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Appendix C Nuclear Criticality DEFINITIONS Nuclear criticality refers to the precise state of an assembly of fissionable material in which one neutron from each fission event causes one subsequent fission. If less than one additional fission results, the assembly is subcritical, while if more than one new fission is caused by each fission the assembly is super- critical. On Me average, about 2.5 neutrons are produced by the fission of a uranium-235 nucleus, and about 3 neutrons come mom the fission of a plutonium- 239 nucleus. Not all neutrons produced in a fission event interact with other nuclei, however. Almost all the neurons appear immediately in the fission process (prompt neutrons), but a few, something less than 1 percent, do not. The latter are called delayed neutrons; the delay in them appearance can range from less than a second to almost a minute. The tenn critical in this context means that the assembly uses all neutrons, including those delayed, to maintain criticality. The delayed Freon, under this condition, pennits convenient control because small changes in the reactivity of a system are manifest with times characteristic of the delay periods. If, however, only the prompt neutrons are necessary for criticality, the system does not have this controllability. Such a system is said to have achieved "prompt criticality," and the power output will rise very rapidly. AN ILLUSTRATION Let us start our illustration with a bare sphere of highly enriched uranium of mass 25 kg. At a density of 18 kg/1, such a sphere would have a radius of 6.92 cm. 113

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114 APPENDIX C Were 100 neutrons to be distributed in our sphere, 65 would leave it without interacting with any uranium nucleus. The remaining 35 participate in nuclear reactions, with three being captured and producing only a gamma ray photon to carry off excess energy (radiative capture). The other 32 neutrons cause fissions, and with 2.5 neutrons per fission, the second generation consists of 80 neutrons to replace our original 100. These 80 in turn will produce another 64, and these 51.2, then 41, and so on. The reproduction factoror in the terminology of nuclear engineering, the multiplication factoris 0.~. If we sum the series 100, 80, 64, 51, 41, . . ., the total is 100/~1 - 0.8), or 500. The total number of neutrons produced by fission for each original neutron is referred to as the neutron multiplication; in this illustration the multiplication is 5. In this assembly of the fissile material, the fission neutrons, which are born with a velocity near the speed of light, traverse the assembly in less than 1~9 s (one billionth of a second), and this is approximately the time for one generation. Thus the neutron chain will die out very rapidly. If we now add 12 kg of the same material to our uranium sphere, for a total of 37 kg, the radius will increase by 0.97 cm. The neutron leakage will be reduced by this shell, and now only 60 of 100 neutrons will escape interaction. Four of the remaining 40 will undergo radiative capture, and 36 will result in fission. The 36 fissions will produce a neutron chain of first 90 neutrons, then 81, 73, 66, 59, which sums to 900. The multiplication factor is 0.9. and the multiplication is 10. One more shell of about the same thickness will increase our assembly mass to 50 kg, with radius 8.72 cm. The probability of neutron leakage is now 55 percent, and 45 neutrons will be involved in nuclear reactions, 5 of which will be radiative capture. The 40 fissions will produce 100 fission neutrons, and these will generate another 100, and so on. The multiplication factor is now unity, the assembly is critical, and the multiplication is infinite. An additional shell with a thickness of about 0.02 cm would change our sphere from delayed criticality to prompt criticality. In this illustration we have taken some liberties with precise values in the interest of simplification, but the numbers and results are approximately correct FACTORS AFFECTING CRITICALITY Density The quantity of fissionable material required for criticality (the critical mass) is strongly dependent on the material density. As the density of a system is reduced, leakage of neurons is facilitated, and more material is required for criticality. For an unreflected system, the critical mass varies inversely with the square of the density. A two-fold reduction in density results in a four-fold increase in critical mass. Delta-phase plutonium has a density about 8/10 that of alpha-phase

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APPENDIX C 115 plutonium, so its bare critical mass is more than 50 percent larger. This effect is very important for handling oxides and over low density compounds, and for storage arrays where the low average density of material permits the safe accumulation of hundreds or thousands of kilograms of material. Increases in material density are not a concern in ordinary situations, but they play a significant role in the design of nuclear weapons. Moderation When fissionable material is in solution, or present as finely divided particles, the presence of a "neutron moderator," such as water or a hydrocarbon, can effect a significant reduction in Me amount of Missile material required for criticality. The interaction of neutrons with light nuclei, such as hydrogen, lithium, beryllium, or carbon, reduces the neutron energy after only a few collisions. Slow neutrons interact much more readily with nuclei, and in particular they have a far greater probability of causing fission in uranium-235 or plutonium-239 nuclei. There exists an optimum degree of moderation because if the ratio of hydrogen nuclei to uranium nuclei becomes too large, neutron capture in the hydrogen becomes competitive with fission in the uranium. Reflection Fissile material can also be surrounded by other materials that reflect neutrons back into the fissile volume, increasing their opportunity for nuclear interaction. Water, for example, is an effective neutron reflector. While the critical mass for a bare sphere of highly enriched uranium is about 50 kg, and for plutonium-239 about 11 kg, reflection by water reduces Me mass required by about half. Six inches of water constitutes an effectively infinite reflector. Some other materials are even more effective reflectors, but for purposes of criticality safety, water reflection is commonly assumed to be appropriate because it is not to be expected that close-fitting reflection by other materials will occur inadvertently. The critical mass of uranium-235 at optimum moderation is about 800 g for a reflected sphere, and for plutonium-239 the corresponding value is about 500 g. Geometrical Shape The shape of an assembly of Missile material is also a significant parameter in considering the potential for criticality. As the shape of a quantity of material is changed from a sphere to a slender cylinder, leakage of neutrons without interaction is facilitated. For material of any specified composition there exists a cylinder diameter below which criticality cannot be achieved. As an example, for highly enriched uranium nitrate at any achievable concentration, criticality cannot be achieved in a water-reflected stainless steel or boro-silicate glass cylinder of 6 in.

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116 APPENDIX C diameter. Process vessels enjoying such characteristics are often referred to as "favorable geometry" vessels. Most criticality safety people avoid the tenn "safe geometry" because some other fissile material filling the 6 in. cylinder could constitute a critical mass. The favorable geometry vessel may be favorable for only the one material for which it is intended. Also, it is thought that use of the term '~safe" might foster a false sense of security. Neutron Absorbers Some materials, cadmium and boron in particular, are effective neutron absorbers. Such neutron absorbers may be used to provide criticality control in vessels of large volume or in locations where many vessels are in close proximity and there is concern about neutron interaction occurring between vessels. ASSESSING CRITICALITY SAFETY Knowledge of the many conditions under which criticality can occur is fundamental to effective and economical safety in the processing of fissionable material. A substantial body of data on criticality has been accumulated over the past 45 years, much of it obtained in the critical experiment facilities. The facility at Oak Ridge generally specialized in experiments involving uranium solutions; most experiments with plutonium solutions were conducted at the Hanford facility, and Los Alamos provided much of the data on unmoderated, or fast, systems. Both the Oak Ridge and Hanford facilities for studying criticality are now closed. The only other similar facility for criticality studies in the United States is at Rocky Flats, and its use is dedicated to that facility. The French have a fine critical experiments laboratory at Valduc, with which some limited cooperation has been possible. Computational techniques are also used to assess criticality safety. The capabilities of the large computers are extremely helpful, particularly for interpolation and limited extrapolation of experimental data. It is, however, difficult to develop confidence in calculations that are not tested against experimental data. While such data are available for the materials that are being used in nuclear systems today, more experiments will be required as future progress involves additional materials. Alternatively, large and frequently uneconomic safety margins must be applied. Effective and efficient criticality control practices are generally recognized to depend on close cooperation between the criticality safety specialist and the process designer and process engineer. The process supervisor usually has the best feeling for the sort of upset conditions that may occur, and the process designer can provide guidance regarding equipment reliability. The criticality safety specialist, who should be skilled at interpreting critical data and evaluatin calculations, is responsible for evaluating the degree of criticality associated with

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APPENDIX C 117 conditions that may arise. The objective is to assure that the entire process will maintain an acceptable margin of safety under normal and all credible abnormal ~ cone 1tlons. CRITICALITY ACCIDENTS IN MATERIALS PROCESSING Unplanned nuclear criticality events have occurred in the past, sometimes with fatal consequences. In process areas, such events have typically produced radiation that is potentially lethal within a distance of about 10 m. None of the eight process accidents that have been reported resulted in an explosive release of energy. All occurred in solutions of fissionable material. Thus nuclear criticality accidents in He weapons complex have historically had consequences comparable to industrial accidents. Since the mid-1960s criticality accidents have occurred at a frequency lower than those characteristic of industrial threats. The history of criticality accidents is illuminating. The first process accident occurred at the Oak Ridge Y-12 Plant in 1958. Between that time and the middle of 1964 there were five more, or a total of six in about 6 years. These incidents stimulated increased awareness of criticality safety and brought criticality safety organizations into existence at all major processing facilities. In the following 27 years there have been two more such accidents. The improved record must be attributed at least in part to the effectiveness of the safety organizations, staffed largely with people trained at the critical experiment facilities. All eight process accidents occurred with materials in solutions: three involved plutonium solutions and five involved uranium solutions. Many were associated with off-normal process activities. Three occurs behind heavy shielding and resulted in only modest radiation exposures, but five were basically unshielded and caused two fatalities and numerous significant exposures. None of these occurrences caused ladiadon exposures off-site or significant damage to equipment. Four of the process accidents were terminated in less Man a few seconds, whereas the other four persisted for many minutes or hours. For all eight, the energy release associated with the first few seconds was about 1 kWh. One persistent reaction had a total energy output of about 100 times this value, but the rate of energy release was moderate. Future accidents may be expected to have similar characteristics because of features inherent to any critical system. The difficulties associated with obtaining a large energy release from an accumulation of fissionable material are demonstrated by the sophistication required of Be weapon designer.