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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)
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TREDI is a multi-purpose macroparticle 3D Monte
Carlo, devoted to the simulation of electronbeams through
Rf-gunsLinacs (TW & SW)SolenoidsBendingsUndulatorsqQuads
q
where Self Fields are accounted for by meansof Lienard-Wiechert retarded potentials
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SELF FIELDS
( )[ ]( )
( )
( )
EnB
Rn
n
Rn
nnE
=
+
=
23
2
31
1
1
&
c
tRtt
R
Rn
)(timeRetarded
=
=
R(t)
Target
Source
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Motivations
q Three dimensional effects in photo-injectorsInhomogeneities of cathode quantum efficiency
Laser misalignmentsMultipolar terms in accelerating fields
q 3-D injector for high aspect ratio beamproduction
. on the way
q Study of coherent radiation emission in bendingsand interaction with beam emittance and energyspread
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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
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FEL lasing (1998)
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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
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TREDI
FlowChart
Start
Load configuration
& init phase space
Charge distribution & externalfields 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
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Parallelization
Node 3Node 2Node 1
Node n
Particle
trajec
tory
1
Time
Particle
trajec
tory
2
Particle
trajec
tory
3
Particle
traject
ory
k-2
Particle
traject
ory
k-1
Particle
trajec
tory
k
..
Present BeamNOW
Self Fields
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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
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R(t)
Targets
Source
Target
Source
Collective (coherent)
effect
2 Particles interaction
incoherent collision
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Effect of Noise (1st bend - no screening)
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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 obtainedby giving macroparticles a finite sizein momentum space
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Suppression of noise II
retpPP
retP
rdrrrEpdpppE
rdpdrprprpEE
=
00
),()(),()(
),,,(),(
01r01
001
rrrrrrrr
rrrrrrrr
The spatial integral istreated applying the Gauss
theorem
The momentum integralcan be estimated by assigning
a minimum momentum dispersion
0 1 2 3 4 5 6 7 81
0.5
0
Transverse momentum dispersionNo dispersion
Exkk
Eax k
k
.Transverse
Electric
Field
View angle
= 10-4
= 104
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Suppression of noise IIIThe integral in momentum space with a Gaussiandistribution is CPU time consuming
Alternative:Limit angle of influence of particlesto force collective interactions
P = impact parameter
P=0 point like particles - no smoothing
collisions dominateP=1 limited spread particles - collective effectsare dominant
P>1 spread out macroparticle - reduced interaction
nn 11
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Effect of impact parameter(Simulation of first bend - basic case)
0 0.5 1 1.5 2 2.5 30.8
0.9
1
1.1
1.2
1.3
1.4
P=0.1
P=0.5
P=1.0
P=2.0
Z (m)
XEmitta
nce(mm-mrad)
.
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Step s 188=
Z 15.96=
Angle 0=
Optic functions
x 2.173=
x 34.184=
x 0.167=
y 1.582=
y 31.015=
y 0.113=
z 0.665=
z 0.036=
z 39.54=
0 5 10 150
0.1
0.2
X - Z Trajectory
Z (m)
X
(mm)
0.1 0.05 0 0.05 0.1 0.15 0.250
0
50
100Z Projection
Z (mm)
Pz(mc)
0.1 0 0.1
0.05
0
0.05
Y Projection
Y (mm)
Py(mc)
2 1 0 1 2 3 4 52
1
0
1
2
3X Projection
X (mm)
Px(mc)
Phase space at exit still noisy !
Basic case - P=1 - No compression - 5 GeV 1.0 nC
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No compression - 5 GeV 1.0 nCEstimation of emittance
0 10 20 30 40 50 60 70 80 90 1001
10
100
1.
10
3
Charge (%)
Emittance/(%C
harge) 85
.
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No compression - 5 GeV 1.0 nC - x=10.1 mm-mrad
Step s 188=
Z 15.96=
Angle 0=
Optic functionsx 1.768=
x 31.572=
x 0.131=
y 1.542=
y 30.57=y 0.11=
z 0.266=
z 0.06=
z 17.905=
0 5 10 150
0.1
0.2
X - Z Trajectory
Z (m)
X
(mm)
0.04 0.02 0 0.02 0.04
10
5
0
5
10Z Projection
Z (mm)
Pz(mc)
0.4 0.2 0 0.2 0.4
0.5
0
0.5X Projection
X (mm)
Px(mc)
0.1 0 0.1
0.05
0
0.05
Y Projection
Y (mm)
Py(mc)
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No compression - 5 GeV 1.0 nCEmittances
0 2 4 6 8 10 12 14 160
5
10
15
X
YBounds of devices
Z (m)
Emittance(mm-mrad)
.
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0 2 4 6 8 10 12 14 160
0.02
0.04
0.06
X
Bounds of devices
Z (m)
EnergySpread(%)
.
No compression - 5 GeV 1.0 nC
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Energy variation ??
0 2 4 6 8 10 12 14 166 .10
7
4 .107
2 .107
0
X
Bounds of devices
Z (m)
EnergyVaria
tion(MeV)
.
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No compression - 5 GeV 1.0 nCTransverse rms
0 2 4 6 8 10 12 14 160
50
100
150
200
X RMS
Y RMS
Bounds of devices
Z (m)
TransverseRMS(um)
.
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E= 5 GeV - Q=1 nC
0 2 4 6 8 10 12 14 160
50
100
150
200
Z RMS
Bounds of devices
Z (m)
ZRMS(um)
.
Bunch Length
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Phase space at exit still noisy !
2 1.5 1 0.5 0 0.52
1
0
1
2X Projection
X (mm)
Px(mc)
0.1 0.05 0 0.05 0.10.2
0.1
0
0.1
0.2Y Projection
Y (mm)
Py
(mc)
Step s 94=
Z 15.881=
Angle 1.819 105
=
Optic functions
x
0.724=
x 6.403=
x 0.238=
y 1.099=
y 15.131=
y 0.146=
z 2.406=
z 7.384 103
=
z 919.209=
0.08 0.06 0.04 0.02 0 0.02 0.04 0.06400
200
0
200Z Projection
Z (mm)
P
z(mc)
0 5 10 150
0.1
0.2
X - Z Trajectory
Z (m)
X
(mm)
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Estimation of emittance
0 10 20 30 40 50 60 70 80 90 1001
10
100
Charge (%)
Em
ittance/(%C
harge) 85
.
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0 2 4 6 8 10 12 14 160
20
40
60
80
X
Y
Bounds of devices
Z (m)
Emittan
ce(mm-mrad)
.
Emittance vs. z
dispersion
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Energy spread
0 2 4 6 8 10 12 14 160.697198
0.697199
0.6972
0.697201
Z (m)
EnergyS
pread(%)
s1
% s1
Rs1( )2
m
Rs1( )2
m, M km 0,,
.
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Phase space at exit with 85% of the charge, x=2.3 mm-mrad
0.15 0.1 0.05 0 0.050.2
0.1
0
0.1
0.2
X Projection
X (mm)
Px(mc)
0.1 0.05 0 0.05 0.10.1
0
0.1
0.2Y Projection
Y (mm)
Py(mc)
Step s 94=
Z 15.881=
Angle 2.632 105
=
Optic functions
x
0.45=
x 4.582=
x 0.263=
y 1.276=
y 16.83=
y 0.156=
z 5.33=
z 0.015=
z 1.95 103
=
0.06 0.04 0.02 0 0.02 0.04 0.06400
200
0
200Z Projection
Z (mm)
Pz(mc)
0 5 10 150
0.1
0.2
X - Z Trajectory
Z (m)
X
(mm)
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0 2 4 6 8 10 12 14 160
50
100
150
200
Z RMS
Bounds of devices
Z (m)
ZRMS
(um)
.
E= 5 GeV - Q=0.5 nC
Bunch Length
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Phase space at exit with 85% of the charge, x=1.4 mm-mrad
0.15 0.1 0.05 0 0.050.2
0.1
0
0.1
0.2X Projection
X (mm)
Px(mc)
0.15 0.1 0.05 0 0.05 0.1 0.150.2
0.1
0
0.1
0.2Y Projection
Y (mm)
Py(mc)
Step s 94=
Z 15.93=
Angle 3.468 105
=
Optic functionsx 0.466=
x 5.188=
x 0.235=
y 1.178=
y
16=
y 0.149=
z 5.839=
z 0.016=
z 2.146 103
=
0.06 0.04 0.02 0 0.02 0.04 0.06400
200
0
200Z Projection
Z (mm)
Pz(m
c)
0 5 10 150
0.1
0.2
X - Z Trajectory
Z (m)
X(mm
)
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0 2 4 6 8 10 12 14 160
50
100
150
200
Z RMS
Bounds of devices
Z (m)
ZRMS(um)
.
E= 500MeV - Q=1.0 nC
Bunch Length
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Emittance at exit - 500 MeV - 1.0 nC ??
0 10 20 30 40 50 60 70 80 90 1001
10
100
Charge (%)
Emittance/(%C
harge)
.
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Phase space at exit with 92% of the charge, x=21 mm-mrad
1 0.5 0 0.5 1
0.2
0
0.2
X Projection
X (mm)
Px(mc)
0.6 0.4 0.2 0 0.2 0.4 0.6
0.05
0
0.05Y Projection
Y (mm)
Py(mc)
Step s 94=
Z 15.89=
Angle 0.003=
Optic functionsx 0.493=
x 3.967=
x 0.313=
y 2.065=
y
22.26=
y 0.237=
z 0.869=
z 6.571 103
=
z 267.046=
0.1 0.05 0 0.05 0.120
10
0
10
20Z Projection
Z (mm)
Pz(mc
)
0 5 10 15
0
0.1
0.2
X - Z Trajectory
Z (m)
X
(mm)
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Conclusions
The noise suppression method has reduced the effects of SF onlongitudinal phase space, without being completely effective in thetransverse phase space
A rigorous model of fields regularization, relying on a realisticmomentum dispersion of macroparticles will be soon implemented
The low number of macroparticles in severely limiting the reliabilityof the results
Diagnostic on fields will be implemented to improve insight on thesmoothing procedure
The reason of the slow down of the code must be understood
Before the end of the workshop the 1000 particles case will befinished - we will see.