TREDI test for
Photo-injectors
L. Giannessi – M. Quattromini
C.R. ENEA-Frascati
Presented at
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’
…
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
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
Features
•
•
•
•
•
15000 lines in C language;
Scalar & Parallel (MPI 2.0);
Unix & Windows versions;
Tcl/Tk Gui (pre-processing);
Mathematica & MathCad frontends (postprocessing);
• Output format in NCSA HDF5 format
(solve endian-ness/alignement problems)
Start
Load configuration
& init phase space
TREDI
FlowChart
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
Particle trajectory 3
Particle trajectory 2
Particle trajectory 1
Node 1
……………………..
Node 2
Node 3
…………
Node n
Particle trajectory k
Particle trajectory k-1
NOW
Particle trajectory k-2
Time
Parallelization
Present Beam
Self Fields
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)
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
?
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)

done
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)
Eqs Of motion…








d 
 d


 d

 d
N.B. : τ = c·t
 r
 

p
mc
p

mc


e 

E   B
2 

mc 





SELF FIELDS…
Self Fields are accounted for by means of
Lienard-Wiechert retarded potentials
Source
R(t’)
Target
Retard Condition
tret  x  r    0
2
EM fields:
Accel.
term

 
Velocity t erm


nˆ   nˆ     
 

nˆ  
q


E  q
3 2
3
2
c
 1  nˆ   R
1  nˆ   R



B  nˆ  E








 
x  r t ret  Rt ret 
nˆ   
 
x  r t ret  Rt ret 
R(t )
Retarded time t   t 
c
Problem: fields regularization
• Real beam~ 1010 particles
• Macroparticles ~ 103-106
huge charges
Pseudo-collisional effects
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.
Alternative
• Get rid of 3-anything (i.e. • Use 4-quantities instead
quantities not possessing a
definite Lorentz character)
q,
( x  r ) V
V
 
E , B, cos ,  dR...
R
0

,W

(x  r) V 
F 
Field strength produced by an
accelerated charge (covariant form)
(see e.g. Classical Electrodynamics, J. D. Jackson)
 


q
d x  r  V  x  r  V  


F  x  r V d 


x  r V

 ret
 is the (source) proper time and

V is the (source) 4-velocity: V   ,  

Separation in vel.+accel. terms
F



  V 





W
W
 q T 3
T 2
 S W  T 3

S V 
S V  
 S V 
Velocity t erm


q

V 

T
3
S V 
terms
Accelerati

on



q
q


W   3 S W T W 
 2
T
S V 
S V 
Separation in vel.+accel. terms (cont’d)
• Where:
dV

W


d


S U 
 U  x  r 


  U    x  r  U    x  r  U 
T
S U 
Note:
 S U , R  e.g.
T  U   T  U , R 
is the 4 - accelerati on
is a Lorentz scalar
is an antisymmet ric tensor


SV   R 1  nˆ  

The natural decomposition of EM fields
can be cast in a covariant form!
F

F
V

F
A

Velocity term:
R  0  S V   0
Lorentz scalar

FV
q

 3 T V 
S V 
Lorentz scalar
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
Qeff x  r 
lim
0
3
R 0
S V 
• A scaled replica of the (retarded) beam:
• Same aspect ratio
 mp 
 beam
3
N
Boosts change macroparticles’ shape


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:
Rest
frame





 0 0 0 0



ˆ 1   0

1
0

ˆ


0



Lab frame (primed)

13
11








 T 1

T
1
  ˆ  
  ˆ  

ˆ 1  
 31

3

3





 

  ˆ 1 
ˆ 1 


Smoothing of vel. fields (cont’d)
Rest Frame(3 - vectors)
Lab Frame (4 - vectors)


 

 T 1 
2
T ˆ 1
ˆ
R0  x    x  x    x
e.g.: gaussian shape:

 r  
 r 
Rest Frame (3 - vectors)


 T 1 
 x  ˆ  x 
q

exp  
3
2

2  det ˆ 

Lab Frame (4 - vectors)



 xT  ˆ 1  x 
q


 exp  

3
2
2  det ˆ 


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:

Q eff R  xT  ˆ 1  x
E eff R 

 R
 R 2 
2

 q erf   
R  exp  

 2 
 2


Q eff R  xT  ˆ 1  x
 2
x

Smoothing of vel. fields (cont’d)
Eff. Charge
Un-smoothed (1/R2) fields
Effective vel. field
Acceleration term
Lorentz scalars

FA
q
q


 2 T W   3
S W T W 
S V 
S V 
Lorentz scalars
Smoothing of accel. fields

• Fields blow up when   n̂ (“collinear divergencies)
• Solution: target macro particles are given a finite
extension in space:
• Let be



S0  x V   x 1  nˆ  

Smoothing of accel. fields (cont’d)
 1

 2
 S V 

 1

 2
 S V 
Where:

 2  2
S
d  exp 
 G 2 S 0 
2
3 
2  0
 2 
2
0

 2  2
S 02
d  exp 
 G 2 S 0 
2
3 
2  0
 2 
S 02  2S0   2
G2 S 0   2 4
S0  2S 02  2 1   2  2   4
 

and G3 is a too complicated to be worth seeing
Effectiveness of smoothing
• S0 ~10-5 (“collinear”)
Qeff
σ
vs
R
Effectiveness of smoothing (cont’d)
• S0 ~10-3 (“non collinear”)
Qeff
σ
vs
R
SPARC INJECTOR
SOLENOID
RF-GUN
LINAC
SOLENOID
(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
Energy Spread:
Tredi
Homdyn
Homdyn data: courtesy of M. Ferrario
Envelopes
Tredi
Homdyn
Parmela
Parmela data: courtesy of C. Ronsivalle
The emittance in the Gun+Sol
Tredi
Homdyn
Sol. at standard position
Tredi
Homdyn
Sol. 2cm ahead
Tredi
Tredi, sol 2cm ahead
Homdyn
Sol. 1cm ahead
Tredi
Tredi, B 2cm ahead
Tredi, B 1cm ahead
Homdyn
The emittance in the Gun revisited
Tredi
Tredi, B 2cm ahead
Tredi, B 1cm ahead
Homdyn
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
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?
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.
Energy spread (cont’d)
Tredi
Homdyn