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The International Linear Collider is a planned electron-positron linearcollider with its positron source producing positrons by aiming undulatorradiation onto a rotating target. The resulting, highly divergent positron beamrequires immediate optical matching to improve the luminosity and therefore thesuccess of the intended collision experiments. Here, optical matching refers tothe process of capturing particles and making them available for downstreambeamline elements like accelerators. In the past, this has been done withsophisticated coils, but more recently the usage of a current-carrying plasma,a so-called plasma lens, has been proposed as an alternative. For theInternational Linear Collider idealised particle tracking simulations havealready been done with the purpose of finding the optimal plasma lens designwith respect to the captured positron yield. The proposed design ischaracterised by a linearly widened radius in beam direction. Now furtherresearch and development of this design is required, including both experimentswith a prototype set-up as well as corresponding simulations modelling thehydrodynamics of the current-carrying plasma and the resulting magnetic field.The accuracy of the latter will benefit greatly from the former. In this work,first preliminary hydrodynamic simulations instil confidence into furtherendeavours.

Status Report on the Hydrodynamic Simulations of a Tapered Plasma Lens for Optical Matching at the ILC $e^+$ Source