Nuclear chain reaction
In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series or "positive feedback loop" of these reactions. The specific nuclear reaction may be the fission of heavy isotopes (e.g., uranium-235, 235U). A nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.
History[edit]
Chemical chain reactions were first proposed by German chemist Max Bodenstein in 1913, and were reasonably well understood before nuclear chain reactions were proposed.[1] It was understood that chemical chain reactions were responsible for exponentially increasing rates in reactions, such as produced in chemical explosions.
The concept of a nuclear chain reaction was reportedly first hypothesized by Hungarian scientist Leó Szilárd on September 12, 1933.[2] Szilárd that morning had been reading in a London paper of an experiment in which protons from an accelerator had been used to split lithium-7 into alpha particles, and the fact that much greater amounts of energy were produced by the reaction than the proton supplied. Ernest Rutherford commented in the article that inefficiencies in the process precluded use of it for power generation. However, the neutron had been discovered by James Chadwick in 1932, shortly before, as the product of a nuclear reaction. Szilárd, who had been trained as an engineer and physicist, put the two nuclear experimental results together in his mind and realized that if a nuclear reaction produced neutrons, which then caused further similar nuclear reactions, the process might be a self-perpetuating nuclear chain reaction, spontaneously producing new isotopes and power without the need for protons or an accelerator. Szilárd, however, did not propose fission as the mechanism for his chain reaction since the fission reaction was not yet discovered, or even suspected. Instead, Szilárd proposed using mixtures of lighter known isotopes which produced neutrons in copious amounts. He filed a patent for his idea of a simple nuclear reactor the following year.[3]
In 1936, Szilárd attempted to create a chain reaction using beryllium and indium but was unsuccessful. Nuclear fission was discovered by Otto Hahn and Fritz Strassmann in December 1938[4] and explained theoretically in January 1939 by Lise Meitner and her nephew Otto Robert Frisch.[5] In their second publication on nuclear fission in February 1939, Hahn and Strassmann used the term uranspaltung (uranium fission) for the first time and predicted the existence and liberation of additional neutrons during the fission process, opening up the possibility of a nuclear chain reaction.[6]
A few months later, Frédéric Joliot-Curie, H. Von Halban and L. Kowarski in Paris[7] searched for, and discovered, neutron multiplication in uranium, proving that a nuclear chain reaction by this mechanism was indeed possible. On May 4, 1939, Joliot-Curie, Halban, and Kowarski filed three patents. The first two described power production from a nuclear chain reaction, the last one called Perfectionnement aux charges explosives was the first patent for the atomic bomb and is filed as patent No. 445686 by the Caisse nationale de Recherche Scientifique.[8] In parallel, Szilárd and Enrico Fermi in New York made the same analysis.[9] This discovery prompted the letter from Szilárd and signed by Albert Einstein to President Franklin D. Roosevelt, warning of the possibility that Nazi Germany might be attempting to build an atomic bomb.[10]
On December 2, 1942, a team led by Fermi (and including Szilárd) produced the first artificial self-sustaining nuclear chain reaction with the Chicago Pile-1 experimental reactor in a racquets court below the bleachers of Stagg Field at the University of Chicago. Fermi's experiments at the University of Chicago were part of Arthur H. Compton's Metallurgical Laboratory of the Manhattan Project; the lab was renamed Argonne National Laboratory and tasked with conducting research in harnessing fission for nuclear energy.[11]
In 1956, Paul Kuroda of the University of Arkansas postulated that a natural fission reactor may have once existed. Since nuclear chain reactions may only require natural materials (such as water and uranium, if the uranium has sufficient amounts of 235U), it was possible to have these chain reactions occur in the distant past when uranium-235 concentrations were higher than today, and where there was the right combination of materials within the Earth's crust. Uranium-235 made up a larger share of uranium on Earth in the geological past because of the different half-lives of the isotopes 235
U and 238
U, the former decaying almost an order of magnitude faster than the latter. Kuroda's prediction was verified with the discovery of evidence of natural self-sustaining nuclear chain reactions in the past at Oklo in Gabon in September 1972.[12] To sustain a nuclear fission chain reaction at present isotope ratios in natural uranium on Earth would require the presence of a neutron moderator like heavy water or high purity carbon (e.g. graphite) in the absence of neutron poisons, which is even more unlikely to arise by natural geological processes than the conditions at Oklo some two billion years ago.
Timescales[edit]
Prompt neutron lifetime[edit]
The prompt neutron lifetime, , is the average time between the emission of neutrons and either their absorption in the system or their escape from the system.[17] 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 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 (slow-neutron) 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.[16] These extremely short lifetimes mean that in 1 second, 10,000 to 10,000,000 neutron lifetimes can pass. The average (also referred to as the adjoint unweighted) prompt neutron lifetime takes into account all prompt neutrons regardless of their importance in the reactor core; the effective prompt neutron lifetime (referred to as the adjoint weighted over space, energy, and angle) refers to a neutron with average importance.[18]
Mean generation time[edit]
The mean generation time, Λ, is the average time from a neutron emission to a capture that results in fission.[16] 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: