source modelling using geant4

7-9th April 2008 Positron Source Meeting 1

Source Modellingusing Geant4

S. Riemann, A. Schälicke, A. Ushakov

7-9 April 2008 Positron Source Meeting

Outline

• Geant4 capabilities–Polarised processes–Magnetic field (T-BMT equation)

• Modelling–Geometry–Photon spectrum (Input)–Results

• Summery & Outlook

2


Geant4 in Source SimulationPolarisation extension to Geant4• 5 polarised processes (since Dec. 2006)• 1 polarised process add Dec. 2007 (E166 needs)• support for polarised media (for polarimetery)

Magnetic fields• Runge-Kutta integrator• equation of motion for magnetic field• equation of motion for electric & magnetic field

• T-BMT equation for spin transport

3

(new since Dec. 2007 release 9.1)

dσ(ξ(1),ξ(2),ξ(3),ξ(4))dΩ

= Φ(ξ(1),ξ(2)) + A(ξ(1),ξ(2)) · ξ(3) + B(ξ(1),ξ(2)) · ξ(4)

+ ξ(3)TM(ξ(1),ξ(2)) ξ(4)


Polarised Geant4

• Physics processes:– Pair production– Bremsstrahlung– Compton scattering– Moller/Bhabha scattering– Photo electric effect

4

• Implementation:– based on Stokes vectors– polarisation transfer– asymmetries (polarised target)

scatterd electron energy / MeV0 1 2 3 4 5 6 7 8 9 10

helic

ity

-1

-0.5

0

0.5

1

Electron polarisation transfer


Polarised Geant4• well tested:

– based on old publications (from 60’)– independent recalculation of selected

processes (P. Starovoitov)– comparison with EGS (where possible)– comparison with Whizard generator– data from E166 experiment

• further documentation:– Geant4 Physics reference manual– K. Laihem, A.S., P. Starovoitov,

arXiv:0712.2336, DESY 07-202.

5

scatterd electron energy / MeV0 1 2 3 4 5 6 7 8 9 10

even

ts

0

1

2

3

4

5

6

7

8310×

Compton scattering

Electron distribution

=+1e-=+1 P!Geant4 P

=-1e-=+1 P!Geant4 P

=+1e-=+1 P!Whizard P

=-1e-=+1 P!Whizard P

http://de.arxiv.org/abs/0712.2336

http://de.arxiv.org/abs/0712.2336

(MeV)±eE

3 4 5 6 7 8

Longitudin

al pola

rization (

%)

20

40

60

80

100

+e-e

polarization+Expected e polarization-

Expected e


Polarised Geant4

• Applications:– E166 experiment

• Analysing power• Expected Positron polarisation

– ILC Polarised Positron Source– ILC Low Energy Polarimeter

6

[rad]θ0.05 0.1 0.15 0.2 0.25

E / M

eV

20

40

60

80

100

120

140

160

180

1

10

210

electron distribution

[rad]θ0.05 0.1 0.15 0.2 0.25

E / M

eV20

40

60

80

100

120

140

160

180

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1

electron asymmetry distribution


T-BMT equation• Particle trajectories in

electrical and magnetic field• Spin precession according to

T-BMT equation

7

• E-field dependence not included in Geant4 yet

dS

dt= − e

mγ

[(γa + 1)BT + (a + 1)BL − γ

(a +

1γ + 1

)βev ×

E

c

]× S


Source ModellingUndulator (inside G4 or independent ROOT script)• Energy distribution• angle distribution• correlation between energy & angle

8

Energy E / MeV0 10 20 30 40 50 60

dN/d

E

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Pola

rizat

ion

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1

Photon Energy Spectrum and PolarizationHelical Undulator: K = 0.92, λ = 11.5 mm. Photon Collimator Aperture: 4.6 mm

Photon Energy Distribution

E [MeV]

0 5 10 15 20 25 30 35 40

Nu

mb

er

of

Ph

oto

ns [

a.u

.]

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

Polarization of Photons

Conventional Undulator Based

γ Polarization – 73.8 %e+ Polarization – 45.0 %

A. Ushakov (DESY Zeuthen) Design Simulation – Zeuthen Zeuthen, 07 Apr 2008 5 / 14


Source modelling

Target & Capture section• simple Geometry

– Target– AMD– first accelerator structures

• simple Field– OMD field– Solenoid field– time dependent electrical field

9


Results• Energy and polarisation spectrum of produced

positrons

10

E [MeV]0 5 10 15 20 25 30 35 40

Pola

rizat

ion

0.1

0.2

0.3

0.4

0.5

E [MeV]0 5 10 15 20 25 30 35 40

]-1

/dE

[ M

eVe+

dN

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09


Results• Positron yield and polarisation depending on

magnetic field

11

[T]0B0 2 4 6 8 10

]γ/+Yi

eld

[e

00.0020.004

0.0060.008

0.010.0120.014

0.0160.018

0.020.022

[T]0B0 2 4 6 8 10

Pola

rizat

ion

0.2

0.22

0.24

0.26

0.28

0.3

0.32


Results• Phase space distribution of positrons

– after Production target– after first accelerator structures (120MeV)

(including DR acceptance cut)

12

x [cm]

-3 -2 -1 0 1 2 3

/px

p

-0.03

-0.02

-0.01

0

0.01

0.02

0.03 13mEntries 60407

RMS x 0.6132

RMS y 0.003338

1

10

21013m

Entries 60407

RMS x 0.6132

RMS y 0.003338

x [cm]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

/px

p

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1 target

Entries 218461

RMS x 0.2328

RMS y 0.3518

1

10

210

target

Entries 218461

RMS x 0.2328

RMS y 0.3518


Summary & OutlookSummary• Geant4 provides powerful tool for target

simulations• T-BMT already included (w/o electrical field)• developed for E166 needs but also applicable to

ILC setup Outlook• Publication on G4 Polarisation (over due!)• Extension of simulation scope (perhaps using a

polarised version of ASTRA)• continue discussion with other groups doing

“start to end” simulations ... 13

source modelling using geant4

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