Plasma Lens Prototype Progress: Plasma Diagnostics And Particle Tracking For ILC $e^+$ Source

In recent years, the concept of high-gradient, symmetric focusing using active plasma lenses has regained notable attention owing to its potential benefits in terms of compactness and beam dynamics when juxtaposed with traditional focusing elements. An enticing application lies in the optical matching of extensively divergent positrons originating from the undulator-based ILC positron source, thereby enhancing the positron yield in subsequent accelerating structures. Through a collaboration between the University of Hamburg and DESY Hamburg, a scaled-down prototype for this purpose has been conceptualized and fabricated. In this presentation, we provide an overview of the ongoing progress in the development of this prototype. Furthermore, first insights into the development of a particle tracking code especially designed for plasma lenses with implemented Bayes optimization, are given