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The feasibility of indefinite recycling in the Encapsulated Nuclear Heat Source (ENHS) core without changing the pitch-to-diameter (P/D) ratio, while maintaining a nearly zero burnup reactivity swing, is investigated. The P/D ratio required to achieve a nearly burnup-independent keff over the life of the ENHS core was found sensitive to the initial composition of the transuranium (TRU) loaded and to the number of recycles this fuel underwent. The longer the cooling time is of the TRU from light water reactor (LWR) spent fuel, the larger the optimal P/D ratio becomes. Whereas the optimal P/D ratio of the reference ENHS core that is fueled with TRU from LWR spent fuel discharged at 50 GWd/t heavy metal (HM) and cooled for 10 yr is 1.36, it is 1.54 for the equilibrium core that features a substantially smaller concentration of 241Pu as well as of 242Pu, a larger concentration of 239Pu, and a substantially larger concentration of minor actinides. It was found that by increasing the cooling period of the above LWR TRU to ~32 yr, the optimal first core P/D ratio is that of the equilibrium core. The burnup reactivity swing of the subsequent cores fueled with successive recycling of the ENHS discharged HM is satisfactory. There is no need to adjust the core P/D ratio from recycle to recycle. The power level that can be removed by natural circulation from the P/D = 1.54 core is ~36% higher than that of the reference ENHS core. The physical phenomena affecting the observed trends are discussed, and the neutronic characteristics of the equilibrium cores identified are summarized.