Reflective light concentrators with hexagonal entrance and exit apertures are frequently used at the focal plane of gamma-ray telescopes in order to reduce the size of the dead area caused by the geometries of the photodetectors, as well as to reduce the amount of stray light entering at large field angles. The focal plane of the large-sized telescopes (LSTs) of the Cherenkov Telescope Array (CTA) will also be covered by hexagonal light concentrators with an entrance diameter of 50 mm (side to side) to maximize the active area and the photon collection efficiency, enabling realization of a very low energy threshold of 20 GeV. We have developed a prototype of this LST light concentrator with an injection-molded plastic cone and a specular multilayer film. The shape of the plastic cone has been optimized with a cubic B{e}zier curve and a ray-tracing simulation. We have also developed a multilayer film with very high reflectance ($gtrsim95$%) along wide wavelength and angle coverage. The current status of the prototyping of these light concentrators is reported here.
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