A
nuclear chain reaction occurs when one
nuclear reaction causes an average of one
or more nuclear reactions, thus leading to a selfpropagating
number of these reactions. The specific nuclear reaction may be the
fission of heavy isotopes (e.g.
^{235}U) or the fusion of
light isotopes (e.g.
^{2}H and
^{3}H). The nuclear
chain reaction is unique since it releases several million times
more energy per reaction than any
chemical reaction.
History
The
concept of a nuclear chain reaction was first realized by Hungarian scientist Leó
Szilárd in 1933. He filed a patent for his idea of a
simple nuclear reactor the following year.
The total quantitative chain chemical reactions theory was created
by Soviet physicist N.N.Semyonov in 1934. The idea of the
chain reactions, developed by Semyonov, is
the basis of various high technologies using the incineration of
gas mixtures. The idea was also used for the description of the
nuclear reaction..
In 1936, Szilárd attempted to create a chain reaction using
beryllium and
indium, but was unsuccessful. In 1939, Szilárd and
Enrico Fermi discovered neutron
multiplication in uranium, proving that a chain reaction was indeed
possible. This discovery prompted
the letter from
Albert Einstein to President
Franklin D. Roosevelt warning of the possibility
that
Nazi Germany might be attempting
to build an atomic bomb.
Enrico
Fermi created the first artificial selfsustaining nuclear chain
reaction, called Chicago
Pile1 (CP1), in a racquets court below the bleachers of
Stagg
Field at the University of Chicago on December 2, 1942. Fermi's experiments at
the University of Chicago were part of
Arthur H. Compton's
Metallurgical Laboratory facility,
which was part of the
Manhattan
Project.
In 1956,
Paul Kuroda of the University of Arkansas postulated that a natural fission reactor may have
once existed. Since nuclear chain reactions only require
natural materials (such as water and uranium), it is possible to
have these chain reactions occur where there is the right
combination of materials within the Earth's crust.
Kuroda's prediction
was verified with the discovery of evidence of natural
selfsustaining nuclear chain reactions in the past at Oklo in Gabon,
Africa in September 1972.
Fission chain reaction
Fission chain reactions occur because of interactions between
neutrons and
fissile
isotopes (such as
^{235}U). The chain reaction requires
both the release of neutrons from fissile isotopes undergoing
nuclear fission and the subsequent
absorption of some of these neutrons in fissile isotopes. When an
atom undergoes nuclear fission, a few neutrons (the exact number
depends on several factors) are ejected from the reaction. These
free neutrons will then interact with the surrounding medium, and
if more fissile fuel is present, some may be absorbed and cause
more fissions. Thus, the cycle repeats to give a reaction that is
selfsustaining.
Nuclear power plants operate by
precisely controlling the rate at which nuclear reactions occur,
and that control is maintained through the use of several redundant
layers of safety measures. Moreover, the materials in a nuclear
reactor core and the uranium enrichment level make a nuclear
explosion impossible, even if all safety measures failed. On the
other hand,
nuclear weapons are
specifically engineered to produce a reaction that is so fast and
intense it cannot be controlled after it has started. When properly
designed, this uncontrolled reaction can lead to an explosive
energy release.
Nuclear fission fuel
Nuclear fission weapons must use an extremely high quality,
highlyenriched fuel exceeding the critical size and geometry
(
critical mass) in order to
obtain an explosive chain reaction. The fuel for a nuclear fission
reactor is very different, usually consisting of a lowenriched
oxide material (e.g. UO
_{2}). It is impossible for a
nuclear power plant to undergo an explosive nuclear chain reaction.
Chernobyl was a steam explosion, not a nuclear
explosion. Furthermore, all power plants licensed in the
United States require a negative
void
coefficient of reactivity, which completely eliminates the
possibility of the accident that occurred at Chernobyl (which was
due to a positive void coefficient).
Fission reaction products
When a heavy atom undergoes nuclear fission it breaks into two or
more fission fragments. Also, several free neutrons,
gamma rays, and
neutrinos are emitted, and a large amount of
energy is released. The sum of the rest masses of the fission
fragments and ejected neutrons is less than the sum of the rest
masses of the original atom and incident neutron (of course the
fission fragments are not at rest). The mass difference is
accounted for in the release of energy according to the equation
E=Δmc²:
mass of released energy = \frac{E}{c^2} =
m_\mbox{original}m_\mbox{final}
Due to the extremely large value of the
speed of light, c, a small decrease in mass
is associated with a tremendous release of active energy (for
example, the kinetic energy of the fission fragments). This energy
(in the form of radiation and heat)
carries the
missing mass, when it leaves the reaction system (total mass, like
total energy, is always
conserved). While typical chemical
reactions release energies on the order of a few
eV (e.g. the binding energy of the electron to
hydrogen is 13.6 eV), nuclear fission reactions typically
release energies on the order of hundreds of millions of eVs.
Two typical fission reactions are shown below with average values
of energy released and number of neutrons ejected:
 {}^{235}U + \mbox{neutron} \rightarrow \mbox{fission fragments}
+ 2.4\mbox{ neutrons} + 192.9\mbox{ MeV}
 {}^{239}Pu + \mbox{neutron} \rightarrow \mbox{fission
fragments} + 2.9\mbox{ neutrons} + 198.5\mbox{ MeV}
Note that these equations are for fissions caused by slowmoving
(thermal) neutrons. The average energy released and number of
neutrons ejected is a function of the incident neutron speed. Also,
note that these equations exclude energy from neutrinos since these
subatomic particles are extremely nonreactive and, therefore,
rarely deposit their energy in the system.
Timescales of nuclear chain reactions
Prompt neutron lifetime
The
prompt neutron lifetime,
l, is the
average time between the emission of neutrons and either their
absorption in the system or their escape from the system. The term
lifetime is used because the emission of a neutron is often
considered its "birth," and the subsequent absorption is considered
its "death." For thermal (slowneutron) fission reactors, the
typical prompt neutron lifetime is on the order of 10
^{−4}
seconds, and for fast fission reactors, the prompt neutron lifetime
is on the order of 10
^{−7} seconds. These extremely short
lifetimes mean that in 1 second, 10,000 to 10,000,000 neutron
lifetimes can pass.
Mean generation time
The
mean generation time, Λ, is the average time
from a neutron emission to a capture that results in fission. The
mean generation time is different from the prompt neutron lifetime
because the mean generation time only includes neutron absorptions
that lead to fission reactions (not other absorption reactions).
The two times are related by the following formula:
 \Lambda = \frac{l}{k}
In this formula, k is the effective neutron multiplication factor,
described below.
Effective neutron multiplication factor
The
effective neutron
multiplication factor,
k, is the average
number of neutrons from one fission that cause another fission. The
remaining neutrons either are absorbed in nonfission reactions or
leave the system without being absorbed. The value of
k
determines how a nuclear chain reaction proceeds:
 k 1 (subcriticality):
The system cannot sustain a chain reaction, and any beginning of a
chain reaction dies out over time. For every fission that is
induced in the system, an average total of
1/(1 − k) fissions occur.
 k = 1 (criticality): Every
fission causes an average of one more fission, leading to a fission
(and power) level that is constant. Nuclear power plants operate
with k = 1 unless the power level is being increased or
decreased.
 k > 1 (supercriticality): For every fission in the
material, it is likely that there will be "k" fissions
after the next mean generation time. The result is that
the number of fission reactions increases exponentially, according
to the equation e^{(k1)t/\Lambda}, where t is the elapsed time.
Nuclear weapons are designed to operate under this state. There are
two subdivisions of supercriticality: prompt and delayed.
When describing kinetics and dynamics of nuclear reactors and also
in the practice of reactor operation is used the concept of
Reactivity , which
characterizes the deflection of reactor from the critical state.
ρ=(k1)/k.
In a nuclear reactor,
k will actually oscillate from
slightly less than 1 to slightly more than 1, due primarily to
thermal effects (as more power is produced, the fuel rods warm and
thus expand, lowering their capture ratio, and thus driving
k lower). This leaves the average value of
k at
exactly 1. Delayed neutrons play an important role in the timing of
these oscillations.
In an infinite medium, the multiplication factor may be described
by the
four factor
formula.
Prompt and delayed supercriticality
Not all neutrons are emitted as a direct product of fission, some
are instead due to the
radioactive
decay of some of the fission fragments. The neutrons that occur
directly from fission are called "
prompt
neutrons," and the ones that are a result of radioactive decay
of fission fragments are called "delayed neutrons." The fraction of
neutrons that are delayed is called β, and this fraction is
typically less than 1% of all the neutrons in the chain
reaction.
The delayed neutrons allow a nuclear reactor to respond several
orders of magnitude more slowly than just prompt neutrons would
alone. Without delayed neutrons, changes in reaction rates in
nuclear reactors would occur at speeds that are too fast for humans
to control.
The region of supercriticality between k = 1 and k = 1/(1β) is
known as
delayed supercriticality (or
delayed criticality). It is in this
region that all nuclear power reactors operate. The region of
supercriticality for k > 1/(1β) is known as
prompt
supercriticality (or
prompt
criticality), which is the region in which nuclear weapons
operate.
The change in k needed to go from critical to prompt critical is
defined as a
dollar
Neutron multiplication in nuclear weapons
Nuclear fission weapons require a mass of fissile fuel that is
prompt supercritical.
For a given mass of fissile material the value of k can be
increased by increasing the density. Since the probability per
distance traveled for a neutron to collide with a nucleus is
proportional to the material density, increasing the density of a
fissile material can increase k. This concept is utilized in the
implosion
method for nuclear weapons. In these devices, the nuclear chain
reaction begins after increasing the density of the fissile
material with a conventional explosive.
In the
guntype fission
weapon two subcritical pieces of fuel are rapidly brought
together. The value of k for a combination of two masses is always
greater than that of its components. The magnitude of the
difference depends on distance, as well as the physical
orientation.
The value of k can also be increased by using a
neutron reflector surrounding the fissile
material
Once the mass of fuel is prompt supercritical, the power increases
exponentially. However, the exponential power increase cannot
continue for long since k decreases when the amount of fission
material that is left decreases (i.e. it is consumed by fissions).
Also, the geometry and density are expected to change during
detonation since the remaining fission material is torn apart from
the explosion.
Predetonation
Detonation of a nuclear weapon involves bringing fissile material
into its optimal supercritical state very rapidly. During part of
this process, the assembly is supercritical, but not yet in an
optimal state for a chain reaction. Free neutrons, in particular
from
spontaneous fissions, can
cause the device to undergo a preliminary chain reaction that
destroys the fissile material before it is ready to produce a large
explosion, which is known as
predetonation. To
keep the probability of predetonation low, the duration of the
nonoptimal assembly period is minimized and fissile and other
materials are used which have low spontaneous fission rates. In
fact, the combination of materials has to be such that it is
unlikely that there is even a single spontaneous fission during the
period of supercritical assembly. In particular, the gun method
cannot be used with plutonium (see
nuclear weapon design).
Fusion chain reaction
In a more generalized sense, a
nuclear
fusion reaction can be considered a nuclear chain reaction: it
occurs under extreme pressure and temperature conditions, which are
maintained by the energy released in the fusion process.
See also
References
 L. Szilárd, "Improvements in or relating to the transmutation
of chemical elements," British patent number: GB630726 (filed: 28
June 1934; published: 30 March 1936). esp@cenet document view

http://www.markaart.ru/catalogs/StampSeries.jsp?&id=29264&lang=en
 H. L. Anderson, E. Fermi, and Leo
Szilárd, "Neutron production and absorption in uranium," The
Physical Review, vol. 56, pages 284–286 (1 August 1939).
Available online at:
http://www.fdrlibrary.marist.edu/psf/box5/a64g01.html .
 http://www.aip.org/history/einstein/ae43a.htm,
http://www.atomicarchive.com/Docs/Begin/Einstein.shtml
 Oklo: Natural Nuclear Reactors—Fact Sheet
 http://www.sizes.com/units/dollar.htm
External links