A Review of Criticality Accidents A Review of Criticality Accidents

Figure 63. Energy model computation of power and energy release vs time. The initial reactivity is 1.2 $ above
delayed critical. Neutron lifetime values are 10 -8 , 10 -6 , and 10 -4 seconds. The bottom panel shows the corresponding
curves of reactivity vs time.
constant power following the spike is the plateau.
During the spike, the reactivity changes by 2 ∆k 0 —that
is, it reflects about prompt criticality. The characteristics
of such spikes are established almost entirely by
the prompt neutrons. The traces for l =10 -4 (simulating
a solution system or a moderated reactor) do not show
the reflection about prompt criticality, and there is no
well–defined plateau following the spike. The time
scale is of the order of the decay times of the shorter
delayed neutron precursor; the effects of these neutrons
cannot be ignored.
Figure 64 illustrates comparable data for a step
increase in reactivity of 1.0 $. The time history of the
reactivity and power in this case is quite different and
is typical of excursions in the delayed critical region.
The time scale is much extended, allowing the possibility
of mechanical devices shutting off the transient;
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power excursion peaks are broader; and the reactivity
now attempts to reflect about delayed criticality. It
should be noted that the implicit assumption of no heat
loss from the system cannot be realized in practice.
Any such loss of energy would result in power values
greater than those plotted.
Some of the results shown in Figures 63 and 64 can
be obtained analytically. For sufficiently large step
increases in reactivity above prompt criticality, the
delayed neutrons may be ignored and the kinetic
equations integrated to give the total excursion yield. *
dE/dt = 2 ∆k p / b (2)
where ∆k p is the step increase relative to prompt
criticality. The half–width of the spike is given by
* A similar result can be obtained for the delayed critical region, but the nonadiabatic behavior vitiates the result.