The use of different nuclear reactor systems as power source of deep-space explorers has been studied over the past decades as solar power cannot be expected in deep-space beyond Jupiter. In the preceding study, a cylindrical solid moderator reactor concept of about 500 kg in weight, which consists of 20% enriched UN fuel, YH1.5 moderator and Be reflector without using working fluid, was developed. In this study, we propose to further extend use of the developed core concept for the in-depth ice layer's investigation of Europa (one of the moons of Jupiter). At the end of the journey, the bare reactor is to be landed on the ice layer of Europa and sink down through the ice-layer as it melts the ice layer with its thermal power. For this purpose, this study aims to flatten the core power distribution to increase the core surface temperature for efficient ice melting while keeping the peak temperature of the core below a design limit. The core neutronics characteristics and power distributions are evaluated with neutron diffusion approximation and ablation and sinking behavior of the reactor through the ice layer is analyzed with Moving Particle Semi-implicit (MPS) method. Among different designs, the Hollow core could reduce the radial power peaking relatively well. The trial analysis by MPS method showed that modeling convective heat loss of the core surface and / or modifications to the core design may be necessary to prevent excess heat-up of the core before it sufficiently melts the ice and sinks down into the ice layer.