Light concentrator design for the large array of imaging atmospheric Cherenkov Telescopes (LACT)

The light concentrator, as an important component of the optical detector of the imaging atmospheric Cherenkov telescopes is mainly used to collect and focus the Cherenkov light generated by the extensive air shower. In order to achieve higher angular resolution than the large high altitude air shower observatory (LHAASO), the Large Array of imaging atmospheric Cherenkov Telescope (LACT) project in LHAASO site is proposed in China. In this paper, we specifically focus on the research of the reflective square light concentrator for LACT based on the fundamental principles of the Winston cone, and then optimize it by Bézier functions. The light concentrator with an entrance size of 24.4 mm $\times$ 24.4 mm and an exit size of 13 mm $\times$ 13 mm has been designed. It exhibits an absolute cutoff angle of 37.02° and an effective cutoff angle of 28.85°, with a parallel light collection efficiency exceeding 90% when the incident angle $<$22°, meanwhile the inconsistency in collection efficiency at different positions in the field of view is less than 0.28%. Additionally, we summarized the research process and proposed a standardized process for light concentrator design.