The effectiveness of a control rod varies with the relative neutron flux in which the rod is operating; ‘relative’ in this case means relative to the reactor as a whole, i. e., moving a given rod up or down in a high relative neutron flux has more effect than in a low relative neutron flux. The variation is manifested in a number of ways.

First, and most important, is the variation of ef­fectiveness with rod insertion. The neutron flux is higher in the middle region of the core than it is at the top and bottom, therefore moving a control rod a given amount around mid-insertion will give rise to a larger change in reactivity than moving it the same amount around the top or bottom of its travel. This variation in effectiveness is shown in curve 1 of Fig 3.23.

Second, the shape of the curve of rod worth versus rod position depends on the axial flux shape in which the rods are working. The slope of the curve at a given rod position is related to the relative neutron flux at that axial position in the core — the greater the neutron flux the greater the slope. Thus if the axial flux shape is distorted from the natural cosine­like shape, for instance by virtue of a group of bulk rods being inserted halfway into the core as may be the case shortly after start-up, then the curve of rod worth versus rod position will be as shown in curve 2 of Fig 3.23.

Third, if the neutron flux is uniformly affected (relative to the reactor as a whole) in the region in which our control rod is operating, i. e., the magni­tude of the flux is modified but it retains its natural cosine-like shape, then the rod worth will be modified. In the example shown in curve 3 of Fig 3.23 a group oi bulk rods is fully inserted in the core as may be the case shortly after start-up of a magnox reactor; the neutron tlux is depressed in the immediate vici­nity of the inserted bulk rods but the average flux across the core is unchanged (because reactor power

is unchanged) so the neutron flux in the regions in which the sector rods are working is higher than the average, therefore their worth is increased. Similarly the worth of an individual rod is influenced by con­ditions in its immediate vicinity, for example, if a sector rod is close to a bulk rod which is fully in­serted, or if it is close to a channel of absorber (see magnox fuel cycle in Section 8 of this chapter), then the worth of that sector rod will be reduced because it is working in a lower-than-average relative neutron flux. Figure 3.23 is plotted for the group of 28 sector rods at Dungeness A.

In practice the second and third effects described here are barely noticeable to the reactor control en­gineer amongst the many other parameters affecting the reactor performance, but they are taken into account in theoretical analyses for reactor optimisa­tion and fault studies. The first effect, however, the basic S-shape, is very apparent and important to him.