Six Factor Formula - h1019v2

Fast Non-Leakage Probability

Figure 1 Neutron Life Cycle with keff = 1

Nuclear Physics and Reactor Theory Volume 2 of 2
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NEUTRON LIFE CYCLE DOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters) 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 (k_eff) can then be determined by the product of six terms. k_eff = _f p _t f h (3-3) 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 N_o. The first process is fast fission and the population has been increased by the neutrons from this fast fission process. From the definition of the fast fission factor it is possible to calculate its value based on the number of neutrons before and after fast fission occur. number of fast neutrons produced by all fissions number of fast neutrons produced by thermal fissions 1040 1000 1.04 The total number of fast neutrons produced by thermal and fast fission is represented by the quantity N_o . 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. f number of fast neutrons that do not leak from reactor number of fast neutrons produced by all fissions 1040 140 1040 0.865 The number of neutrons that remain in the core during the slowing down process is represented by the quantity N_o _f. NP-03 Rev. 0 Page 10

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