The foregoing delayed neutron data and calculations have been based on thermal fission of U-235. Other fissile materials have different delayed neutron char­acteristics, for example, Table 3.3 gives the yield and mean life values (for the 6-group model) in the case of thermal fission of Pu-239.

Note from Table 3.3 that the total delayed neu­tron yield from Pu-239 is significantly less than that from U-235. Thus as the isotopic content of the fuel in a power reactor changes with the irradiation, the time-dependent behaviour of the neutron population also changes. For example, the doubling times in an AGR on an equilibrium fuel cycle at current discharge irradiations are approximately 20% shorter than at start of life,

4.3.2 Shutdown kinetics

The shutdown state is a special case in reactor kine­tics. In order to provide a reading on the neutron flux instrumentation during shutdown and start-up, so that the operator is not ‘flying blind’, a neutron source is located in the reactor core. A typical neu­tron source is antimony/beryllium, Sb-124 being a ~r emitter and Be-10 responding with a (7,n) reaction (see Chapter 1, Section 3).

Consider a shutdown reactor with a given value of multiplication constant k, a typical value being 0.97. Suppose the neutron population is zero when a neutron source is suddenly introduced into the core. Consider in small timesteps the time-dependent be­haviour of the neutron population. Let the neutron source emit Q neutrons in each timestep. In each successive timestep, the neutron population will be multiplied by the multiplication constant к and an­other Q neutrons will be added by the source, so the neutron population will change from timestep to timestep as follows;

Q

Qk + Q — Q (k + 1)

(Qk + Q, к + Q = Q (к2 + к + 1) etc.

The value of к is less than unity, therefore the neu­tron population will build up to a final value given by the sum of the geometric progression in k:

Q (1 + к + к2 + etc) = Q x 1/1 — к (3.22)

This is illustrated in Fig 3.22.

In a reactor start-up, during the approach to cri­ticality, as the value of к increases towards unity the neutron population rises. If the control rods are withdrawn in stages, pausing between successive stages, the neutron population will settle at each stage at a value given by Equation (3.22). This behaviour is a clear indication to the operator that the reactor is subcritical. Because of the delayed neutrons and the time taken for the geometric progression in к to converge, it may take several minutes for the neutron population to settle.

At criticality, when к is exactly equal to unity, the neutron population will rise steadily according to the expression Q + Q + Q + … etc. Since Q is small, the rate of rise is slow.

At first sight this may appear to conflict with our understanding of criticality, which up to now has been that a chain reaction is just sustained and neutron population is constant. It must be emphasised, how­ever, that the presence of the neutron source is a special case in which the chain reaction set up by

the artificial introduction of a number of neutrons Q in each timestep is just sustained, and in each successive timestep a further Q neutrons is added.

In practice the linear rise at criticality is not im­portant. During a start-up it is usual to balance the reactor power at a low power of say 100 kW, which is several orders of magnitude above the source con­tribution, so the linear rise due to the source is not apparent. In this situation, criticality is indicated by the ability to sustain a steady power level.

In the foregoing analysis we supposed that a neu­tron source was suddenly introduced into the reactor core. In practice the neutron source is usually loaded into the reactor core during commissioning and re­mains there for the life of the reactor. Sb-124 has a haltlile of approximately 60 days, so the strength of the neutron source decays with time. Sb-123, one of the stable isotopes ot antimony, is an absorber of neutrons, changing to Sb-124 when it absorbs the neutron, therefore the neutron source is reactivated while the reactor is at power. Unless the reactor is shut down for a long period of time, it will there­fore not normally be necessary to remove the neu­tron source from the reactor core during the life of the reactor. Also, when the reactor has been operating at power for some time, the neutron source is sup­plemented by neutrons derived from some of the heavy nuclei formed in the fuel and from r, ,n) re­actions induced in various reactor materials by the у activity arising from the decay of fission products; this supplementary source activity also decays with time.

At some CEGB stations which during their life have suffered shutdowns of the order of 2 years after having operated for several years, special procedures were necessary to undertake the start-ups following the long shutdowns because of the low’ neutron source strength in the reactor cores, which meant that there was insufficient neutron flux in the cores to give an adequate reading on the start-up instrumentation. The detailed procedure varied from station to station, but basically the coarse rods were pulled in stages of about 50 mN each with a pause of a few minutes between stages to allow the neutron flux to reach equilibrium and to check if the flux was giving a meaningful reading on the start-up instrumentation; when the flux was giving an adequate reading the start-up could proceed normally. A similar procedure was adopted for the initial start-up of the AGRs, which were fitted with non-activated neutron sources and relied on spontaneous fission for the neutrons necessary for start-up.