A
nuclear chain reaction occurs when on average more than one
nuclear reaction is caused by another nuclear reaction, thus leading to an
exponential increase in the number of nuclear reactions.
An uncontrolled chain reaction within a sufficiently large amount of fission fuel (
critical mass) can lead to an explosive energy release and is the concept behind nuclear weapons. The chain reaction could also be adequately controlled and used as an
energy source (
nuclear reactor).
The only known natural self-sustaining nuclear chain reaction was at
Oklo.
The first artificial self-sustaining nuclear chain reaction was initiated by the
Metallurgical Laboratory, led by
Enrico Fermi, in a
racquets court below the bleachers of
Stagg Field at the
University of Chicago on
December 2, 1942 during the
Manhattan Project.
The
effective neutron multiplication factor k is the average number of neutrons from a nuclear fission reaction that cause another fission reaction, as opposed to neutrons produced by the fission which are being absorbed without causing a new fission, and those travelling out of the system.
We can distinguish the following cases:
- k<1 (sub-critical mass): starting with one fission, we have on average a total of 1/(1-''k'') fissions.
- k=1 (critical mass): starting with one fission, we have on average one fission per unit time; this unit of time is the time it takes for the neutron to hit another nucleus; the distance is something like the diameter of a critical mass; e.g. the speed may be 10 000 km/s and the distance 10 cm, then the time is 10 ns.
- k>1 (super-critical mass): starting with one fission, we have on average in every generation of the chain reaction, say again once every 10 ns, a multiplication of the number of fissions by a factor a. This cannot continue, of course: k decreases when the amount of fission material that is left decreases, or when the remaining fission material is torn apart. In a nuclear weapon this may e.g. happen after 80 generations of 10 ns, is 800 ns, when there have been fissions.
When
k is close to 1, this calculation somewhat over-estimates the
doubling rate. When a uranium nucleus absorbs a neutron it enters a very-short-lived excited state which then decays by several possible routes. Typically it decays into two fragments,
fission products, typically isotopes of Iodine and Caesium, with expulsion of a number of neutrons. The fission products are themselves unstable, with a wide range of lifetimes, but typically several seconds, and decay producing further neutrons.
It is usual to split the population of neutrons which are emitted into two sorts -
prompt neutrons and
delayed neutrons Typically, the
delayed neutron fraction is less than 1 percent of the whole.
In a nuclear reactor the variable
k is typically around 1 to have a steady process. When a value of
k=1 is achieved when
all neutrons produced are considered the reaction is said to be
critical. This is the situation achieved in a nuclear reactor. The power changes are then slow, and controllable e.g. with
control rods. When
k = 1 is achieved counting only the
prompt neutrons, the reaction is said to be
prompt critical - much shorter doubling rates can then occur, depending on the excess criticality (''k''-1). The change in reactivity needed to go from critical to prompt critical (ie the delayed neutron fraction) is defined as a
dollar.
The value of
k is increased by a neutron reflector surrounding the fissile material, and also by increasing the density of the fissile material: the probablity for a neutron per cm travelled to hit a nucleus is proportional to the density, while the distance travelled before leaving the system is only reduced by the cubic root of the density. In the implosion method for nuclear weapons, detonation takes place by increasing the density with a conventional explosive.
See also
he:תגובת שרשרת גרעינית
es:reacción nuclear en cadena
zh:核連鎖反應
Chain reaction, nuclear