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)

TREDI …… is a multi-purpose macroparticle 3D Monte Carlo,

devoted to the simulation of electron beams through

Rf-gunsLinacs (TW & SW)SolenoidsBendingsUndulatorsQuads’…

where Self Fields are accounted for by means of Lienard-Wiechert retarded potentials

SELF FIELDS

EnB

Rn

n

Rn

nnE

23

2

31

1

1

c

tRtt

R

Rn

)( timeRetarded

R(t’)

Target

Source

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)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

FEL lasing (1998)

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

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

CSR Tests with TREDIProblems:

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

R(t’)

Targets

Source

Target

Source

Collective (coherent) effect

2 Particles interaction incoherent “collision”

Effect of Noise (1st bend - no screening)

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 obtained

by giving macroparticles a finite sizein momentum space

Suppression of noise II

retpPP

retP

rdrrrEpdpppE

rdpdrprprpEE

00

),( )( ),( )(

),,,( ),(

01r

01

001

The spatial integral istreated applying the Gauss theorem …

The momentum integral can be estimated by assigninga minimum momentum dispersion

0 1 2 3 4 5 6 7 81

0.5

0

Transverse momentum dispersionNo dispersion

Exkk

Eaxk

k

.Tra

nsv

ers

e

Ele

ctri

c Fi

eld

View angle

= 10-4

= 104

Suppression of noise III

The integral in momentum space with a Gaussiandistribution is CPU time consuming

Alternative: Limit angle of “influence” of particles to force collective interactions

P = impact parameter

P=0 point like particles - no smoothing collisions dominate

P=1 limited spread particles - collective effects are dominant

P>1 spread out macroparticle - reduced interaction

nn 11

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=0.1P=0.5P=1.0P=2.0

Z (m)

X E

mitt

ance

(m

m-m

rad)

.

Definitions

Step s 188Z 15.96Angle 0

Optic functionsx 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

No compression - 5 GeV 1.0 nCEstimation of emittance

0 10 20 30 40 50 60 70 80 90 1001

10

100

1 103

Charge (%)

Em

ittan

ce/(

% C

harg

e)

85

.

No compression - 5 GeV 1.0 nC - x=10.1 mm-mradDefinitions

Step s 188Z 15.96Angle 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 0.0410

5

0

5

10Z Projection

Z (mm)

Pz

(mc)

0.4 0.2 0 0.2 0.40.5

0

0.5X Projection

X (mm)

Px

(mc)

0.1 0 0.1

0.05

0

0.05

Y Projection

Y (mm)

Py

(mc)

No compression - 5 GeV 1.0 nCEmittances

0 2 4 6 8 10 12 14 160

5

10

15

XYBounds of devices

Z (m)

Em

ittan

ce (

mm

-mra

d)

.

0 2 4 6 8 10 12 14 160

0.02

0.04

0.06

X

Bounds of devices

Z (m)

Ene

rgy

Spr

ead

(%)

.

No compression - 5 GeV 1.0 nC

Energy variation ??

0 2 4 6 8 10 12 14 166 10

7

4 107

2 107

0

XBounds of devices

Z (m)

Ene

rgy

Var

iatio

n(M

eV)

.

No compression - 5 GeV 1.0 nCTransverse rms

0 2 4 6 8 10 12 14 160

50

100

150

200

X RMSY RMS

Bounds of devices

Z (m)

Tra

nsve

rse

RM

S (

um)

.

0 2 4 6 8 10 12 14 160

10

20

30

Z RMS

Bounds of devices

Z (m)

Z R

MS

(um

)

E= 5 GeV - Q=1 nC0 2 4 6 8 10 12 14 16

0

500

1000

1500

2000

X RMSY RMSBounds of devicestrace 4

Z (m)T

rans

vers

e R

MS

(um

)

0 2 4 6 8 10 12 14 160

50

100

150

200

Z RMS

Bounds of devices

Z (m)

Z R

MS

(um

)

.

Bunch Length

Phase space at exit still noisy !

Definitions

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 94Z 15.881

Angle 1.819 105

Optic functionsx 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)

Pz

(mc)

0 5 10 150

0.1

0.2

X - Z Trajectory

Z (m)

X (

mm

)

Estimation of emittance

0 10 20 30 40 50 60 70 80 90 1001

10

100

Charge (%)

Emitt

ance

/(% C

harg

e)

85

.

0 2 4 6 8 10 12 14 160

20

40

60

80

XY

Bounds of devices

Z (m)

Em

ittan

ce (

mm

-mra

d)

.

Z (m)E

nerg

y (G

eV)

7.154 106

0

15.9810.1

Emittance vs. z

dispersion

Energy spread

0 2 4 6 8 10 12 14 160.697198

0.697199

0.6972

0.697201

Z (m)

Ene

rgy

Spr

ead

(%)

s1

% s1

Rs1 2

m

Rs1 2

m M km 0

.

Phase space at exit with 85% of the charge, x=2.3 mm-mrad

Definitions

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 94Z 15.881

Angle 2.632 105

Optic functionsx 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

)

0 2 4 6 8 10 12 14 160

500

1000

1500

2000

X RMSY RMSBounds of devicestrace 4

Z (m)Tr

ansv

erse

RM

S (u

m)

0 2 4 6 8 10 12 14 160

50

100

150

200

Z RMS

Bounds of devices

Z (m)

Z R

MS

(um

)

.

E= 5 GeV - Q=0.5 nC

Bunch Length

Phase space at exit with 85% of the charge, x=1.4 mm-mradDefinitions

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 94Z 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

(mc)

0 5 10 150

0.1

0.2

X - Z Trajectory

Z (m)

X (

mm

)

0 2 4 6 8 10 12 14 160

500

1000

1500

2000

X RMSY RMSBounds of devicestrace 4

Z (m)

Tra

nsve

rse

RM

S (

um)

0 2 4 6 8 10 12 14 160

50

100

150

200

Z RMSBounds of devices

Z (m)

Z R

MS

(um

)

.

E= 500MeV - Q=1.0 nC

Bunch Length

Emittance at exit - 500 MeV - 1.0 nC ??

0 10 20 30 40 50 60 70 80 90 1001

10

100

Charge (%)

Em

ittan

ce/(

% C

harg

e)

.

Phase space at exit with 92% of the charge, x=21 mm-mrad

Definitions

1 0.5 0 0.5 10.2

0

0.2

X Projection

X (mm)

Px

(mc)

0.6 0.4 0.2 0 0.2 0.4 0.60.05

0

0.05Y Projection

Y (mm)

Py

(mc)

Step s 94Z 15.89Angle 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 10 150

0.1

0.2

X - Z Trajectory

Z (m)

X (

mm

)

Conclusions

• The noise suppression method has reduced the effects of SF on longitudinal phase space, without being completely effective in the transverse phase space

• A rigorous model of fields regularization, relying on a realistic momentum dispersion of macroparticles will be soon implemented

• The low number of macroparticles in severely limiting the reliability of the results

• Diagnostic on fields will be implemented to improve insight on the smoothing procedure

• The reason of the slow down of the code must be understood

• Before the end of the workshop the 1000 particles case will be finished - we will see.