The Nuclear Chain Reaction

The fact that the fission process involves the emission of secondary neutrons leads immediately to the possibility of setting up a chain-reacting system. We start by considering the problem of designing a nuclear reactor in which the fuel is natural uranium. The criterion for a successful chain reaction is the following starting with a certain number of fission events taking place per unit time, it is necessary that the fraction of the secondary neutrons produced in fission which survive to cause further fissions should be sufficient to maintain the fission rate in the system at a constant level. 

This condition may be described quantitatively by introducing a parameter known as the neutron multiplication factor, k. Consider a reactor in which at some instant a large number of fission events occur simultaneously. These events give rise to a number, Nq, of fission neutrons (which are all assumed to be prompt neutrons for the purposes of the present argument). Some of these secondary neutrons will be lost to the chain reaction by various processes which will be considered in detail later, and a certain fraction will survive to cause further fissions. Let the number of secondary neutrons produced as a result of these fissions be N. The neutron multiplication factor, k, may be defined by the relation 

In order to study the neutron balance in a reactor, we have to consider the processes which compete with fission absorption by for the available neutrons. These processes include (i) leakage of neutrons out of the reactor volume (ii) capture by elements other than uranium, e.g., structural materials, moderator, coolant, and fission products (iii) capture by to form leading to production of Pu (iv) nonfission capture by leading to the formation of 

The magnitude of the leakage will obviously depend on the size of the reactor. It is because of leakage that even an assembly of pure will not attain a multiplication factor of unity until a certain mass of the material, known as the critical mass, is present. The calculation of the leakage from a reactor of given size and shape will be dealt with in Chapter 3. For the present we shall separate out the effect of leakage by writing the multiplication factor in the form 

Below about 100 keV, the inelastic scattering cross section of drops 

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The nuclear chain reaction can be modeled mathematically by considering the probable fates of a typical fast neutron released in the system. This neutron may make one or more coUisions, which result in scattering or absorption, either in fuel or nonfuel materials. If the neutron is absorbed in fuel and fission occurs, new neutrons are produced. A neutron may also escape from the core in free flight, a process called leakage. The state of the reactor can be defined by the multiplication factor, k, the net number of neutrons produced in one cycle. If k is exactly 1, the reactor is said to be critical if / < 1, it is subcritical if / > 1, it is supercritical. The neutron population and the reactor power depend on the difference between k and 1, ie, bk = k — K closely related quantity is the reactivity, p = bk jk. i the reactivity is negative, the number of neutrons declines with time if p = 0, the number remains constant if p is positive, there is a growth in population. 

CP-1 was assembled in an approximately spherical shape with the purest graphite in the center. About 6 tons of luanium metal fuel was used, in addition to approximately 40.5 tons of uranium oxide fuel. The lowest point of the reactor rested on the floor and the periphery was supported on a wooden structure. The whole pile was surrounded by a tent of mbberized balloon fabric so that neutron absorbing air could be evacuated. About 75 layers of 10.48-cm (4.125-in.) graphite bricks would have been required to complete the 790-cm diameter sphere. However, criticality was achieved at layer 56 without the need to evacuate the air, and assembly was discontinued at layer 57. The core then had an ellipsoidal cross section, with a polar radius of 209 cm and an equatorial radius of309 cm [20]. CP-1 was operated at low power (0.5 W) for several days. Fortuitously, it was found that the nuclear chain reaction could be controlled with cadmium strips which were inserted into the reactor to absorb neutrons and hence reduce the value of k to considerably less than 1. The pile was then disassembled and rebuilt at what is now the site of Argonne National Laboratory, U.S.A, with a concrete biological shield. Designated CP-2, the pile eventually reached a power level of 100 kW [22]. 

Control of the nuclear chain reaction in a reactor is maintained by the insertion of rods containing neutron absorbing materials such as boron, boron carbide, or borated steel. In state-of-the-art high temperature reactor designs, such as the Gas... 

When the Plutonium Project was established early in 1942, for the purpose of producing plutonium via the nuclear chain reaction in uranium in sufficient quantities for its use as a nuclear explosive, we were given the challenge of developing a chemical method for separating and isolating it from the uranium and fission products. We had already conceived the principle of the oxidation-reduction cycle, which became the basis for such a separations process. This principle applied to any process involving the use of a substance which carried plutonium in one of its oxidation states but not in another. By use of this... 

The nuclear plants now operating in the U.S. are light water reactors, which use water as both a moderator and coolant. These are sometimes called Generation II reactors. In these Generation II Pressurized Water Reactors, the water circulates through the core where it is heated by the nuclear chain reaction. The hot water is turned into steam at a steam generator and the steam is used by a turbine generator to produce electric power. 

In the new designs, if coolant were lost, the nuclear chain reaction would be terminated by the reactor s negative temperature coefficient after a modest temperature rise. Core diameter of the modular units would be limited so that decay heat could be conducted and radiated to the environment without overheating the fuel to the point where fission products might escape. Thus, inherent safety would be realized without operator or mechanical device intervention. 

The techniques used to produce a nuclear explosion (i.e., an essentially instantaneous, self-perpetuating nuclear chain reaction) are very complex. A nuclear explosion must utilize a high-energy neutron spectrum (fast neutrons, that is, neutrons with energies > 1 MeV). This results basically from the fact that, for an explosion to take place, the nuclear chain reaction must be very rapid—of the order of microseconds. Each generation in the chain reaction must occur within... 

For obvious reasons, an atomic bomb is never assembled with the critical mass already present. Instead, the critical mass is formed by using a conventional explosive, such as TNT, to force the fissionable sections together, as shown in Figure 23.9. Neutrons from a source at the center of the device trigger the nuclear chain reaction. Uranium-235 was the fissionable material in the bomb dropped on Hiroshima, Japan, on August 6, 1945. Plutonium-239 was used in the bomb exploded over Nagasaki three days later. The fission reactions generated were similar in these two cases, as was the extent of the destruction. 

The fact that the number of neutrons produced per neutron absorbed exceeds 1.0 for each fuel indicates that each will support a nuclear chain reaction. Neutrons in excess of the one needed to sustain the nuclear chain reaction may be used to produce new and valuable isotopes, for example, to produce Pu from or from thorium by the reactions cited earlier. 

Sachs, Robert G., ed. 1984. The Nuclear Chain Reaction—Forty Years Later. University of Chicago Press. 

The primary coolant is a substance that transports the heat generated by the nuclear chain reaction away from the reactor core. In a pressurized water reactor, which is the most common commercial reactor design, water acts as both the moderator and the primary coolant. 

In order to design a method for controlling the reaction rate of the nuclear chain reaction a knowledge of the variation with temperature of the number of neutrons absorbed at the resonances by uranium is, therefore, important. 

In addition to the above-mentioned losses which are inherently a part of the nuclear chain reaction process impurities present in both the slowing material and the uranium add a very important neutron loss factor in the rhaiti. The effectiveness of various elements as neutron absorbers varies tremendously. Certain elements such as boron, cadmium samarium gadolinium and some others, if present even in a few parts per million could prevent a self-sustaining chain reaction from taking place. 

In addition to the above-mentioned losses, which are inherently a part of the nuclear chain reaction process. 

FIG. 11 is a fragmentary view of a portion of our apparatus used to limit the nuclear chain reaction therein ... 

As indicated above, the nuclear chain reaction in the reaction tank is controlled by varying the level of the slurry therein to change the volume above or below that corresponding to critical size. As an emergency safety... 

The nuclear chain reaction within the reaction tank 1 is dependent upon the nuclear fission of the constituent of the uranous material of the slurry when sub-. . . . ... 

Slurry space 16 may be filled with a thorium-DaO slurry, for example, circulation started, and the device is ready for the start of the nuclear chain reaction. The control rod 45 Is then slowly removed from the reaction tank 10 until a point is reached where the neutron reproduction ratio in the reactor tank 10 is greater than... 

Protectipn y tpnis. j e criteria in this section ensure that mechanisms are in place to terminate the nuclear chain reaction under all normal operatinq conditions, AOEs, and DBAs. 

The process components are the reactor (R) itself, where the nuclear chain reaction takes place and the... 

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