Prompt criticality

In nuclear engineering, an assembly is prompt critical if for each nuclear fission event, one or more of the immediate or prompt neutrons released causes an additional fission event. This causes a rapidly exponential increase in the number of fission events. Prompt criticality is a special case of supercriticality.

Critical versus prompt-critical

An assembly is critical if each fission event causes, on average, exactly one other. This causes a self-sustaining fission chain reaction. When a uranium-235 (U-235) atom undergoes nuclear fission, it typically releases 2 or 3 neutrons (with the average being about 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 before it is absorbed by a non-fissile atom or lost to the chain-reaction by other routes. This can be achieved either through enrichment which increases the fraction of fissile U-235 atoms in the uranium fuel, or by slowing down the neutrons by letting them scatter off lighter nuclei called moderators (slow neutrons are more likely to fission U-235 than fast neutrons).

The average number of neutrons that cause new fission events is called the criticality or effective neutron multiplication factor, denoted by the letter k. When k is equal to 1, the assembly is called critical, if k is less than 1 the assembly is said to be subcritical, and if k is greater than 1 the assembly is called supercritical. In addition, a supercritical assembly is said to be prompt-critical if it is supercritical even without the contribution of so called delayed neutrons. Delayed neutrons are neutrons which are emitted by radioactive fission products some time after a fission event has occurred.

In a supercritical (k > 1) assembly, the neutron activity increases exponentially with time. If the assembly is supercritical but not prompt-critical, the increase will be fairly slow (e.g. double every few minutes). If the assembly is prompt-critical, the increase will be extremely rapid and will cause an explosion if kept prompt-critical for long enough (meaning a few millionths of a second or less).

In contrast, in a subcritical assembly, each fission event triggers, on average, less than one new fission event (k < 1). In the case of a one-time injection of neutrons, the number of neutrons resulting from this decreases exponentially with time. In addition a steady rate of spontaneous fissions causes a proportional steady level of neutron activity. The constant of proportionality is higher the higher k is.

In a critical assembly, each fission event triggers, on average, one new fission event (k = 1). In the case of a one-time injection of neutrons, the number of neutrons resulting from this is constant with time. In addition a steady rate of spontaneous fissions causes a level of neutron activity increasing linearly with time.

Nuclear reactors

In order to achieve a self-sustaining controllable fission reaction, the assembly must be neither prompt-critical nor subcritical. In other words, k must equal 1. In nuclear reactors this is possible due to delayed neutrons. Because it takes some time before these neutrons are emitted following a fission event, it is possible to control the nuclear reaction using control rods. The reactor is operated in a state where it is only critical due to the delayed neutrons, but not without their contribution. If it is delayed-supercritical for a while, the exponential increase of reactor activity is slow enough to make it possible to control the criticality factor, k, by rapidly inserting or withdrawing rods of neutron absorbing material. Using control rods it is thus possible to maintain the reactor in a critical, but not prompt-critical, state.

Prompt critical accidents

Prompt criticality must be avoided in the operation of a nuclear reactor as it will cause a rapid uncontrollable increase in reactor activity, and reactors are designed to make it as unlikely as possible. Only two reactor accidents are suspected of having achieved prompt criticality, those of Chernobyl #4 and SL-1. In both cases there is doubt that prompt criticality occurred, although in both the uncontrolled surge in power was sufficient to cause an explosion that destroyed the reactor. At Chernobyl, in 1986, the heat of an overheated reactor core led to the rupturing of the core, vaporization of steam and a steam explosion. Since the reactor was not designed with a containment building capable of containing this catastrophic explosion, the accident released large amounts of radioactive material into the environment.

Many reactor designs do succeed in making prompt criticality practically impossible. A pressurized water reactor (PWR), for example, does not contain enough fuel of high enough enrichment to make a prompt critical assembly with the materials in the core. Such reactors can still overheat and even melt if the ability to cool them is lost (a loss of coolant accident), but they are unlikely to explode.

Nuclear weapons

In the design of nuclear weapons, on the other hand, achieving prompt criticality is essential. Indeed, one of the problems to be overcome in constructing a plutonium-fueled bomb is to achieve prompt criticality and an explosion before the energy released by the reaction in an assembly that is merely supercritical destroys the bomb. This is also the reason that high-grade plutonium is used: lower grades (such as the plutonium produced by most nuclear power stations) make the timely assembly of a prompt critical configuration even more difficult.

References and links

"Nuclear Energy: Principles", Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt; apparently excerpted from notes from the University of Washington Department of Mechanical Engineering; themselves apparently summarized from Bodansky, D. (1996), Nuclear Energy: Principles, Practices, and Prospects, AIP
DOE Fundamentals Handbook

Critical versus prompt-critical

Nuclear reactors

Prompt critical accidents

Nuclear weapons

See also

References and links