If it were not for the build-up of plutonium isotopes reactivity would decrease rapidly as a function of ir­radiation. In a natural uranium reactor the plutonium build-up is in fact sufficient to cause a net increase in reactivity with time over a substantial part of the fuel life. The k« of a magnox lattice shown in Fig

3.4 (a) as a function of time is typical of magnox reactor lattices and varies only little from one station to another due to small differences in the fuel-to — graphite ratio and reactor operating conditions.

The consequence of this k«, variation is that once the reactor is fuelled there is a long interval before any refuelling is needed in order to maintain criti­cality. This is a useful level of flexibility which has been utilised in practice when difficulties in the fuelling route have occurred-

With the enriched fuel of an AGR, the burn-up of U-235 dominates and the reactivity decreases sig­nificantly from the start of irradiation. The variation of k« for typical inner-zone feed fuel of an AGR is shown in Fig 3.4 (b). Also shown is the variation of kco with time for fuel containing burnable poisons designed to reduce the reactivity change and the local rating effects of new fuel.

In a PWR the change of k* with burn-up is even more pronounced, largely because of the higher en­richment and therefore greater importance of burn-up of the U-235. The k® for a 3.1% enriched PWR lattice with constant boron level in the water and at a constant water density of 0.67 gm/cm3 is shown on Fig 3.4 (c). The large change in reactivity resulting from this к я, drop is accommodated partly by refuel­ling, done in batches; for example, one-third of the core may be refuelled at a time, in which case the change in reactivity within a fuel cycle is about one — third that indicated by Fig 3.4 (c) and is counteracted by reductions in boron level. There are limits to the level of boron dosing because of the positive contri-

bution to the temperature coefficient of reactivity contributed by boron density reduction as water tem­perature increases. Burnable poisons may be incor­porated in initial fuel charges as a further reactivity control.