We present a detailed design treatment for a concentrating photovoltaic mini module subsystem with a specific power of up to 4.1 kW/kg for integration into a space solar power system. Concentrating designs are required to achieve specific power over 1 kW/kg with current high-efficiency III-V multijunction solar cells. The 15 sun, linear concentration concept detailed here reduces the system mass by replacing cell and radiation shield area with ultralight carbon fiber reinforced polymer (CFRP) optics. Reducing the cell size to 1 mm width as well as careful optimization of cell architecture and CFRP material and thickness are critical for maintaining cell temperatures under 100 C despite the concentration. We also describe ultralight multilayer optical coatings to increase the thermal emissivity of the concentrator surfaces and enhance radiative transfer for cell cooling, which is a critical technological component of the total system design.