The effects of the temperatures of the many different parts of the reactor structure on reactivity depend on the detailed design of the reactor. The possible overall effects can be illustrated by the following examples, but the reality may be much more complex.

The radial dimensions of the reactor core are determined by the temperature of the structure that supports it while the axial dimen­sions of the core may depend mainly on the temperature of the fuel cladding, so radial and axial dimensions may change independently with temperature. If the structural temperatures increase the mean “smeared” densities of the solid materials decrease, but the coolant mean density may remain the same or it may actually increase. If, for

example, the temperatures of all the materials in the core are constant while the temperature of the structure that supports it increases so that its radius increases by 1%, the core volume will increase by 2%. The actual volume and mass of fuel and structural material in the core will remain the same, so their “smeared” densities will decrease by 2%. If the fuel and structure made up 50% of the original core, however, they will now form only 49% of the expanded core, so that the coolant volume fraction will have increased from 50 to 51%.

Figure 1.25 shows the effects of 1% increases in the radial and axial dimensions of a typical cylindrical oxide-fuelled breeder core as a function of the ratio of height to radius, H/R. In all cases the reactivity decreases with expansion because the leakage increases (in simple terms the “gaps” between the atoms are greater so the neutrons are more likely to diffuse out), but if H/ R is small the effect of increased height is small. In principle, in the limit of an infinite slab reactor (R ^ to), uniform expansion in the axial direction has no effect on reactivity at all.

1.6.3 Bowing

As the power density is higher at the centre of the core than at the edge there is a tendency for fuel elements in the outer part of the core to be hotter on the side facing the core centre. If they are straight when they are cold — i. e. when the reactor is shut down — they tend to become curved when the reactor is at power with the convex side towards the core centre. The effect on reactivity depends on how they are supported. If they were cantilevered at one end they would tend to move outwards as the power increases, reducing reactivity, but if they were held at both ends they would tend to move inwards, adding reactivity and giving positive feedback.

In practice, however, the core structure is designed so that the individual fuel elements cannot move freely at all (see Chapter 3). For this reason the effect of bowing on reactivity is likely to be small, but there may be complicated nonlinear effects as fuel elements or sub­assemblies distort to take up small clearances within the manufacturing tolerances.