Reactor Theory (Nuclear Parameters)DOE-HDBK-1019/2-93REACTIVITY COEFFICIENTSBecause the moderator-to-fuel ratio affects the thermal utilization factor and the resonance escapeFigure 2 Effects of Over and Under Moderation on k_{eff}probability, it also affects k_{eff}. The remaining factors in the six factor formula are also affectedby the moderator-to-fuel ratio, but to a lesser extent than f and p. As illustrated in Figure 2,which is applicable to a large core fueled with low-enriched fuel, there is an optimum pointabove which increasing the moderator-to-fuel ratio decreases k_{eff} due to the dominance of thedecreasing thermal utilization factor. Below this point, a decrease in the moderator-to-fuel ratiodecreases k_{eff} due to the dominance of the increased resonance absorption in the fuel. If the ratiois above this point, the core is said to be over moderated, and if the ratio is below this point, thecore is said to be under moderated.In practice, water-moderated reactors are designed with a moderator-to-fuel ratio so that thereactor is operated in an under moderated condition. The reason that some reactors are designedto be under moderated is if the reactor were over moderated, an increase in temperature woulddecrease the N^{m}/N^{u} due to the expansion of the water as its density became lower. This decreasein N^{m}/N^{u} would be a positive reactivity addition, increasing k_{eff} and further raising power andtemperature in a dangerous cycle. If the reactor is under moderated, the same increase intemperature results in the addition of negative reactivity, and the reactor becomes moreself-regulating.Rev. 0NP-03Page 25