Due to electricity needs of scenarios such as remote areas and emergency situations, mobile nuclear power sources with high reliability and long life are needed. A conceptual design scheme of a small mobile helium-xenon cooled solid reactor has been proposed in previous work. This study aims to obtain a lightweight and compact core design and improve the design scheme of sliding reflector segments for reliable reactivity control. Firstly, under the design constraints of reactor life and thermal safety, the core geometry optimization analysis was performed using OpenMC, and a design scheme to obtain minimal mass of core was achieved. Secondly, the study analyzed the influence of burnable poison on power distribution and by adding a 2% mass fraction of Gd₂O₃ to the fuel rods near the reflector region, the radial power factor was reduced from 2.22 to 1.43 at the beginning of life. Finally, by partitioning the sliding reflector, a linear introduction of reactivity was achieved, and it can also ensure the reactor safety in case of accidents. This study provides a certain reference for the design of small gas-cooled solid reactor.