Prompt critical

In nuclear engineering, prompt criticality is said to be reached during a nuclear fission event if one or more of the immediate or prompt neutrons released by an atom in the event causes an additional fission event resulting in a rapid, exponential increase in the number of fission events. Prompt criticality is a special case of supercriticality.

An assembly is critical if each fission event causes, on average, exactly one additional such event in a continual chain. Such a chain is a self-sustaining fission chain reaction. When a uranium-235 (U-235) atom undergoes nuclear fission, it typically releases between one and seven neutrons (with an average of 2.4). In this situation, an assembly is critical if every released neutron has a 1/2.4 = 0.42 = 42% probability of causing another fission event as opposed to either being absorbed by a non-fission capture event or escaping from the fissile core.

The average number of neutrons that cause new fission events is called the effective neutron multiplication factor, usually denoted by the symbols k-effective, k-eff or k. When k-effective is equal to 1, the assembly is called critical, if k-effective is less than 1 the assembly is said to be subcritical, and if k-effective is greater than 1 the assembly is called supercritical.

In a supercritical assembly the number of fissions per unit time, N, along with the power production, increases exponentially with time. How fast it grows depends on the average time it takes, T, for the neutrons released in a fission event to cause another fission. The growth rate of the reaction is given by:

Most of the neutrons released by a fission event are the ones released in the fission itself. These are called prompt neutrons, and strike other nuclei and cause additional fissions within nanoseconds (an average time interval used by scientists in the Manhattan Project was one shake, or 10 nanoseconds). A small additional source of neutrons is the fission products. Some of the nuclei resulting from the fission are radioactive isotopes with short half-lives, and nuclear reactions among them release additional neutrons after a long delay of up to several minutes after the initial fission event. These neutrons, which on average account for less than one percent of the total neutrons released by fission, are called delayed neutrons. The relatively slow timescale on which delayed neutrons appear is an important aspect for the design of nuclear reactors, as it allows the reactor power level to be controlled via the gradual, mechanical movement of control rods. Typically, control rods contain neutron poisons (substances, for example boron or hafnium, that easily capture neutrons without producing any additional ones) as a means of altering k-effective. With the exception of experimental pulsed reactors, nuclear reactors are designed to operate in a delayed-critical mode and are provided with safety systems to prevent them from ever achieving prompt criticality.

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