Status of the undulator-based ILC positron source

The design of the positron source for the International Linear Collider (ILC) is still under consideration. The baseline design plans to use the electron beam for the positron production before it goes to the IP. The high-energy 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. In this paper the status of the design studies is presented with focus on ILC250. In particular, the target design and cooling as well as issues of the optical matching device are important for the positron yield. Some possibilities to optimize the system are discussed.