Prompt critical
Encyclopedia
In nuclear engineering
Nuclear engineering
Nuclear engineering is the branch of engineering concerned with the application of the breakdown as well as the fusion of atomic nuclei and/or the application of other sub-atomic physics, based on the principles of nuclear physics...

, an assembly is prompt critical if for each nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

 event, one or more of the immediate or prompt neutron
Prompt neutron
In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron decay which can occur within the same context, emitted by one of the fission products anytime from a few milliseconds to a few minutes later.-Principle:Using U-235...

s released causes an additional fission event. This causes a rapid, exponential increase
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...

 in the number of fission events. Prompt criticality is a special case of supercriticality
Critical mass
A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The...

.

Criticality

An assembly is critical if each fission event causes, on average, exactly one other. This causes a self-sustaining fission chain reaction
Nuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...

. When a uranium
Uranium
Uranium is a silvery-white metallic chemical element in the actinide series of the periodic table, with atomic number 92. It is assigned the chemical symbol U. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons...

-235 (U-235) atom undergoes nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

, 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
Nuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...

, 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
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...

 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 product
Fission product
Nuclear fission products are the atomic fragments left after a large atomic nucleus fissions. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons and a large release of energy in the form of heat , gamma rays and neutrinos. The...

s. Some of the nuclei resulting from the fission are radioactive isotopes with short half-lives
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

, and nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...

s 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 (for example boron or hafnium) 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 system
Control system
A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...

s such as control rod
Control rod
A control rod is a rod made of chemical elements capable of absorbing many neutrons without fissioning themselves. They are used in nuclear reactors to control the rate of fission of uranium and plutonium...

s, and as such all nuclear reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...

s 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 neutron
Delayed neutron
In nuclear engineering, a delayed neutron is a neutron emitted after a nuclear fission event by one of the fission products anytime from a few milliseconds to a few minutes later....

s and super-prompt-critical if it is supercritical without any contribution from delayed neutron
Delayed neutron
In nuclear engineering, a delayed neutron is a neutron emitted after a nuclear fission event by one of the fission products anytime from a few milliseconds to a few minutes later....

s. 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 weapon
Nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission or a combination of fission and fusion. Both reactions release vast quantities of energy from relatively small amounts of matter. The first fission bomb test released the same amount...

s 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 neutron
Delayed neutron
In nuclear engineering, a delayed neutron is a neutron emitted after a nuclear fission event by one of the fission products anytime from a few milliseconds to a few minutes later....

s. Because it takes some time before these neutrons are emitted following a fission event, it is possible to control the nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...

 using control rod
Control rod
A control rod is a rod made of chemical elements capable of absorbing many neutrons without fissioning themselves. They are used in nuclear reactors to control the rate of fission of uranium and plutonium...

s.

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
Chernobyl disaster
The Chernobyl disaster was a nuclear accident that occurred on 26 April 1986 at the Chernobyl Nuclear Power Plant in Ukraine , which was under the direct jurisdiction of the central authorities in Moscow...

, the U.S. Army's SL-1
SL-1
The SL-1, or Stationary Low-Power Reactor Number One, was a United States Army experimental nuclear power reactor which underwent a steam explosion and meltdown on January 3, 1961, killing its three operators. The direct cause was the improper withdrawal of the central control rod, responsible for...

, and Soviet submarine K-431
Soviet submarine K-431
The Soviet submarine K-431 was a Soviet nuclear-powered submarine that had a reactor accident on August 10, 1985. An explosion occurred during refueling of the submarine at Chazhma Bay, Vladivostok...

. In all these examples the uncontrolled surge in power was sufficient to cause an explosion that destroyed each reactor and released radioactive fission product
Fission product
Nuclear fission products are the atomic fragments left after a large atomic nucleus fissions. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons and a large release of energy in the form of heat , gamma rays and neutrinos. The...

s into the atmosphere.

It has been argued that the explosion at Fukushima Dai-ichi
Fukushima Daiichi nuclear disaster
The is a series of equipment failures, nuclear meltdowns, and releases of radioactive materials at the Fukushima I Nuclear Power Plant, following the Tōhoku earthquake and tsunami on 11 March 2011. The plant comprises six separate boiling water reactors originally designed by General Electric ,...

 #3 may have also involved a prompt criticality, either before or immediately after the hydrogen explosion. Nuclear engineer Arnie Gunderson has suggested that the detonation wave visible from the explosion videos is evidence that a more energetic reaction than a hydrogen explosion was involved .

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
Steam explosion
A steam explosion is a violent boiling or flashing of water into steam, occurring when water is either superheated, rapidly heated by fine hot debris produced within it, or the interaction of molten metals A steam explosion (also called a littoral explosion, or fuel-coolant interaction, FCI) is a...

, and a graphite
Graphite
The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Ancient Greek γράφω , "to draw/write", for its use in pencils, where it is commonly called lead . Unlike diamond , graphite is an electrical conductor, a semimetal...

 fire. Since the reactor was not designed with a containment building
Containment building
A containment building, in its most common usage, is a steel or reinforced concrete structure enclosing a nuclear reactor. It is designed, in any emergency, to contain the escape of radiation to a maximum pressure in the range of 60 to 200 psi...

 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
Neutron moderator
In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....

 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
Control rod
A control rod is a rod made of chemical elements capable of absorbing many neutrons without fissioning themselves. They are used in nuclear reactors to control the rate of fission of uranium and plutonium...

. 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 26000 pounds (11,793.4 kg) reactor vessel jumped 9 in 1 in (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:
In the K-431 reactor accident, 10 were killed during a refueling operation. 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.

Many reactor designs succeed in making prompt criticality practically impossible. Some pressurized water reactor
Pressurized water reactor
Pressurized water reactors constitute a large majority of all western nuclear power plants and are one of three types of light water reactor , the other types being boiling water reactors and supercritical water reactors...

s, for example, do 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.

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
CRAC-II
CRAC-II is both a computer code and the 1982 report of the simulation results performed by Sandia National Laboratories for the Nuclear Regulatory Commission...

, KEWB, SPERT-I, Godiva device
Godiva device
The Lady Godiva device was an unshielded, pulsed nuclear reactor originally situated at the Los Alamos National Laboratory , New Mexico, U.S. It was one of a number of criticality devices within Technical Area 18 . Specifically, it was used to produce bursts of neutrons and gamma rays for...

, and BORAX experiments
BORAX experiments
The BORAX Experiments were boiling water reactor experiments done at the National Reactor Testing Station, now the Idaho National Laboratory....

 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
    SL-1
    The SL-1, or Stationary Low-Power Reactor Number One, was a United States Army experimental nuclear power reactor which underwent a steam explosion and meltdown on January 3, 1961, killing its three operators. The direct cause was the improper withdrawal of the central control rod, responsible for...

    , 3 January 1961, 4 x 1018 fissions or 130 megajoules (36.1 kW·h)
  • Idaho Chemical Processing Plant, 25 January 1961
  • Los Alamos Scientific Laboratory, 11 December 1962
  • Sarov (Arzamas-16), 11 March 1963
  • White Sands Missile Range
    White Sands Missile Range
    White Sands Missile Range is a rocket range of almost in parts of five counties in southern New Mexico. The largest military installation in the United States, WSMR includes the and the WSMR Otera Mesa bombing range...

    , 28 May 1965
  • Oak Ridge National Laboratory, 30 January 1968
  • Chelyabinsk-70, 5 April 1968
  • Aberdeen Proving Ground
    Aberdeen Proving Ground
    Aberdeen Proving Ground is a United States Army facility located near Aberdeen, Maryland, . Part of the facility is a census-designated place , which had a population of 3,116 at the 2000 census.- History :...

    , 6 September 1968
  • Mayak Production Association, 10 December 1968 (2 prompt critical excursions)
  • Kurchatov Institute
    Kurchatov Institute
    The Kurchatov Institute is Russia's leading research and development institution in the field of nuclear energy. In the Soviet Union it was known as I. V. Kurchatov Institute of Atomic Energy , abbreviated KIAE . It is named after Igor Kurchatov....

    , 15 February 1971
  • Idaho Chemical Processing Plant, 17 October 1978 (very nearly prompt critical)
  • Sarov (Arzamas-16), 17 June 1997
  • JCO Fuel Fabrication Plant
    Tokaimura nuclear accident
    The Tokaimura nuclear accident , which occurred on 30 September 1999, resulted in two deaths. At that time, it was Japan's worst civilian nuclear radiation accident. The criticality accident occurred in a uranium reprocessing facility operated by JCO , a subsidiary of Sumitomo Metal Mining Co...

    , 30 September 1999

Nuclear weapons

In the design of nuclear weapon
Nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission or a combination of fission and fusion. Both reactions release vast quantities of energy from relatively small amounts of matter. The first fission bomb test released the same amount...

s, 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
Fizzle (nuclear test)
In nuclear weapons, a fizzle occurs when the testing of a nuclear bomb fails to meet its expected yield. The reason for the failure can be linked to improper bomb design, poor construction, or lack of expertise. All countries that have had a nuclear weapons testing program have experienced fizzles...

) 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
Richard C. Tolman
Richard Chace Tolman was an American mathematical physicist and physical chemist who was an authority on statistical mechanics. He also made important contributions to theoretical cosmology in the years soon after Einstein's discovery of general relativity...

, Robert Serber
Robert Serber
Robert Serber was an American physicist who participated in the Manhattan Project. He was born in Philadelphia, Pennsylvania; he was the eldest son of David Serber and Rose Frankel. He married Charlotte Leof in 1933. Rose Serber died in 1922; David married Charlotte's cousin Frances Leof in...

, and other scientists at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

 in 1942.

See also

  • Critical mass (nuclear)
  • Nuclear weapon design
    Nuclear weapon design
    Nuclear weapon designs are physical, chemical, and engineering arrangements that cause the physics package of a nuclear weapon to detonate. There are three basic design types...

  • Neutron capture
    Neutron capture
    Neutron capture is a kind of nuclear reaction in which an atomic nucleus collides with one or more neutrons and they merge to form a heavier nucleus. Since neutrons have no electric charge they can enter a nucleus more easily than positively charged protons, which are repelled...

  • Neutron moderator
    Neutron moderator
    In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....

  • Subcritical reactor
    Subcritical reactor
    A subcritical reactor is a nuclear fission reactor that produces fission without achieving criticality. Instead of a sustaining chain reaction, a subcritical reactor uses additional neutrons from an outside source...

  • Thermal neutron
  • Void coefficient
    Void coefficient
    In nuclear engineering, the void coefficient is a number that can be used to estimate how much the reactivity of a nuclear reactor changes as voids form in the reactor moderator or coolant...

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