1. Progress with Spin Tracking in GEANT4
Sabine Riemann, DESY
ILC-BDIR, European Regional Workshop, RHUL, June 22, 2005
GEANT4 with Polarization: Report on the work
of Ralph Dollan, Karim Laihem, Thomas
Lohse, Andreas Schälicke and Achim Stahl
Plans for the future

2. Progress with polarization in GEANT4
Motivation
MC simulations of
spin dependent processes
- in the target
polarimeter
PPMODL
PTCD
LEPOL
June 22, 2005
Progress with polarization in GEANT4

3. Relevant processes for polarization studies
Target
Diagnostics
Photons:
g conversion
Compton scattering
photoelectric effect
 Spin transfer to e+, e-
Electrons, positrons:
multiple scattering
ionization
Bremsstrahlung
 Polarization tracking
spin dependent cross sections:
Compton scattering
Bhabha scattering
Moller scattering
Annihilation in flight
June 22, 2005
Progress with polarization in GEANT4

4. Status of Simulation Software
GEANT4:
- only low energy Compton scattering (linear
polarized optical photons on unpolarized e-)
- No polarization of the medium
- Placeholder for polarization vector (3-vector)
exists
EGS4: Implementation of Stokes formalism in a seperate extension (K. Flöttmann);
 polarization transfer & depolarization included, no asymmetric cross section
LEPOL: Need simulation also for asymmetric processes
June 22, 2005
Progress with polarization in GEANT4

5. Progress with polarization in GEANT4
Stokes parameters
G.Stokes, Trans. Cambridge Phil. Soc. 9 (1852) 399
Wave function :
Jones vector :
Spin density matrix :
Stokes parameter :
June 22, 2005
Progress with polarization in GEANT4

6. Stokes parameters Stokes parameter Photon observation
Fermion observation x1
Plane polarization
Spin in z - direction x2
Plane polarization at an angle of p/4 to the right
Spin in x - direction x3
Left/Right circular polarization
Spin in y - direction
Example linear polarized photon:
Dollan, Laihem, Lohse, Schälicke, Stahl

7. Matrix formalism Differential cross section Asymmetry Polarization
W.H. McMaster, Rev.Mod.Phys. 33 (1961) 8
Transformation matrix
Differential cross section
Asymmetry
Polarization
Depolarization and polarization transfer
Dollan, Laihem, Lohse, Schälicke, Stahl

8. Pair production in field of nucleus
Dollan, Laihem, Lohse, Schälicke, Stahl

9. Compton scattering Independent of electron spin S: (I, A, B, C, D)
Dependent on
electron spin S:
(E, F, Gi, Hi)
Dollan, Laihem, Lohse, Schälicke, Stahl

10. Proposal for the implementation
Input:
Stokes parameters of the particle (beam) -> G4ThreeVector
(bookkeeping already included in GEANT4)
Polarization of the Volume -> G4ThreeVector (PolarizationManager)
Calculate cross sections (total, differential) -> interaction length
Derive polarization transfer from initial to final state
Summary of our proposal
Output:
Stokes parameters of the final states
Dollan, Laihem, Lohse, Schälicke, Stahl

11. Results Compton scattering
Polarized:
Pe=+1
Pg=+1
Pe=-1
Pg=+1
Unpolarized:
Pe= 0
Pg= 0
Eg=10 MeV
Dollan, Laihem, Lohse, Schälicke, Stahl

12. Polarization transfer in the pair production process-1
Conversion
target e+
Positron Polarization profile from polarized Undulator photons (creation point)
Polarized Photon Beam
Stokes
Vector
Dollan, Laihem, Lohse, Schälicke, Stahl

13. Polarization transfer in the pair production process
Random
Conversion
target e+
Positron Polarization profile from polarized Undulator photons (creation point)
Unpolarized Photon Beam
Stokes
Vector
Dollan, Laihem, Lohse, Schälicke, Stahl

14. Target studies - results
0.5 X0 W
Polarization profile of the first harmonic undulator photons
Positron Polarization profile created by the undulator photons (creation point)
e+ Energy distribution (inside/outside target)
The target may filter positrons
with high degree of polarization
Dollan, Laihem, Lohse, Schälicke, Stahl

15. Outlook (GEANT4)
Continue the implementation of Polarization in G4 processes
Focus on Stokes formalism (describes all polarization states for g, e+, e-)
First priority to processes needed for the for polarized positron source
Other processes will not be neglected
Cross check with other existing simulation packages (EGS4…)
Possibility to simulate and cross check with experimental results (E166)
Contact and collaborate with other groups (developing polarized Geant4)
Coordinate the work and the approach on the implementation.
Propose the polarized processes to the G4 collaboration (official release)
Dollan, Laihem, Lohse, Schälicke, Stahl

16. Progress with polarization in GEANT4
e+ Polarimetry at a PPS
Peter Schueler in Daresbury:
June 22, 2005
Progress with polarization in GEANT4

17. Progress with polarization in GEANT4
P. Schueler, Daresbury
Transmission method:
Compton scattering of g’s from re-converted e+ on 3d e- in magnetized iron
BUT:
huge pair creation background for higher g energies
destructive method
June 22, 2005
Progress with polarization in GEANT4

18. e+ Polarimetry at the PPS (LEPOL)
Polarimetry at the ILC PPS:
where ?
E(e+) > 100 MeV after AMD
E(e+) ~ 5 GeV at the DR
which process?
destructive methods?
accuracy?
Bhabha scattering (~10mm Fe foil, 110K):
Alexander, Reinherz-Aronis; Starovoitov, Suarez:
could work at ~250 MeV,
at ~10 MeV high background;
at 5 GeV insensitive
more detailed studies needed; analyzing power ?
June 22, 2005
Progress with polarization in GEANT4

19. Progress with polarization in GEANT4
Summary
First steps done for G4 with polarization
Target modelling with GEANT4
Collaboration with Tel Aviv:
- find a process for the LE polarimetry,
Collaboration with Minsk (INTAS??)
- implementation of polarisation into MC (EGS4)
- polarimetry
Milestone: E166
June 22, 2005
Progress with polarization in GEANT4

20. Progress with polarization in GEANT4
June 22, 2005
Progress with polarization in GEANT4