Updated status of the undulator-based ILC positron source

The design of the positron source for the International Linear Collider (ILC) is still under discussion. The baseline design plans to use the high-energy electron beam for the positron production before it goes to the IP. The electrons pass a long helical undulator and generate an intense circularly polarized photon beam which hits a thin conversion target to produce $e^+e^-$ pairs. The resulting positron beam is longitudinally polarized which provides an important benefit for precision physics analyses at the ILC. In this paper the status of the positron target design studies is presented. Focus is the positron yield for center-of-mass energies of 250 GeV and also the Z peak. Possibilities to improve the positron collection system and thus to increase the positron yield are discussed