In order to achieve the physics goals of future Linear Colliders, it is important that electron and positron beams are polarized. The baseline design at the International Linear Collider (ILC) foresees an e+ source based on helical undulator. Such a source provides high luminosity and polarizations. The positron source planned for ILC is based on a helical undulator system and can deliver a positron polarization of 60%. To ensure that no significant polarization is lost during the transport of the e- and e+ beams from the source to the interaction region, precise spin tracking has to be included in all transport elements which can contribute to a loss of polarization, i.e. the initial accelerating structures, the damping rings, the spin rotators, the main linac and the beam delivery system. In particular, the dynamics of the polarized positron beam is required to be investigated. In the talk recent results of positron spin tracking simulation at the source are presented. The positron yield and polarization are also discussed depending on the geometry of source elements.
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