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Non-Leakage Probability (%) In
a realistic reactor of finite size, some of the fast neutrons leak out of the
boundaries of the reactor core before they begin the slowing down process. The fast
non-leakage probability ( Thermal
Non-Leakage Probability ( Neutrons can also leak out of a finite reactor core after they reach thermal energies. The thermal non-leakage probability (Sft) is defined as the ratio of the number of thermal neutrons that do not leak from the reactor core to the number of neutrons that reach thermal energies. The thermal non-leakage probability is represented by the following. number of thermal neutrons that do not leak from reactor number of neutrons that reach thermal energies The
fast non-leakage probability ( Six Factor Formula With the inclusion of these last two factors it is possible to determine the fraction of neutrons that remain after every possible process in a nuclear reactor. The effective multiplication factor (keff ) can then be determined by the product of six terms. Equation
(3-3) is called the six factor formula.
Using this six factor formula, it is possible to trace the entire
neutron life cycle from production by fission to the initiation of subsequent
fissions. Figure 1 illustrates a neutron life cycle with nominal values
provided for each of the six factors. Refer to Figure 1 for the remainder of
the discussion on the neutron life cycle and sample calculations. The
generation begins with 1000 neutrons. This initial number is represented by The
total number of fast neutrons produced by thermal and fast fission is
represented by the quantity Next, it can be seen that 140 neutrons leak from the core before reaching the thermal energy range. The fast non-leakage probability is calculated from its definition, as shown below. The
number of neutrons that remain in the core during the slowing down process is
represented by the quantity Figure
1 Neutron Life Cycle with The next step in the analysis is to consider the number of neutrons that are absorbed in the intermediate energy level. The probability of escaping this resonance absorption (p) is stated as follows. The
number of neutrons entering the thermal energy range is now represented by the
quantity After
reaching thermal energies, 100 neutrons leak from the core. The value for The
number of thermal neutrons available for absorption anywhere in the core is
represented by the quantity Figure 1 indicates that 125 neutrons were absorbed in non-fuel materials. Since a total of 620 thermal neutrons were absorbed, the number absorbed by the fuel equals 620 - 125 = 495. Therefore, the thermal utilization factor can be calculated as follows. The final factor numerically describes the production of fission neutrons resulting from thermal neutrons being absorbed in the fuel. This factor is called the reproduction factor (Tj). The value for the reproduction factor can be determined as shown below. The number of fission neutrons that exist at the end of
the life cycle which are available to start a new generation and cycle is
represented by the quantity In the example illustrated in Figure 1, keff is equal to one. available to start the next generation. Therefore, 1000 neutrons are Example: 10,000 neutrons exist at the beginning of a generation. The values for each factor of the six factor formula are listed below. Calculate the number of neutrons that exist at the points in the neutron life cycle listed below. 1) Number of neutrons that exist after fast fission. 2) Number of neutrons that start to slow down in the reactor. 3) Number of neutrons that reach thermal energies. 4) Number of thermal neutrons that are absorbed in the reactor. 5) Number of thermal neutrons absorbed in the fuel. 6) Number of neutrons produced from thermal fission. Solution: |
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