Editing Prompt criticality (section)

== Critical versus prompt-critical ==
In a supercritical assembly, the number of fissions per unit time, ''N'', along with the power production, increases [[Exponential growth|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:

: <math>N(t) = N_0 k^\frac{t}{T} \,</math>

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 [[nanosecond]]s (an average time interval used by scientists in the [[Manhattan Project]] was one [[shake (unit)|shake]], or 10&nbsp;ns).  A small additional source of neutrons is the [[fission product]]s.  Some of the nuclei resulting from the fission are [[radioactive isotope]]s with short [[Half-life|half-lives]], and [[nuclear reaction]]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 (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.
[[File:Criticality Diagram.png|thumb|Diagram explaining criticality types. <math>k_{\mathrm{eff}}</math> is the [[effective neutron multiplication factor]].]]
In a [[delayed criticality|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, of 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]]s such as [[control rod]]s, and accordingly all [[nuclear reactor]]s are designed to operate in the delayed-criticality regime.

In contrast, a critical assembly is said to be prompt-critical if it is critical (''k&nbsp;=&nbsp;1'') without any contribution from [[delayed neutron]]s and prompt-supercritical if it is supercritical (the fission rate growing exponentially, ''k&nbsp;>&nbsp;1'') without any contribution from delayed neutrons.  In this case the time between successive generations of the reaction, ''T'', is limited only by the fission rate from 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]]s and some specially designed research experiments.

The difference between a prompt neutron and a delayed neutron 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 that have been imparted to them. A nuclear weapon relies heavily on prompt-supercriticality (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.