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 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 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 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.
Critical versus prompt-critical 
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 microseconds. However 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.
In a delayed-critical assembly, the delayed neutrons are needed to make k-effective greater than one. Thus the time between successive generations of the reaction, T, is dominated by the time it takes for the delayed neutrons to be released, on the order of seconds or minutes. Therefore the reaction will increase slowly, with a long time constant. This is slow enough to allow the reaction to be controlled with electromechanical control systems such as control rods, and as such all nuclear reactors are designed to operate in the delayed-criticality regime.
In contrast, a supercritical assembly is said to be prompt-critical if it is critical without any contribution from delayed neutrons and super-prompt-critical if it is supercritical without any contribution from delayed neutrons. In this case the time between successive generations of the reaction, T, is only limited by the lifetime of the prompt neutrons, and the increase in the reaction will be extremely rapid, causing a rapid release of energy within a few milliseconds. Prompt-critical assemblies are created by design in nuclear weapons and some specially designed research experiments.
When differentiating between a prompt neutron versus a delayed neutron, the difference between the two has to do with the source from which the neutron has been released into the reactor. The neutrons, once released, have no difference except the energy or speed which have been imparted to them. A nuclear weapon relies heavily on super-prompt-criticality (to produce a high peak power in a fraction of a second), whereas nuclear power reactors use delayed-criticality to produce controllable power levels for months or years.
Nuclear reactors 
In order to start up a controllable fission reaction, the assembly must be delayed-critical. In other words, k must be greater than 1 (supercritical) without crossing the prompt-critical threshold. 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.
A steady-state (constant power) reactor is operated so that it is critical due to the delayed neutrons, but would not be so without their contribution. During a gradual and deliberate increase in reactor power level, the reactor is delayed-supercritical. The exponential increase of reactor activity is slow enough to make it possible to control the criticality factor, k, by inserting or withdrawing rods of neutron absorbing material. Using careful control rod movements, it is thus possible to achieve a supercritical reactor core without reaching an unsafe prompt-critical state.
Once a reactor plant is operating at its target or design power level, it can be operated to maintain its critical condition for long periods of time.
Prompt critical accidents 
Nuclear reactors can be susceptible to prompt-criticality accidents if a large increase in k-effective (or reactivity) occurs, e.g., following failure of their control and safety systems. The rapid uncontrollable increase in reactor power in prompt-critical conditions is likely to irreparably damage the reactor and in extreme cases, may breach the containment of the reactor. Nuclear reactors' safety systems are designed to prevent prompt criticality and, for defence in depth, reactor structures also provide multiple layers of containment as a precaution against any accidental releases of radioactive fission products.
With the exception of research and experimental reactors, only a small number of reactor accidents are thought to have achieved prompt criticality, for example Chernobyl #4, the U.S. Army's SL-1, and Soviet submarine K-431. In all these examples the uncontrolled surge in power was sufficient to cause an explosion that destroyed each reactor and released radioactive fission products into the atmosphere.
At Chernobyl in 1986, an unusual and unsafe test was performed that resulted in an overheated reactor core. This led to the rupturing of the fuel elements and water pipes, vaporization of water, a steam explosion, and a graphite fire. Estimated power levels prior to the incident suggest that it operated in excess of 30 GW, ten times its 3 GW maximum thermal output. The reactor chamber's 2000-ton lid was lifted by the 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. The catastrophic fire in the graphite neutron moderator compounded the problem, sending massive amounts of radioactive debris into the atmosphere.
In the other two incidents, the reactor plants failed due to errors during a maintenance shutdown that was caused by the rapid and uncontrolled removal of at least one control rod. The SL-1 was a prototype reactor intended for use by the US Army in remote polar locations. At the SL-1 plant in 1961, the reactor was brought from shutdown to prompt critical state by manually extracting the central control rod too far. As the water in the core quickly converted to steam and expanded, the 26,000-pound (12,000 kg) reactor vessel jumped 9 feet 1 inch (2.77 m), leaving impressions in the ceiling above. All three men performing the maintenance procedure died from injuries. 1,100 curies of fission products were released as parts of the core were expelled. It took 2 years to investigate the accident and clean up the site. The excess prompt reactivity of the SL-1 core was calculated in a 1962 report:
The delayed neutron fraction of the SL-1 is 0.70%... Conclusive evidence revealed that the SL-1 excursion was caused by the partial withdrawal of the central control rod. The reactivity associated with the 20 inch withdrawal of this one rod has been estimated to be 2.4% δk/k which was sufficient to induce prompt criticality and place the reactor on a 4 millisecond period.
In the K-431 reactor accident, 10 were killed during a refueling operation. The K-431 explosion destroyed the adjacent machinery rooms and ruptured the submarine's hull. In these two catastrophes, the reactor plants went from complete shutdown to extremely high power levels in a fraction of a second, damaging the reactor plants beyond repair.
List of accidental prompt critical excursions 
A number of research reactors and tests have purposely examined the operation of a prompt critical reactor plant. CRAC, KEWB, SPERT-I, Godiva device, and BORAX experiments contributed to this research. However, many accidents have also occurred, primarily during research and processing of nuclear fuel. SL-1 is the notable exception.
The following list of prompt critical power excursions is adapted from a report submitted in 2000 by a team of American and Russian nuclear scientists who studied criticality accidents, published by the Los Alamos Scientific Laboratory, the location of many of the excursions. A typical power excursion is about 1 x 1017 fissions.
- Los Alamos Scientific Laboratory, 11 February 1945
- Los Alamos Scientific Laboratory, December 1949, 3 or 4 x 1016 fissions
- Los Alamos Scientific Laboratory, 1 February 1951
- Los Alamos Scientific Laboratory, 18 April 1952
- Argonne National Laboratory, 2 June 1952
- Oak Ridge National Laboratory, 26 May 1954
- Oak Ridge National Laboratory, 1 February 1956
- Los Alamos Scientific Laboratory, 3 July 1956
- Los Alamos Scientific Laboratory, 12 February 1957
- Mayak Production Association, 2 January 1958
- Oak Ridge Y-12 Plant, 16 June 1958 (possible)
- Los Alamos Scientific Laboratory, 30 December 1958
- SL-1, 3 January 1961, 4 x 1018 fissions or 130 megajoules (36 kWh)
- Idaho Chemical Processing Plant, 25 January 1961
- Los Alamos Scientific Laboratory, 11 December 1962
- Sarov (Arzamas-16), 11 March 1963
- White Sands Missile Range, 28 May 1965
- Oak Ridge National Laboratory, 30 January 1968
- Chelyabinsk-70, 5 April 1968
- Aberdeen Proving Ground, 6 September 1968
- Mayak Production Association, 10 December 1968 (2 prompt critical excursions)
- Kurchatov Institute, 15 February 1971
- Idaho Chemical Processing Plant, 17 October 1978 (very nearly prompt critical)
- Sarov (Arzamas-16), 17 June 1997
- JCO Fuel Fabrication Plant, 30 September 1999
Nuclear weapons 
In the design of nuclear weapons, on the other hand, achieving prompt criticality is essential. Indeed, one of the design problems to overcome in constructing a bomb is to contract the fissile materials and achieve prompt criticality before the chain reaction has a chance to force the core to expand. A good bomb design must therefore win the race to a dense, prompt critical core before a less-powerful chain reaction (known as a fizzle) disassembles the core without allowing a significant amount of fuel to fission. This generally means that nuclear bombs need special attention paid to the way the core is assembled, such as the novel implosion method hypothesized by Richard C. Tolman, Robert Serber, and other scientists at the University of California, Berkeley in 1942.
See also 
- Critical mass (nuclear)
- Nuclear weapon design
- Neutron capture
- Neutron moderator
- Subcritical reactor
- Thermal neutron
- Void coefficient
- Tucker, Todd (2009). Atomic America: How a Deadly Explosion and a Feared Admiral Changed the Course of Nuclear History. New York: Free Press. ISBN 978-1-4165-4433-3. See summary: 
- Stacy, Susan M. (2000). Proving the Principle (PDF). U.S. Department of Energy, Idaho Operations Office. ISBN 0-16-059185-6. Unknown parameter
|subtitle=ignored (help) Chapter 15.
- IDO-19313 Additional Analysis of the SL-1 Excursion, Final Report of Progress July through October 1962, November 1962.
- A Review of Criticality Accidents, Los Alamos National Laboratory, LA-13638, May 2000. Thomas P. McLaughlin, Shean P. Monahan, Norman L. Pruvost, Vladimir V. Frolov, Boris G. Ryazanov, and Victor I. Sviridov.
- "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