Chain reactors

Stanley G. Thompson joined my group on October 1, 1942 and it fell to his lot to discover the process that was chosen for use at Clinton Laboratories (in Tennessee) and the Hanford Engineer Works (in the state of Washington) for the separation of plutonium from uranium and the immense intensity of radioactive fission products with which it was produced in the nuclear chain reactors. Again I turn to my journal to tell the story ... 

Breeder reactor A nuclear chain reactor in which transmutation produces a greater number of fissionable atoms than the number of consumed parent atoms. 

Radioisotopes that decay by spontaneous fission with the direct accompanying release of neutrons are usually associated with the natural elements of uranium and thorium and the manmade element plutonium. However, the rate of decay of these elements by fission is so slow that it is only by incorporating them into large nuclear piles or chain reactors that they can be utilized as intense neutron sources. In the US Dept of Energy National Transplutonium Program, small quantities of elements heavier than plutonium are produced for basic research studies and to discover new elements with useful properties. One of these new elements, californium-252 (2S2Cf), is unique in that it emits neutrons in copious quantities over a period of years by spontaneous fission... 

Minor amounts of 4He and 3He are produced in ternary fission. Spontaneous fission of 2 i2Th has also been observed (Whetherill, 1953), as has induced fission of 23,Pu in the Oklo natural chain reactor (Drozd et al., 1974). b Except as noted, data from review/compilation by Hyde (1974). 

Stanley G, it fell to his use at Clinton neer Works (in plutonium from active fission chain reactors,... 

Fig. 13 Ploymerare chain reactor system on a chip reported by Ramsey et al. (A) Layout of chip. (B) On-chip Peltier heater/cooler for thermal cycling of PCR process. (From Ref...

The plutonium-239, of course, is made by bombarding natural uranium-238 with neutrons in a nuclear chain reactor, or pile as it is sometimes called. 

W3. Weinberg, A. M., and E. P. Wigner The Physical Theory of Neutron Chain Reactors, University of Chicago Press, Chicago, 1958. 

The ability of diethyl ether to extract uranyl nitrate from aqueous solution has been known for a hundred years and was the method chosen by the Manhattan Project to purify the uranium used in the first nuclear chain reactors. This solvent has numerous disadvantages. It is very volatile, very flammable, and toxic, and it requires addition of sodium, aluminum, or calcium nitrate to the aqueous phase to enhance extractions. When solvent extraction was first applied to recovery of uranium and plutonium from irradiated fuel, other oxygenated solvents less volatile than diethyl ether that were first used were methyl isobutyl ketone, dibutyl... 

Antioxidants (or inhibitors). The action of these additives is to scavenge fi ee radicals that may be formed in the process stream (see Section 11.2.4) in order to reduce or eliminate chain reactors. Equations 11.4 to 11.6 give the mechanism of free radical propagation, i.e. 

In those earliest days, I suppose Szilard was the more deeply absorbed in the fission problem - after all, he had worked out the theory of a nuclear chain reaction even before fission had been discovered and on March 20, 1939, he applied for a U.S. patent on what he called an Apparatus for Nuclear Transmutation - i.e. a neutron chain reactor based on the fission of uranium (6). Wigner was fully aware of Szilard s thinking and with his powerful grasp of the mathematical and physical principles underlying the chain reaction, Wigner was, even then, able to make independent estimates of the critical conditions. 

Wigner and I wrote a somewhat more detailed account of reactor physics. The Physical Theory of Neutron Chain Reactors, which appeared in 1958. Copies of the book were presented to all the delegates at the 1958 Geneva Conference on the Peaceful Uses of Atomic Energy. The book summarized what we knew about the physics of chain reactors at that time. 

Therefore, the problems which faced the would-be designers of chain reactors early in 1941 were (1) the choice of the proper moderator to uranium ratio, and (2) the size and shape of the uranium lumps which would most likely lead to a self-sustaining chain reaction, i.e., give the highest multiplication factor. In order to solve these problems, one had to understand the behavior of the fast, of the resonance, and of the thermal neutrons. We were concerned with the second problem which itself consisted of two parts. The first was the measurement of the characteristics of the resonance lines of isolated uranium atoms, the second, the composite effect of this absorption on the neutron spectrum and total resulting absorption. One can liken the first task to the measurement of atomic constants, such as molecular diameter, the second one, to the task of kinetic gas theory which obtains the viscosity and other properties of the gas from the properties of the molecules. The first task was largely accomplished by Anderson and was fully available to us when we did our work. Anderson s and Fermi s work on the absorption of uranium, and on neutron absorption in general, also acquainted us with a number of technics which will be mentioned in the third and fourth of the reports of this series. Finally, Fermi, Anderson, and Zinn carried out, in collaboration with us in Princeton, one measurement of the resonance absorption. This will be discussed in the third article of this series. 

Wigner had co-authored the Physical Theory of Neutron Chain Reactors in 1958. In paper 28, which was given in April of 1959, he reports progress on several mathematical problems that he had identified while writing the book. 

This invention relates to nuclear physics and more particularly to fast neutron nuclear fission chain reactors such as those described in a copending Szilard application. rial No. 698,334. filed September 20, 1946. 

The above methods heretofore used are adequate in cases where either the absorber under measurement has a higli nuclear cross-section for neutron absorption or where large quantities of the sample under measurement are available to be inserted into the reactor for the purpose of making the measurement. The limitation on these methods, both as to accuracy and sensitivity, lies in the commonly observed fact that neutronic chain reactors, even through reasonable precautions are taken to maintain all conditions constant, undergo random changes and perturbations in both the neutron reproduction factor and instantaneous power output. In the methods previously in use as described above, such variations, which are caused by conditions other than the insertion of the absorber under measurement, such as temperature and barometric pressure for example, are indistinguishable from the variations caused by the absorber, which latter variations constitute the measure of the absorption characteristics. 

For all well-known results of reactor theory, reference is made to The physical theory of neutron chain reactors by Weinberg and Wigner [8]. 

For the reasons outlined above, I think the problem of constructing rigorous mathematical theories of criticahty, in neutron chain reactors, will supply useful and interesting problems to mathematicians, for many years to come I hope reactor physicists will regard the technical solution of such problems with due respect in recent years, the phrase by physical intuition has been too freely used as a substitute for I do not know why ... 

Alvin M. Weinberg and Eugene P. Wigner, The physical theory of neutron chain reactors, Chicago, The University of Chicago Press, 1958. 

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