start Load configuration & init phase space Charge distribution & external fields known at time t Adaptive algorithm tests accuracy & evaluates step length  t Trajectories are intagrated to t+  t Self Fields are evaluated at time t+  t Exit if Z>Zend

9. Parallelization Node 3Node 2Node 1 ………… Node n Particle trajectory 1 Time Particle trajectory 2Particle trajectory 3 Particle trajectory k-2Particle trajectory k-1 Particle trajectory k …………………….. Present Beam NOW Self Fields

10. CSR Tests with TREDI Problems: CSR cases are memory and cpu consuming  Parallelization required  very few particles (300 particles  4h on IBM SP3/16 nodes - 400 MHz each) The program seems much slower than expected The real enemy is the noise: Analysis and suppression of numerical noise Test cases Basic - No compression 5 nC - 5 GeV 500 MeV -1.0 nC - Gaussian 5 GeV - 1.0 nC/0.5nC - Gaussian

11. R(t’) Targets Source Target Source Collective (coherent) effect 2 Particles interaction incoherent “collision”

12. Effect of Noise (1st bend - no screening)

13. Suppression of noise Acceleration fields Can be very large in high energy cases Decrease only with distance as 1/R Produce transverse forces In the case of pure coulomb fields  Regularization is obtained by giving macroparticles a finite size In the case of radiative fields  Regularization is obtained by giving macroparticles a finite size in momentum space

14. Suppression of noise II The spatial integral is treated applying the Gauss theorem … The momentum integral can be estimated by assigning a minimum momentum dispersion Transverse Electric Field View angle   = 10 -4  = 10 4

15. Suppression of noise III The integral in momentum space with a Gaussian distribution is CPU time consuming Alternative: Limit angle of “influence” of particles to force collective interactions P = impact parameter P=0 point like particles - no smoothing collisions dominate P=1limited spread particles- collective effects are dominant P>1 spread out macroparticle - reduced interaction

16. Effect of impact parameter (Simulation of first bend - “basic” case)

17. Phase space at exit  still noisy ! Basic case - P=1 - No compression - 5 GeV 1.0 nC

18. No compression - 5 GeV 1.0 nC Estimation of emittance

19. No compression - 5 GeV 1.0 nC -  x =10.1 mm-mrad

20. No compression - 5 GeV 1.0 nC Emittances

21. No compression - 5 GeV 1.0 nC

22. Energy variation ??

23. No compression - 5 GeV 1.0 nC Transverse rms

24. E= 5 GeV - Q=1 nC Bunch Length

25. Phase space at exit  still noisy !

26. Estimation of emittance

27. Emittance vs. z dispersion

28. Energy spread

29. Phase space at exit with 85% of the charge,  x =2.3 mm-mrad

30. E= 5 GeV - Q=0.5 nC Bunch Length

31. Phase space at exit with 85% of the charge,  x =1.4 mm-mrad

32. E= 500MeV - Q=1.0 nC Bunch Length

33. Emittance at exit - 500 MeV - 1.0 nC ??

34. Phase space at exit with 92% of the charge,  x =21 mm-mrad

35. Conclusions The noise suppression method has reduced the effects of SF on longitudinal phase space, without being completely effective in the transverse phase space A rigorous model of fields regularization, relying on a realistic momentum dispersion of macroparticles will be soon implemented The low number of macroparticles in severely limiting the reliability of the results Diagnostic on fields will be implemented to improve insight on the smoothing procedure The reason of the slow down of the code must be understood Before the end of the workshop the 1000 particles case will be finished - we will see.