For the successful steady state operation of deuterium-tritium (DT) fusion reactors, helium (He) ash needs to be removed continuously from the burning core, along with unburned hydrogenic fuel particles, to sustain the power generation. This will require enormous particle pumping capabilities despite the fact that helium is the most difficult gas to be pumped by means of cryogenic condensation. In the present work, zero-dimensional, four-reservoir (core-plasma, SOL-plasma, gas-phase, and wall material) global particle balance modeling has been conducted for both DT-fuel and He-ash particles. Modeling results indicate that, for the density control of He-ash particles in the burning core, passive wall pumping via codeposition with eroded plasma-facing materials would definitely be necessary to compensate for the lack of pumping speed provided by conventional vacuum equipment. Recent experimental data on helium codeposition with lithium have been used as input for modeling and results indicate that lithium-gettered moving-surface plasma-facing components can meet the He-ash pumping requirements.