Nuclear Power
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MORE CHAPTER 11, #6 Nuclear Power Nuclear Fission Reactors The discovery that several neutrons are emitted in the fission process led to specula- tion concerning the possibility of using these neutrons to initiate other fissions, thereby producing a chain reaction. On December 2, 1942, less than four years after Hahn and Strassmann’s discovery of fission, a group led by Enrico Fermi produced the first self-sustaining chain reaction in a nuclear reactor that they had constructed at the University of Chicago.24 To sustain a chain reaction in a fission reactor, one of the neutrons (on the average) emitted in the fission of 235U must be captured by another 235U nucleus and cause it to fission. The reproduction factor k of a reactor is defined as the average number of neutrons from each fission that cause a subsequent fission. In the case of 235U the maximum possible value of k is about 2.4, but it is normally less than this for two important reasons: (1) some of the neutrons may escape from the region contain- ing fissionable nuclei, and (2) some of the neutrons may be captured by nonfissioning nuclei in the reactor. If k is exactly 1, the reaction will be self-sustaining. If it is less than 1, the reaction will die out. If k is significantly greater than 1, the reaction rate will increase rapidly and “run away.” In the design of nuclear bombs, such a runaway reaction is necessary. In power reactors, the value of k must be kept very nearly equal to 1 (see Figure 11-50). If k is exactly equal to 1, the reactor is said to be critical; for k Ͻ 1, it is described as being subcritical and for k Ͼ 1 as supercritical. Since the neutrons emitted in fission mostly have energies of the order of 1 MeV or higher (see Figure 11-51), whereas the cross section for neutron capture leading to fission in 235U is largest at small energies as illustrated in Figure 11-52, the chain reaction can be sustained only if the neutrons are slowed down before they escape from the reactor. At high energies (1 to 2 MeV), neutrons lose energy rapidly by inelastic scattering from 238U, the principal constituent of natural uranium. (Natural uranium contains 99.28 percent 238U and only 0.72 percent fissile 235U.) Once the neu- tron energy is below the excitation energies of the nuclei in the reactor (about 1 MeV), the main process of energy loss is by elastic scattering, in which a neutron collides with a nucleus at rest and, by conservation of momentum, transfers some of its kinetic energy to the nucleus. Such energy transfers are efficient only if the masses of the two bodies are comparable. A neutron will not transfer much energy in an elastic collision with a heavy 238U nucleus. Such a collision is analogous to one between a marble and a billiard ball. The marble will be deflected by the much more massive billiard ball with essentially no change in its kinetic energy. Therefore, a moderator consisting of 75 76 More Chapter 11 FIGURE 11-50 Schematic representation of a fission chain reaction in 235U. The fission fragments are shown only for the first three fissions. The average number of neutrons produced is 2.4 per fission. In this example k ϭ 1.6. Notice that, while there are 42 neutrons in the diagram, the judicious placement of absorbers to absorb as few as two of those causing fission would be sufficient to make k ϭ 1 and control the reaction. 235U nucleus Fission fragments Neutron FIGURE 11-51 The energy spectrum of 1000 the neutrons emitted in the thermal- 235 neutron-induced fission of U. [Data Cloud chamber from R. B. Leachman, Proceedings of the Time of flight International Conference on the Peaceful 100 Emulsions Uses of Atomic Energy, vol. 2, United Nations, New York, 1956.] 10 Neutron abundance (relative) Neutron abundance 1 08110112 3 456 7 912 Neutron energy, MeV material such as water or graphite that contains light nuclei is placed around the fissile material in the core of the reactor to slow down the neutrons with relatively few colli- sions so as to minimize the number lost from the reactor. The neutrons are slowed down by elastic collisions with the nuclei of the moderator until they are in thermal equilibrium with the moderator, at which time they have approximately a Maxwell- Boltzmann energy distribution with average energy of 13>22kT. Table 11-5 lists the approximate number of collisions needed to reduce 1 MeV neutrons to thermal energy for a few nuclei. Reactors using ordinary water as a moderator cannot easily achieve k ϭ 1 using natural uranium as a fuel for a combination of reasons. First, although the average number of neutrons emitted per fission is 2.4 (equal to the maximum value of k), we have noted that some of these are lost by escaping from the reactor or being absorbed in nonfission reactions. Recalling from Section 11-7 that the total cross section is the More Chapter 11 77 4 10 FIGURE 11-52 Neutron-induced fission cross 235 238 103 sections for U and U. The region below 0.01 eV for 235U shows the 1>v dependence, as 2 584 b 10 does the cross section for the (n, ␥) reaction and 101 for the same reason. The radiative absorption 235U reaction competes with fission and has a cross 10 0 section of 97 b at 0.025 eV. The numerous –1 resonances between 1 eV and 100 eV are 10 236 238U associated with excited states of the U* Fission cross section, b 10 –2 nucleus. 0.025 eV 10 –3 10–3 10–2 10–1 10 0 101 10 2 103 10 4 10 5 106 10 7 Neutron energy, eV Table 11-5 Properties of selected nuclei as moderators Number of collisions Nucleus (n, ␥) barns to thermalize 1H 0.333 18 2H 0.51 ϫ 10Ϫ3 25 4He 0 43 12C 3.5 ϫ 10Ϫ3 110 238U 2.75 2200 sum of the partial cross sections and recognizing that the ratio of the cross section for a particular reaction (Equation 11-62) and the total cross section is the relative proba- bility of that reaction occurring, we see that then the relative probability that a thermal >1 + 2 neutron will cause a fission reaction is given by f f a , where f is the partial cross section for fission and a is the partial cross section for all other kinds of absorp- tion of thermal neutrons. The latter are mainly (n, ␥) reactions. Thus, we can write k as = f k 2.4 + 11-68 f a The values of f and a for natural uranium are computed from the isotopic abun- dances above and the cross sections for each isotope. The fission cross section for 235U is 584 b for thermal neutrons, while that for 238U is zero. The cross sections for the (n, ␥) reactions are 97 b for 235U and 2.75 b for 238U (see Table 11-5 and Figure 11-52). The values of f and a are then given by 0.72 98.28 = 1235 2 + 1238 2 = + = U U 4.20 0 4.20 b f 100 f 100 f and 0.72 98.28 = 1235 2 + 1238 2 = + = U U 0.70 2.73 3.43 b a 100 a 100 a 78 More Chapter 11 FIGURE 11-53 Schematic diagram of the nuclear fuel cycle for uranium-fueled light-water reactors. The UF6 Fuel fabrication conversion plant converts Nuclear power plant solid U3O8, called yellowcake because of its color, into Plutonium Storage gaseous UF6 for the 235 enrichment facility. UF6 is Gaseous-diffusion Uranium 238 separated from UF6 based enrichment plant on the fact that both Reprocessing molecules have the same UF6 conversion and conversion average kinetic energy, > (3 2)kT, and hence different Mining diffusion rates due to their and High-level milling Low-level slightly different masses. The waste waste complete cycle includes the repository reprocessing facility and the repository for highly Trench burial radioactive fission products. Therefore, the largest possible value of k that we Table 11-6 Thermal-neutron fission cross can expect from natural uranium used as a reactor sections for selected nuclei fuel is, from Equation 11-68, Cross section Critical energy = f = 4.20 = Nuclide (barns) for A ϩ 1 (MeV) k 2.4 + 2.4 + 1.32 f a 4.20 3.43 229Th 30 8.3 This value is already quite close to 1.0, so if loss of neutrons by leakage from the reactor or by 230Th Ͻ10Ϫ3 8.3 absorption in the moderator is significant, the 230Pa 1500 7.6 value of k may be easily less than 1.0. Because of Ϫ the relatively large neutron capture cross section 233Pa Ͻ10 1 7.1 for the hydrogen nucleus (see Table 11-5), reactors 233U 531 6.5 using ordinary water as a moderator and natural Ϫ uranium as a fuel have difficulty reaching k ϭ 1. 234U Ͻ5 ϫ 10 3 6.5 By enriching the uranium fuel in 235U, that is, by 235U 584 6.2 increasing the 235U content from 0.7 percent to, Ϫ for example, 3 percent, the value of k computed 238U 2.7 ϫ 10 6 5.9 from Equation 11-68 becomes 1.82, sufficient to 236Np 3000 5.9 make k ϭ 1 attainable in operation. (Figure 11-53 238Np 17 6.0 shows where the enrichment process fits into the uranium fuel cycle.) Natural uranium can be used 239 Pu 742 6.0 if heavy water (D2O) is used instead of ordinary 240Pu Ͻ8 ϫ10Ϫ2 6.3 (light) water (H2O) as the moderator.