tredi test for photo-injectors
DESCRIPTION
TREDI test for Photo-injectors. Presented at. L. Giannessi – M. Quattromini C.R. ENEA-Frascati. 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. - PowerPoint PPT PresentationTRANSCRIPT
TREDI test forPhoto-injectors
L. Giannessi – M. QuattrominiC.R. ENEA-Frascati
Presented at
TREDI …… is a multi-purpose macroparticle 3D Monte Carlo,
devoted to the simulation of electron beams through
Rf-gunsLinacs (TW & SW)SolenoidsBendingsUndulatorsQuads’…
Motivations
Three dimensional effects in photo-injectors Inhomogeneities of cathode quantum efficiency
Laser misalignmentsMultipolar 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)FEL1996 - 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 (post-
processing);• Output format in NCSA HDF5 format
(solve endian-ness/alignement problems)
TREDI FlowChart
StartLoad 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 timet+ t
Exit if Z>Zend
Parallelization
Node 3Node 2Node 1
…………Node n
Par
ticl
e tr
aje
cto
ry 1
Time
Par
ticl
e tr
aje
cto
ry 2
Par
ticl
e tr
aje
cto
ry 3
Par
ticl
e tr
aje
cto
ry k
-2
Par
ticl
e tr
aje
cto
ry k
-1
Par
ticl
e tr
aje
cto
ry k
……………………..
Present BeamNOW
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 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: 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 faster still experimental)
Eqs Of motion…
mc
p
r
N.B. : τ = c·t
BEmc
e
d
d
mc
p
d
d
2
SELF FIELDS…
R(t’)
Target
Source
Self Fields are accounted for by means of Lienard-Wiechert retarded potentials
Retard Condition
02ret rxt
EM fields:
EnB
Rn
nn
c
q
Rn
nqE
ˆ
termAccel.
ˆ1
ˆˆermVelocity t
ˆ1
ˆ3232
c
tRtt
tR
tR
trx
trxn
)( timeRetarded
ˆret
ret
ret
ret
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. quantities not possessing a definite Lorentz character)
• Use 4-quantities instead
R
dRBE0
...,cos,,
F
Vrx
WV
Vrx
q
)(
,
)(
,
Field strength produced by an accelerated charge (covariant form)
(see e.g. Classical Electrodynamics, J. D. Jackson)
is the (source) proper time and
V is the (source) 4-velocity:
ret
Vrx
VrxVrx
d
d
Vrx
qF
,V
Separation in vel.+accel. terms
on termsAccelerati
ermVelocity t
32
3
323
WWSVS
qW
VS
q
VVS
q
VS
WWS
VS
W
VS
Vq
TT
T
TTTF
Separation in vel.+accel. terms (cont’d)
• Where:
tensorricantisymmetan is
scalar Lorentz a is
onaccelerati-4 theis
UrxUrxU
rxUUS
d
dVW
T
,
ˆ1S e.g. ,
RUTUT
nRVRUSUS
Note:
The natural decomposition of EM fields can be cast in a covariant form!
AV FFF
Velocity term:
VVS
qF TV
3
Lorentz scalar
Lorentz scalar
0 0 VSR
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
0lim
3eff
0
VS
rxQR
3
beammp
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:
(primed) frame Lab
ˆˆ
ˆˆˆ
frameRest
0
ˆ0
0
0000
ˆ33
1
13
1
31
1
11
1
11
1
TT
Smoothing of vel. fields (cont’d)
vectors)-(4 Frame Lab
1120
ˆˆ
vectors)-(3 FrameRest
xxxxR TT
vectors)-(4 Frame Lab
2
ˆexp
ˆdet2
vectors)-(3 FrameRest
2
ˆexp
ˆdet2
1
3
1
3
xxqr
xxqr
T
T
e.g.: gaussian shape:
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:
ˆQE
2exp
2
2erfˆQ
2
1eff
eff
21
eff
x
xxRR
RR
RqxxR
T
T
Smoothing of vel. fields (cont’d)
Eff. Charge
Effective vel. field
Un-smoothed (1/R2) fields
Acceleration term
WWSVS
qW
VS
qF TTA
32
Lorentz scalars
Lorentz scalars
Smoothing of accel. fields
• Fields blow up when (“collinear divergencies)
• Solution: target macro particles are given a finite extension in space:
• Let be
n̂
nxVxS ˆ10
Smoothing of accel. fields (cont’d)
022
02
2
3
20
2
022
02
2
3
20
2
2exp
2
1
2exp
2
1
SGdS
VS
SGdS
VS
Where:
and G3 is a too complicated to be worth seeing
422220
40
20
20
02 12
22
SS
SSSG
Effectiveness of smoothing
• S0 ~10-5 (“collinear”)
R
σQ vseff
Effectiveness of smoothing (cont’d)
• S0 ~10-3 (“non collinear”)
R
σQ vseff
SPARC INJECTOR
RF-GUN LINAC
SOLENOID
SOLENOID
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
(BNL RfGun+Solenoid+Drift)
104 macro-particles x 3·103 grid points ~13h
Energy Spread:
Homdyn data: courtesy of M. Ferrario
Tredi
Homdyn
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?
AcknoledgementsM. 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