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

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

RnnnE

23

2

3 1

1

1

ctRtt

RRn

)( timeRetarded

R(t’)

Target

Source

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)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)

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

Part

icle

traj

ecto

ry 1

Time

Part

icle

traj

ecto

ry 2

Part

icle

traj

ecto

ry 3

Part

icle

traj

ecto

ry k

-2

Part

icle

traj

ecto

ry k

-1

Part

icle

traj

ecto

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 noiseAcceleration 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

.Tran

sver

se

Elec

tric

Fiel

d

View angle

= 10-4

= 104

Suppression of noise IIIThe 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

(mm

-mra

d)

.

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 (m

m)

0.1 0.05 0 0.05 0.1 0.15 0.250

0

50

100Z Projection

Z (mm)

Pz (m

c)

0.1 0 0.1

0.05

0

0.05

Y Projection

Y (mm)

Py (m

c)

2 1 0 1 2 3 4 52

1

0

1

2

3X Projection

X (mm)

Px (m

c)

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 (%)

Emitt

ance

/(% C

harg

e) 85

.

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

Step s 188Z 15.96Angle 0


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 (m

m)

0.04 0.02 0 0.02 0.0410

5

0

5

10Z Projection

Z (mm)

Pz (m

c)

0.4 0.2 0 0.2 0.40.5

0

0.5X Projection

X (mm)

Px (m

c)

0.1 0 0.1

0.05

0

0.05

Y Projection

Y (mm)

Py (m

c)

No compression - 5 GeV 1.0 nCEmittances

0 2 4 6 8 10 12 14 160

5

10

15

XYBounds of devices

Z (m)

Emitt

ance

(mm

-mra

d)

.

0 2 4 6 8 10 12 14 160

0.02

0.04

0.06

XBounds of devices

Z (m)

Ener

gy S

prea

d (%

)

.

No compression - 5 GeV 1.0 nC

Energy variation ??

0 2 4 6 8 10 12 14 166 10 7

4 10 7

2 10 7

0

XBounds of devices

Z (m)

Ener

gy V

aria

tion(

MeV

)

.

No compression - 5 GeV 1.0 nCTransverse rms

0 2 4 6 8 10 12 14 160

50

100

150

200

X RMSY RMSBounds of devices

Z (m)

Tran

sver

se R

MS

(um

)

.

0 2 4 6 8 10 12 14 160

10

20

30

Z RMSBounds 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)Tr

ansv

erse

RM

S (u

m)

0 2 4 6 8 10 12 14 160

50

100

150

200


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 (m

c)

0.1 0.05 0 0.05 0.10.2

0.1

0

0.1

0.2Y Projection

Y (mm)

Py (m

c)

Step s 94Z 15.881

Angle 1.819 10 5


x 6.403

x 0.238

y 1.099

y 15.131

y 0.146

z 2.406

z 7.384 10 3

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 (m

c)

0 5 10 150

0.1

0.2

X - Z Trajectory

Z (m)

X (m

m)

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

XYBounds of devices

Z (m)

Emitt

ance

(mm

-mra

d)

.

Z (m)En

ergy

(GeV

)

7.154 10 6

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)

Ener

gy S

prea

d (%

)

s1

% s1

Rs1 2

m

Rs1 2

m M km 0

.

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

0.15 0.1 0.05 0 0.050.2

0.1

0

0.1

0.2

X Projection

X (mm)

Px (m

c)

0.1 0.05 0 0.05 0.10.1

0

0.1

0.2Y Projection

Y (mm)

Py (m

c)

Step s 94Z 15.881

Angle 2.632 10 5


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 (m

c)

0 5 10 150

0.1

0.2

X - Z Trajectory

Z (m)

X (m

m)

0 2 4 6 8 10 12 14 160

500

1000

1500

2000


Z (m)Tr

ansv

erse

RM

S (u

m)

0 2 4 6 8 10 12 14 160

50

100

150

200


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 (m

c)

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 (m

c)

Step s 94Z 15.93

Angle 3.468 10 5


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 (m

m)

0 2 4 6 8 10 12 14 160

500

1000

1500

2000


Z (m)

Tran

sver

se R

MS

(um

)

0 2 4 6 8 10 12 14 160

50

100

150

200


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 (%)

Emitt

ance

/(% 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 (m

c)

0.6 0.4 0.2 0 0.2 0.4 0.60.05

0

0.05Y Projection

Y (mm)

Py (m

c)

Step s 94Z 15.89Angle 0.003


x 3.967

x 0.313

y 2.065

y 22.26

y 0.237

z 0.869

z 6.571 10 3

z 267.046

0.1 0.05 0 0.05 0.120

10

0

10

20Z Projection

Z (mm)

Pz (m

c)

0 5 10 150

0.1

0.2

X - Z Trajectory

Z (m)

X (m

m)

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.

Documents

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