CONTROL RODSDOE-HDBK-1019/2-93Reactor Theory (Nuclear Parameters)The slope of the curve (Dr/Dx), and therefore the amount of reactivity inserted per unit ofwithdrawal, is greatest when the control rod is midway out of the core. This occurs because thearea of greatest neutron flux is near the center of the core; therefore, the amount of change inneutron absorption is greatest in this area. If the slope of the curve for integral rod worth inFigure 9 is taken, the result is a value for rate of change of control rod worth as a function ofcontrol rod position. A plot of the slope of the integral rod worth curve, also called thedifferential control rod worth, is shown in Figure 10. At the bottom of the core, where there arefew neutrons, rod movement has little effect so the change in rod worth per inch varies little.As the rod approaches the center of the core its effect becomes greater, and the change in rodworth per inch is greater. At the center of the core the differential rod worth is greatest andvaries little with rod motion. From the center of the core to the top, the rod worth per inch isbasically the inverse of the rod worth per inch from the center to the bottom.Differential control rod worthis the reactivity change per unit movement of a rod and isnormally expressed as r/inch, Dk/k per inch, or pcm/inch. The integral rod worth at a givenwithdrawal is merely the summation of all the differential rod worths up to that point ofwithdrawal. It is also the area under the differential rod worth curve at any given withdrawalposition.Figure 10 Differential Control Rod WorthNP-03Rev. 0Page 52

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