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a future international linear collider ( ilc ) provides an outstanding tool for the precise exploration of physics at tev scale @xcite .
in contrast to hadron colliders , the well defined initial state and the cleanliness of the final states allow for a precise measurement of standard model and new physics processes .
having both , positron and electron , beams polarized will be a decisive improvement for physics studies .
a recent review of the physics case of ilc using polarized positrons can be found in @xcite .
one possible layout for the production of polarized positrons is sketched in figure [ fig : ilclayout ] .
circularly polarized photons are created by sending the electron beam through a _
helical undulator _ @xcite . in a thin target
the photons are converted into polarized positrons via pair creation . in comparison to a conventional positron source
this method substantially reduces the heat load in the positron target .        a demonstration experiment to quantify the yield of polarization of an undulator based positron source , e166 @xcite ,
is currently performed at slac .
the experience gained with e166 is decisive for designing and optimising the polarized positron source of the ilc .
the precise simulation of the positron production as well as the polarimetry processes is essential for a complete understanding of the data obtained at e166 .
a simulation toolkit for the investigation of polarized processes based on geant4  is currently under development . in this contribution
a status report of this project is given .
geant4  is a toolkit for the simulation of the passage of particles trough matter @xcite .
individual particles are tracked step by step and each step can lead to creation of particles , destruction of particles , or to a modification of the particle properties .
the aspect of polarization has so far been widely neglected . with our extension
it will be possible to track also polarized particles ( leptons and photons ) .
special emphasis will be put in the proper treatment of polarized matter , which is essential for the simulation of positron polarimetry .
it is planned to create a universal framework for polarization and to implement it in an official geant4  release .
to realise this project , the following polarization dependent processes have to be considered    * compton scattering , + * bhabha / mller scattering , + * pair creation , + * bremsstrahlung .
in addition to these well localised interactions , the influence of magnetic fields on the electron ( or positron ) spin has to be treated properly .    in the following section ,
a brief review of existing simulation tools for polarization transfer is given .
in the subsequent sections the proposed framework for geant4  is presented .
several simulation packages for the realistic description of the development of electromagnetic showers in matter have been developed .
a prominent example of such codes is egs ( electron gamma shower)@xcite . for this simulation framework extensions with the treatment of polarized particles
exist @xcite ; the most complete has been developed by k.  flttmann @xcite .
it is based on the matrix formalism @xcite , which enables a very general treatment of polarization . however , the flttmann extension concentrates on evaluation of polarization transfer , i.e.the effects of polarization induced asymmetries are neglected , and interactions with polarized media are not considered .
another important simulation tool for detector studies is geant3 @xcite . here
also some effort has been made to include polarization @xcite , but these extensions are not publicly available .
the package geant4  is the newest member on the simulation front .
it is entirely written in c++ .
it has a wide range of application , and slowly replaces the fortran based simulation toolkits .
the proposed implementation of polarized processes is based on stokes vectors and allows a convenient description of the polarization transfer by the matrix formalism @xcite . in this formalism , a three - component _ polarization vector _
@xmath0 is assigned to each particle and characterises completely the polarization state of any lepton or photon .
for the simulation of polarized media , a possibility to assign stokes vectors to physical volumes has to be provided in geant4 .
this is handled by a new class , the so - called _
polarization manager_. it also allows the evaluation of stokes vectors in different frames of reference .
the general procedure is very similar to the polarization extension to egs by flttmann @xcite .
any interaction is described by a transfer matrix @xmath1 , which characterises the process completely .
it usually depends on kinematic variables like energy and angle , but it can also depend on polarization states ( e.g. of the media ) . the final state polarization @xmath0 is determined via matrix multiplication with the incoming stokes vector @xmath2 , @xmath3 the components @xmath4 and @xmath5 refer to the incoming and outgoing intensities , respectively . in this framework
the transfer matrix @xmath1 is of the form @xmath6 the matrix elements @xmath7 can be identified as ( unpolarized ) differential cross section ( @xmath8 ) , polarized differential cross section ( @xmath9 ) , polarization transfer ( @xmath10 ) , and ( de)polarization ( @xmath11 ) . in the flttmann extension the elements @xmath9 and @xmath11 have been neglected , thus concentrating on polarization transfer only .
using the full matrix takes now all polarization effects into account .
the structure is illustrated with a few examples in the following section .
here , some preliminary results shall illustrate the field of application .
the first process studied is compton scattering .
this process possesses all basic features : a polarization dependent differential and total cross section , polarization transfer and depolarization effects .
compton scattering is of great importance in polarimetry .    in figure
[ fig : compton ] the angular distribution of the scattered photon is presented . for this simulation a 100% circularly polarized photon beam and a 100%
longitudinally polarized iron foil is assumed% . ] . when flipping the electron spin from an anti - parallel configuration with respect to the photon spin ( blue ) to a parallel orientation ( red ) , the distribution changes drastically , and the total cross section decreases . for illustration ,
the case where both , target and beam , are unpolarized is also plotted ( black ) .
a comparison with an analytic formula ( solid lines ) shows perfect agreement in all cases .    in a next step a more realistic simulation of target properties
will be performed to study the effects of different polarized processes .
the polarization transfer in a undulator based positron source has been investigated . since the target is unpolarized , the total cross section ,
i.e.  the interaction length , does not depend on the photon polarization .
consequently it is sufficient to concentrate on the polarization transfer from incoming photons to outgoing positrons .    50 gev , undulator period @xmath122.4 mm and undulator strength parameter @xmath130.17 .
the peak of the first harmonic ( dipole ) radiation is at 9.62 mev.,width=264 ]    the setup of the simulation consists of an incoming photon beam with the characteristic energy spectrum of a _ helical undulator _ , cf .
fig.[fig : gammaenergy ] . as a first approximation
, the polarization of the photon beam is assumed to be 100% .
the degree of polarization of the positrons created in pair production depends also on the energies of the incoming photon and the outgoing positron . in general the degree of the positron polarization
is increasing with the energy fraction of the created positron , see figure [ fig : posipol1 ] .    .
each dot corresponds to a single answer of the transfer matrix .
the mean degree of polarization is plotted as the ( blue ) profile histogram.,width=294 ]    a simple first check of the polarization routine is provided by assuming an equal mixture of left and right circularly polarized photons as incoming beam . in this case one expects to obtain an unpolarized positron beam .
indeed , in figure [ fig : posipol2 ] this behaviour can be observed .
now the polarization spectrum of the _ helical undulator _ as plotted in figure [ fig : gammapol ] will be included in the study .
the simulation shows the marginal influence on the obtained degree of positron polarization .
in particular , high energy positrons are nearly 100% polarized , see figure [ fig : posipol3 ] .        for a realistic simulation of a polarized positron source based on a _ helical undulator _ the effects of bremsstrahlung , multiple scattering , coulomb and screening correction have to be taken into account . in figure [ fig : posienergy ]
the influence of these processes on the obtained positron energy spectrum is investigated .
it is shown , that only a small fraction ( green ) of all produced positrons ( blue histogram ) will escape from the target .
the energy spectrum of positrons that leave the target is shifted to lower values in comparison to their spectrum at the creation point ( red ) .
consequently , the target acts as a filter for high energy positrons and the created positrons have suffered a substantial loss of energy .
the effect of bremsstrahlung and multiple scattering on the degree of polarization of the produced positrons will be the subject of further investigations .
in this report the current status of a project to implement polarization into the framework of geant4  has been presented .
for this task the stokes formalism is employed , providing a systematic approach for a consistent treatment of polarized leptons and photons .
some preliminary results demonstrate the applicability of this new extension to polarimetry ( compton scattering ) and polarization transfer studies ( positron source ) .
these analyses represent the first steps toward a realistic target simulation of an undulator based positron source for the ilc .
the authors are indebted to a.  stahl as the initiator of this project , and also like to thank t.  lohse for fruitful collaboration , and s.  riemann , p.  starovoitov and j.  suarez for helpful discussions .
k.l . and a.s .
are grateful for the assistance by k.  flttmann and j.  c.  liu concerning the egs polarization extension .
r.d .  acknowledges support by the european community ( eurotev contract number rids  011899 ) .
the full exploitation of the physics potential of an international linear collider ( ilc ) requires the development of a polarized positron beam . 
 new concepts of polarized positron sources are based on the development of circularly polarized photon sources . 
 the polarized photons create electron - positron pairs in a thin target and transfer their polarization state to the outgoing leptons . 
 to achieve a high level of positron polarization the understanding of the production mechanisms in the target is crucial . 
 therefore a general framework for the simulation of polarized processes with geant4  is under development . in this contribution 
 the current status of the project and its application to a study of the positron production process for the ilc is presented .