l. giannessi - m. quattromini - an overview of tredi and csr test cases

8/2/2019 L. Giannessi - M. Quattromini - An Overview of Tredi and Csr Test Cases

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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


3/35

SELF FIELDS

( )[ ]( )

( )

( )

EnB

Rn

n

Rn

nnE

=

+

=

23

2

31

1

1

&

c

tRtt

R

Rn

)(timeRetarded

=

=

R(t)

Target

Source


4/35

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


10/35

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


11/35

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


14/35

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


15/35

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


16/35

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)

.


17/35

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

.


19/35

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)


20/35

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


22/35

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


25/35

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)


30/35

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

=


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=


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.

l. giannessi - m. quattromini - an overview of tredi and csr test cases

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