TREDI test for Photo-injectors

1. TREDI test forPhoto-injectors Presented at L. Giannessi – M. Quattromini C.R. ENEA-Frascati

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’ • …

3. 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

4. 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) J.B.Rosenzweig & P. Musumeci, PRE 58, 27-37, (1998) – Diamagnetic fields due to finite dimensions of intense beams in high-gain FELs 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

5. Features • 15000 lines in C language; • Scalar & Parallel (MPI 2.0); • Unix & Windows versions; • Tcl/Tk Gui (pre-processing); • Mathematica & MathCad frontends (post-processing); • Output format in NCSA HDF5 format (solve endian-ness/alignement problems)

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

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

8. Upgrades to be done (six months ago, in Zeuthen): • 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 • SDDS support for data exchange with FEL code • Fix Data/Architectural dependences (portability of data) • Introduce radiative energy loss • Smooth (regularize) acceleration fields (for CSR tests)

9. six months later, Chia Laguna… • SDDS support for data exchange with FEL code • Fix Data/Architectural depencesdone, now use HDF5 data format support to fix endian-ness/alignments problems (output portability to different platforms) • Introduce radiative energy lossdone • ?Smooth acceleration fields (for CSR tests)done (more work required, no manifestly covariant, CPU consuming) • Big speed up (improved retarded time condition routine): • Zeuthen: 300 particles  4h on IBM-SP3/16x400MHz) • Chia Laguna: 1000 particles 35m • 10000 particles in 27h on a 32CPUs platform! • Many improvements and bug fixes (surely many still lurking in the code); recently introduced a “Parmela-like” mode (instantaneous interactions,MUCH fasterstill experimental)

10. Eqs Of motion… N.B. : τ = c·t

11. Source R(t’) Target SELF FIELDS… Self Fields are accounted for by means of Lienard-Wiechert retarded potentials

12. Retard Condition

13. EM fields:

14. Problem: fields regularization • Real beam~ 1010 particles • Macroparticles ~ 103-106 huge charges Pseudo-collisional effects

15. Known therapy: • Share charge among vertices of a regular grid (require a fine mesh to reduce noise) Typical problems: • non Lorentz invariant; • assume instantaneous interactions • sensible for quasi-static Coulomb fields, low energy spread etc.

16. Get rid of 3-anything (i.e. quantities not possessing a definite Lorentz character) Use 4-quantities instead Alternative

17. Field strength produced by an accelerated charge (covariant form) (see e.g. Classical Electrodynamics, J. D. Jackson) t is the (source) proper time and V is the (source) 4-velocity:

18. Separation in vel.+accel. terms

19. Separation in vel.+accel. terms (cont’d) • Where: Note:

20. The natural decomposition of EM fields can be cast in a covariant form!

21. Velocity term: Lorentz scalar Lorentz scalar

22. Smoothing of vel. fields • Solution: source macro particles are given a form factor (i.e. a finite extension in space: Debye screening, Q.E.D. f.f. corrections to current M.E.) • Effective charge • A scaled replica of the (retarded) beam: • Same aspect ratio

23. Boosts change macroparticles’ shape

24. Smoothing of vel. fields (cont’d) • Velocity (static,Coulomb) fields travel at speed of light, too! introduce a covariant (4D) generalization of purely geometric form factor:

25. Smoothing of vel. fields (cont’d) e.g.: gaussian shape:

26. Smoothing of vel. fields (cont’d) • Effective charge total charge included by the iso-density surface associated to the value of ρ (ρ’) at observer point:

27. Smoothing of vel. fields (cont’d) Un-smoothed (1/R2) fields Eff. Charge Effective vel. field

28. Acceleration term Lorentz scalars Lorentz scalars

29. Smoothing of accel. fields • Fields blow up when (“collinear divergencies) • Solution: target macro particles are given a finite extension in space: • Let be

30. Smoothing of accel. fields (cont’d) Where: and G3 is a too complicated to be worth seeing

31. Effectiveness of smoothing • S0 ~10-5 (“collinear”)

32. Effectiveness of smoothing (cont’d) • S0 ~10-3 (“non collinear”)

33. SOLENOID LINAC RF-GUN SOLENOID SPARC INJECTOR (BNL RfGun+Solenoid+Drift) 104 macro-particles x 3·103 grid points ~13h

34. Energy Spread: Tredi Homdyn Homdyn data: courtesy of M. Ferrario

35. Envelopes Tredi Homdyn Parmela Parmela data: courtesy of C. Ronsivalle

36. The emittance in the Gun+Sol Tredi Homdyn

37. Sol. at standard position Tredi Homdyn

38. Sol. 2cm ahead Tredi Tredi, sol 2cm ahead Homdyn

39. Sol. 1cm ahead Tredi Tredi, B 2cm ahead Tredi, B 1cm ahead Homdyn

40. The emittance in the Gun revisited Tredi Tredi, B 2cm ahead Tredi, B 1cm ahead Homdyn

41. TODO’s • The nature of discrepancies with other codes (Parmela, Homdyn) need to be investigated and/or explained; • Test results obtained in Parmela-like mode; • Speed up the code (Accel. Fields, OpenMP version? 3D runs with 105 -106 particles?) • Make smoothing of Accel. Fields manifestly covariant • Save SC fields onto output to estimate noise

42. CONCLUSIONS • Some internals of the code need to be fully understood but… • TREDI proved to be an usable tool for simulations of quasi-rectilinear set of devices from mildly-to-wildly relativistic regimes (5-5000 MeV): • Start-to-end simulations?

43. Acknoledgements M. Ferrario, P. Musumeci, C.Ronsivalle, J.B. Rosenzweig, L. Serafini For providing results (Homdyn, Parmela), support, hints, feedback or directly partecipating to the development of TREDI.

44. Energy spread (cont’d) Tredi Homdyn