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

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 Septembre 1995
Covariant smoothing of SC Fields
Ported to C/Linux (PC-Pentium – 133MHz)FEL
NIM A393, p.434 (1997) - Procs. of 2nd Melfi works Aracne ed.(2000)
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 NIM A436, p.443 (1999) (not proceedings …)
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. Particle trajectory k-2 Particle trajectory k-1
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 depences done, now use HDF5 data format support to fix endian-ness/alignments problems (output portability to different platforms)
Introduce radiative energy loss done
? Smooth acceleration fields (for CSR tests) done (more work required, no manifestly covariant, CPU consuming)
Big speed up (improved retarded time condition routine):
Zeuthen: 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 faster still experimental)

10. Eqs Of motion…
N.B. : τ = c·t

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

12. Retard Condition

13. EM fields:

14. Problem: fields regularization
Real beam~ 1010 particles
Macroparticles ~ 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. Alternative
Get rid of 3-anything (i.e. quantities not possessing a definite Lorentz character)
Use 4-quantities instead

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. SPARC INJECTOR RF-GUN LINAC (BNL RfGun+Solenoid+Drift)
Gradient
140 MV/m
Charge
1nC
Pulse length
10 ps (flat top)
Spot radius
1 mm
Extraction phase
~35º (center)
Solenoid field
~0.3 T
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. Test results obtained in Parmela-like mode;
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 particles?)
Make smoothing of Accel. Fields manifestly covariant
Save SC fields onto output to estimate noise

42. Some internals of the code need to be fully understood but…
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 ( 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