Genesis /ALICE Benchmarking

Igor Zagorodnov

Beam Dynamics Group Meeting

17.03.08

Genesis 1.3(S.Reiche et al)

ALICE

• only 3D • 3D Cartesian field solver (ADI)• Runge-Kutta integrator• Dirichlet boundary conditions• transverse motion• many other physics• parallel (MPI)

• 1D/2D/3D • 3D azimuthal field solver (Neumann)• Leap-Frog integrator• Perfectly Matched Layer• transverse motion• simplified model• parallel (MPI)• tested by me on the examples from the book of SSY

(~Saldin et al, 2000 „The Physics …“,)

2.5 MeV

100 150 2000

0.5

1

1.5

2x 10

10[GW]P

[m]z

2.5MeVE

0C 4.086e-5 mr

Genesis vs. ALICE / Energy Spread (round Gaussian beam, Gaussian energy spread, parallel motion only)

ALICE

Genesis

W = 4 kW

SASE 2 parameters

0.1 nms

How to simulate emmitance with laminar particle motion only?

22

2 20

ˆT

4 2

2 02 2

ˆ zemit

2 2 2,

ˆ ˆ ˆT eff T emita

1

4a -E. Saldin et al, TESLA-FEL 95-02 (1995);

S.Reiche PhD Thesis (1999).

1a - E. Saldin et al, The Physics of Free Electron Lasers (2000)

2a - E. Saldin et al, DESY 05-164 (2005)

100 150 2000

2

4

6

8

10

12

14

16x 10

9

[W]P

[m]z

0C

4.4038e-005mr

Genesis vs. ALICE / Emmitance(round Gaussian beam, Gaussian energy spread)

47.44m

1MeVE

3MeV

4MeV

5MeV

ALICE (laminar)

Genesis

1MeVE 1.4 mm×mradn

1.4 mm×mradn

0 0.2 0.4 0.6 0.8 1 1.20.057

0.058

0.059

0.06

0.061

0.062

0.063

1.1a

ALICE (laminar)

Genesis

ˆdetuning C

Field growth rate

Genesis vs. ALICE (emittance parameter fit)

0 50 100 150 20010

-6

10-4

10-2

100

102

100 120 140 160 180 2000

5

10

15

20

25

1.1a

ALICE (laminar)

Genesis

[ W]P G

[m]z [m]z

[ W]P G

Detuning corresponds to maximal growth rate in linear regime

0( ) maxC

C

Genesis vs. ALICE with laminar motion

The transverse motion has to be implemented in ALICE

Genesis vs. ALICEwith transverse motion

2.5MeVE

0C P0 = 4 kW

100 150 2000

1

2

3

4

19%Genesis (N=6e4)Genesis (N=3e4)

Alice (N=6e4)

Alice (N=3e4)

The difference in saturation length is 7 %.The difference in power gain is 19 %.

The difference does not reduce with changing of the discrete model parameters ?!.

4.086e-5 mr

[m]z

[ W]P G

I=5KAN ~10 400

0.1 nms

GINGER/GENESIS results for “0-order” 200-

pC case

Observations:• Again, GENESIS shows slightly longer

gain length, 10-m later saturation but 15% higher power

• Again, GINGER shows deeper post-saturation power oscillation

• Little sensitivity (2 m, 7%) in GINGER results to 8X particle number increase

• Possible reasons for differences: bugs slight differences in initial e-beam

properties (e.g. mismatch) grid effects (e.g. outer boundary)???

William M. Fawley, ICFA 2003 Workshop on Start-to-End Numerical Simulations of X-RAY FEL’s

Bridsall C.K., Langdon A.B., Plasma Physics via Computer Simulations, 1991Dawson J.M, Particle simulation of Plasmas // Reviews of Modern Physics, 1983

About advantages of the „quiet start“ see, for example, in

4 23

Ntrans x,

%

y,

%

px,

%

py,

%

Genesis

7500 1.5 7.5 5.1 5.8

15000 4.1 4.7 4.1 3.2

ASTRA

7500 1.6 4.2 0.43 2.3

15000 0.4 3.3 0.62 1.9

Alice

7500 0.8 1.0 0.8 0.8

15000 0.4 0.4 0.5 0.5

4 4

4100%

Properties of the Normal macroparticle distribution

Ntrans Rxy Rpxpy Rxpy Rypx

Genesis

7500 8e-3 2e-2 5e-3 8e-3

15000 8e-3 1e-2 1e-3 3e-3

ASTRA

7500 4e-3 7e-3 5e-3 5e-3

15000 5e-3 4e-3 6e-3 4e-3

Alice

7500 1e-3 2e-3 8e-4 2e-3

15000 5e-4 1e-3 5e-4 8e-4

cov( , )R

Properties of the Normal macroparticle distribution

-4 -2 0 2 40

100

200

300

400

500

600

700

-4 -2 0 2 40

100

200

300

400

500

600

700ALICE Genesis

7500transN

/ yy / yy

4* transn N

clustering

Quiet start ?

What is the reason?

-4 -2 0 2 40

50

100

150

4* transn NtransN

/ yy

ASTRA

The polar form of Box-Muller algorithm (in Genesis) maps the „quiet“ uniform distribution in a clustered normal distribution.

UniformNormal

Quiet start ?

ALICE Genesis

2000transN / rx

/ ry

Quiet start ?

clusteringr x y

ALICE Genesis

2000transN

/rx pp

/ry pp

Quiet start ?

clustering

r x yp p p

-4 -2 0 2 4-4

-3

-2

-1

0

1

2

3

4

ASTRA

2000transN /

rx pp

/ry pp

r x yp p p

100 150 2000

0.5

1

1.5

2

2.5

3[ W]P G

[m]z

Modified Genesis vs. ALICEwith transverse motion

2.5MeVE

0C P0 = 4000 Watt

Genesis(modified) (N=6e4) Alice (N=6e4)

The transformation used in ALICE

12 erf (2 1)i iY X

It transforms the uniform distribution Xi (0,1) to the normal distribution Yi ().This transformation does not destroy the „quiet start“.

It uses the straightforward transformation by inverse error function

Convergence

104

105

2.5

2.7

2.9

3.1

3.3

3.53.5

104

105

106

0

2

4

6

8

10

12

[ W]P G4 4

4100%

Genesis

Genesis (modified)

ALICE

Genesis

Genesis (modified)

ALICE4* transn N 4* transn N

Genesis: Hammersley and Box-MuellerGenesis (modified): Hammersley and the inverse error functionALICE: Sobol and the inverse error function

2.5MeVE 0C I=5KA

N ~10 4000.1 nms

at saturation