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In nuclear technology, criticality refers to both the neutron balance of a nuclear facility and the critical condition of a nuclear reactor or a fissile material arrangement .

An arrangement is critical if as many free neutrons are generated per unit of time as disappear through absorption and leakage (ie loss to the outside). The critical state is the normal operating state of a nuclear reactor in which a self-sustaining chain reaction takes place. The neutron flux and thus the power generated , i.e. the thermal energy released per unit of time, can be higher or lower; Criticality only means that these quantities remain the same over time.

Neutron balance

The neutron balance is numerically expressed by the multiplication factor k . This is the number of neutrons in the next "generation" per neutron of the current generation, or the number of new fission per split nucleus. In practice, instead of k , the reactivity ρ = ( k - 1) / k is usually considered.

  • If the neutron loss predominates in the neutron balance ( k <1), it is a subcritical arrangement .
  • A critical arrangement is achieved with a balanced neutron balance ( k = 1).
  • If the neutron production is greater than the neutron loss ( k > 1), one speaks of a supercritical arrangement .

About 99% of the neutrons generated during nuclear fission are emitted within 10 femtoseconds after the fission ( prompt neutrons ), the rest only after a few milliseconds to minutes. These delayed neutrons contribute a portion β to the multiplication factor k , which depends on the fissile material. At 235 U it is about 0.75%, at 233 U and at 239 Pu about 2.5 to three times less.

Delayed critical

The constant power critical condition described above, k = 1, applies to all neutrons including the delayed ones. It can therefore be described more precisely as delayed critical .

Delayed overly critical

An arrangement with 1 < k <1 + β is delayed supercritical , i.e. H. the reactor output increases, but only through the effect of the delayed neutrons and therefore with their time constant (in the seconds range), so that the reactor can be controlled by technical means. This area is used to "start up" the reactor and increase the power level up to the rated power.

Promptly critical

With k = 1 + β, the prompt neutrons alone are sufficient to maintain the chain reaction. The state is uncertain, since the smallest random increase in k promptly makes the arrangement supercritical. Since such random small fluctuations always occur, the prompt criticality is the limit which a reactor “passes” when it is reached.

Promptly overly critical

An arrangement with k > 1 + β is promptly supercritical ; H. the neutron flux and thus the power increases exponentially due to the prompt neutrons alone . The corresponding time constant is determined by the mean life of the free neutrons, which z. B. in a moderated reactor is about 1.4 milliseconds. This extremely rapid increase leads to a very far-reaching performance excursion for almost every type of reactor , because it can no longer be influenced quickly enough with external technical means. The consequence is a more or less explosive self-destruction of the arrangement with severe effects on the environment. In most reactors, prompt overcriticality must therefore be avoided at all costs, cf. Bethe Tait Incident .

The only exception are certain research reactors in which “pulses” of prompt supercriticality ( prompt bursts ) are generated and used. This requires a negative temperature coefficient of the reactivity, which causes the reactivity to drop rapidly as the temperature rises, so that such a reactor becomes subcritical again sufficiently quickly. One example is the TRIGA research reactor .

Nuclear weapons are very brief but promptly overcritical between the ignition of a conventional explosive charge and a nuclear explosion.


The difference β in criticality between delayed critical and prompt critical is referred to in English-language literature as 1 dollar , divided into 100 cents . Louis Slotin is said to have suggested the name "dollar" .

For example, the reactivity values of control rods are conveniently given in cents. The reactivity values ​​are approximately additive, i.e. H. the retraction of two absorber rods of z. B. every 5 cents causes a reactivity of −10 cents.

Criticality incident

In the case of reactors, an unintentional or carelessly induced positive reactivity supply from critical normal operation - i.e. delayed or even prompt overcriticality - is referred to as a reactivity incident. The SL-1 accident at Idaho National Laboratory in 1961 and the Chernobyl disaster in 1986 were reactivity accidents that destroyed the reactor.

For other nuclear facilities are far below critical in normal operation arrangements (eg. As reprocessing facilities or fuel fabrication plants ), the term reactivity little used. The incident caused by (over) criticality is called criticality incident , such as the 1999 Tōkaimura nuclear accident , in which two technicians from a fuel assembly plant were fatally irradiated. Early fatal accidents of a similar kind occurred e.g. B. 1945 ( Harry Daghlian ) and 1946 ( Louis Slotin ) at the Demon Core test facility in the Los Alamos Laboratory .


  • Thomas P. McLaughlin, Shean P. Monahan, Norman L. Pruvost, Vladimir V. Frolov, Boris G. Ryazanov, Victor I. Sviridov: A Review of Criticality Accidents . 2000 revision. Los Alamos Reports, No. 13638 . Los Alamos National Laboratory, May 2000 (English, [PDF; 3.9 MB ; accessed on January 18, 2019]): “This revision of A Review of Criticality Accidents represents a significant expansion of the prior edition with the inclusion of one Japanese and 19 Russian accidents. In the first two parts of this report, 60 criticality accidents are described. [..] Excursions associated with large power reactors are not included in this report. "

Individual evidence

  1. ^ EB Paul: Nuclear and Particle Physics . North-Holland, 1969, p. 253
  2. ^ Hugh C. Paxton: Glossary of Nuclear Criticality Terms. In: LA-11627-MS. Los Alamos National Laboratory, 1989, accessed January 17, 2019 .
  3. ^ Alvin M. Weinberg, Eugene P. Wigner: The Physical Theory of Neutron Chain Reactors . University of Chicago Press, Chicago 1958, ISBN 978-0-226-88517-9 , pp. 595 .
  4. ^ Joint Committee on Atomic Energy: SL-1 Accident, Investigation Board Report. Congress of the United States, June 1961, accessed January 17, 2019 .

See also

Web links

  • [1] An introduction to the nuclear chain reaction.