CCAT-prime: Optical and cryogenic design of the 850 GHz module for Prime-Cam

Prime-Cam is a first-generation instrument for the Cerro Chajnantor Atacama Telescope-prime (CCAT-prime) Facility. The 850$$GHz module for Prime-Cam will probe the highest frequency of all the instrument modules. We describe the parameter space of the 850$$GHz optical system between the F$\lambda$ spacing, beam size, pixel sensitivity, and detector count. We present the optimization of an optical design for the 850$$GHz instrument module for CCAT-prime. We further describe the development of the cryogenic RF chain design to accommodate $>$30 readout lines to read 41,400 kinetic inductance detectors (KIDs) within the cryogenic testbed.