Prompt Critical Reactor

In a prompt critical reactor, the prompt neutron fraction (1-p) is less than one, so K must be greater than one in order to be prompt critical. The product,... 

By inspection, the form and terms are identical, so in a prompt critical reactor, p=0. 

Figure 4.1 Delayed and Prompt Neutron Fractions in Subcritical Critical, Supercritical, and Prompt Critical Reactors...

The time rate of change of neutron population in a prompt critical reactor is ... 

Equation (4.6) can be used to calculate reactor power in a prompt critical reactor at any time following the start of a transient. Use the example from an earlier chapter P(0) = 3300MW, Keff = 1.001, AK =. 001, t = 1 second. The power level after a one second transient is ... 

For a prompt critical reactor, equation (4.7) can be compared to equation (4.6). Since both express reactor power as functions of time, they are equal at any particular time for the same initial power. Setting them equal and comparing terms means that l/T r AK/l or ... 

Which is the reactor period in a prompt critical reactor in terms of prompt generation time, 1, and AK. 

The subsequent events led to the generation of an increasing number of steam voids in the reactor core, which enhanced the positive reactivity. The beginning of an increasingly rapid rise in power was detected, and a manual attempt was made to stop the chain reaction (the automatic trip, which the test would have triggered earlier, had been blocked). However, there was little possibility of rapidly shutting down the reactor as almost all the control rods had been completely withdrawn from the core. The continuous reactivity addition by void formation led to a prompt critical excursion. It was calculated that the first power peak reached 1(X) times the nominal power within four seconds. Energy released in the fuel by the power excursion suddenly ruptured part of the fuel into minute pieces. Small, hot fuel particles (possibly also evaporated fuel) caused a steam explosion. 

The asymptotic period and the prompt mode decay constant can be related more naturally to reactivities other than the static reactivity. The natural reactivities are related to real flux distributions in the subcritical reactor and to the importance function in the reference critical reactor. 

It is essential for the safety of the reactor to exclude the possibility of super prompt critical state at all times. This requires that the inserted reactivity at potential events should be below 1 under conservative conditions, neglecting reactivity feedback coefficients. 

During the course of the rapid power surge, the reactor became prompt critical . A nuclear chain reaction is maintained within a nuclear reactor because the neutrons produced by fission at one time go on to produce further fissions later on. If the same numbers of fissions are produced, the power remains constant and the reactor is said to be critical if more fissions are produced the power increases and if less are produced the power falls. However, not all the neutrons are produced immediately the fission occurs. The prompt neutrons (over 99%) do appear immediately but the delayed neutrons appear up to a minute later. If the reactor is critical only when the delayed neutrons are taken into account, then the power can change only fairly slowly (over a timescale of a few seconds to a minute) and so is easy to control. However, if enough reactivity is added to make the chain reaction self-sustaining on the prompt neutrons alone, then the power can change much more quickly (over thousandths of seconds). This requires a lot of reactivity to be added, but this is what happened at Chernobyl. 

On Saturday 26 April 1986 at 01.23 local time. Reactor 4 and the surrounding plant and building were destroyed by an explosion caused by a prompt critical power excursion which resulted in a massive release of active debris from the reactor core into the atmosphere. The first effects of this active release felt outside the Soviet Union were measured at the Swedish... 

The xenon-135 isotope is itself radioactive and decays at a slower rate with a 9.2 h half-life. While the reactor is operating at power, the xenon isotope is also removed by neutron capture the resulting xenon-136 isotope has an insignificant cross-section. The first effect of this phenomenon, therefore, is to require some 2-3% additional reactivity to maintain criticality at power as the xenon builds up. This amount is appreciably larger than the reactivity corresponding to prompt criticality. 

It is possible that this peculiarity of rod insertion was the final mechanism for the prompt critical accident. The calculation of the size of the effect depends upon assumptions about the previous operating history of the reactor, but estimates made at the Berkeley Nuclear Laboratory suggest that this final water displacement may have added between Vi% and Vi% reactivity, enough indeed to bring about the prompt critical excursion. 

In general, it is possible to ensure that the additional reactivity due to a control rod expulsion is of the order of 0.15 per cent (but, in any case, well below 0.6 per cent, which would originate a prompt criticality ). The accident reactivity excursion is mitigated by the Doppler coefficient and is terminated by the reactor scram. Roughly 10 per cent of the fuel can be damaged (DNBR < 1) and the effective whole-body doses outside the plant may reach 10-20 mSv in two hours at the edge of the exclusion area. 

An exact calculation by Akcasu [14] of the reactor response to the sinusoidal reactivity input to a critical reactor shows that the amplitude of the SN/No vibration increases steadily with time instead of remaining constant as stated by the linearized result of Equation (120). A related result has been obtained by Potter [15] by considering departures from stable operation of the reactor at positive reactivities. He showed that the reactor is less stable for such departures than for departures from critical operation. These results are consequences of the fact that the reactor is more responsive with increasing reactivity, which may be seen to be the case from the prompt jump Equation (103). 

Some non-linear problems. Consider the problem of a sudden introduction of reactivity into a critical reactor with no source in which the feedback reactivity is proportional to the energy generated, as might be the case for a reactor with no cooling. Assuming that the reactivity is less than j8, the prompt jump approximation may be used, which in the one delay group approximation results in (compare Equation (106))... 

J. Ernest Wilkins, Jr., The behavior of a reactor at prompt critical when the reactivity is a linear function of time, NDA 14-128. 

If the Doppler effect is not strong enough to bring the reactor below prompt critical, then the behavior is, of course, intermediate between these extremes, but is of a character more like the no-Doppler effect accident than the strong Doppler effect accident. 

Doppler coefficient. Since the Doppler coefficient T dkjdT) is assumed to vary as 1/J, the parameter TidkjdT) is a constant (referred to as A op throughout this chapter). The results on Fig. 1 are consistent with previous analyses (5-9), which have shown that a large Doppler coefficient can reduce the energy release by more than a factor of 10. For calibration, it should be noted that the calculated Doppler coefficient for the 1000-MWe reactor (72) is oop = —0.008. Also, for calibration, it is worth noting that the reactivity steps (above prompt critical) of 0.001, 0.0005, and 0.00025 Ak/k would be approximately equivalent to ramps of 45, 15, and 6/sec in a reactor core having a zero Doppler coefficient. 

Under these conditions, an increase of 10% in reactor power takes 19 s. Reactors must always be built in such a way that the construction makes it impossible to reach a criticality of A > 1 -I-( prompt criticality ). This is a basic law of reactor construction since Fermi s first test reactor. In fact, this is how western reactors are designed. In the reactor at Chernobyl, which was destroyed in an explosion, prompt criticality was not made physically impossible. It was only forbidden by regulations that were not followed on the day of the accident. As a result, the reactor exploded. 

However, power reactors require significant amounts of reactivity (i.e., well above the amount needed to go prompt critical if added suddenly) that must be provided by movable control absorber devices (or removable poison dissolved in the piimaiy coolant) under the direction of a licensed operator and following jq>proved procedures during reactor start-up and the transition to equilibrium full-power operation. This positive reactivity is needed to compensate for losses associated widi increased core temperature, reduced coolant density including bubble void formation, and equilibrium fission product poison loads, especially Xe. Consequently, it is only possible to limit the amount of reactivity that could theoretically be inserted to small, intrinsically safe values when the reactor is already in the normal full-power operating mode with all movable control devices very near their maximum withdrawal positions (and when the dissolved poison concentration is close to zero). 

The long prompt neutron lifetime (about 1 ms) means that for reactivity transients even above prompt critical, the rate of rise in power is relatively slow. For example, the reactor period for an insertion of 5 mk is about 0.85 s L whereas for 7 mk it is about 2.4 s 1. The SDSs are, of course, designed to preclude prompt criticality. 

The large lattice pitch and the long neutron diffusion time in the HWR lattice yield a very long prompt-neutron lifetime F, approximately 1 ms in a CANDU reactor, which slows the evolution of power in transients, especially near-prompt-critical power excursions. 

The analyses performed show a high safety potential of the reactor installations of the considered type. For example, even in the event of a postulated combination of such initiating events as the containment destruction, the damage of the reactor installation box-confinement connections and a serious tightness failure of the primary circuit gas system with direct contact of the lead-bismuth coolant surfaces with the atmospheric air, neither a prompt criticality nor the explosion or fire would occur due to the internal causes, and the radioactive release would be lower than that requiring the evacuation of population from the neighbouring territory. 

In such core composition, the bum-up of fuel progresses from the outer core into the inner blanket region, which is beneficial for sustaining the reactivity for long-term burn-up with a small reactivity swing [XXV-6], For the reactor lifetime of 12 years the expected burn-up reactivity swing is around 0.1% (see Fig. XXV-3) and, therefore, the possibility of a prompt criticality is eliminated. 

The FUJI MSR has very low excess reactivity, and even in the case of a malicious action of control rod withdrawal, the reactor would have no prompt criticality accidents with a release of radioactivity to the environment. 

Thus the flux is changing in time only because of the appearance of the delayed neutrons the reactor is critical on the basis of the prompt neutrons alone. It is customary to refer to a reactor system in which the added reactivity is just equal to the fraction of neutrons which are delayed as prompt critical. 

Fast injection of pure water into the core could result in prompt criticality in some reactors with large potential damages to the first barrier (fuel cladding) in a situation where the third barrier (containment) might be open. 

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