{"id":13752,"date":"2017-02-06T09:51:15","date_gmt":"2017-02-06T09:51:15","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=13752"},"modified":"2022-10-21T06:14:18","modified_gmt":"2022-10-21T06:14:18","slug":"reproduction-factor","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reproduction-factor\/","title":{"rendered":"Reproduction Factor"},"content":{"rendered":"
The thermal utilization factor<\/a> gives the fraction of the thermal neutrons<\/a> absorbed in the nuclear fuel<\/a>\u00a0in all isotopes<\/strong> of the nuclear fuel. But the nuclear fuel is an isotopically rich material even in this case, in which we consider only the fissionable nuclei<\/a> in the fuel. In the fresh uranium fuel<\/strong>, only three fissionable isotopes must be included in the calculations – 235<\/sup>U<\/a>, 238<\/sup>U<\/a>, 234<\/sup>U<\/a>. In power reactors, the fuel significantly changes its isotopic content<\/strong> as the fuel burnup<\/strong> increases. The isotope of 236<\/sup>U<\/a> and also trace\u00a0amounts of 232<\/sup>U<\/a> appears. The major consequence of increasing fuel burnup is that the content of the plutonium<\/a> increases (especially 239<\/sup>Pu<\/a>, 240<\/sup>Pu<\/a>, and 241<\/sup>Pu<\/a>). All these isotopes have to be included in the calculations of the reproduction factor<\/strong>.<\/p>\n Another fact is that not all<\/strong> the absorption reactions<\/a> that occur in the fuel result in fission. If we consider the thermal neutron and the nucleus of 235<\/sup>U<\/a>, then about 15%<\/strong> of all absorption reactions result in radiative capture<\/a> of a neutron. About 85%<\/strong> of all absorption reactions result in fission<\/a>. Each fissionable nuclei have a different fission probability, and microscopic cross-sections<\/a> determine these probabilities.<\/p>\n The neutrons<\/a> finish one generation<\/a>, and a new generation of neutrons may be created. The neutron reproduction factor<\/strong> determines the number of neutrons created in the new generation. The reproduction factor, \u03b7<\/strong>, is the ratio of the number of fast neutrons produced by thermal fission to the number 495<\/span><\/strong><\/p>\n \u2193<\/span><\/strong><\/p>\n \u03b7<\/strong>\u00a0~ 2.02<\/span><\/strong><\/p>\n \u2193<\/span><\/strong><\/p>\n 1000<\/span><\/strong><\/p>\n Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<\/p><\/div><\/div>\n <\/a><\/p>\n This factor is determined by the probability<\/strong> that fission reaction will occur times the average number of neutrons produced<\/strong> per one fission reaction. In the case of fresh uranium fuel, we consider only one fissile isotope, 235<\/sup>U,<\/strong> and the numerical value of \u03b7<\/strong> is given by the following equation:<\/p>\n <\/a><\/p>\n in which \u03bd<\/strong> is the average neutrons production of 235<\/sup>U<\/strong>, N5<\/sub> and N8<\/sub> are the atomic number densities<\/a> of the isotopes 235<\/sup>U<\/strong>\u00a0and\u00a0238<\/sup>U<\/strong> (when using other uranium isotopes or plutonium, the equation is modified trivially). This equation can also be written in terms of uranium enrichment<\/strong>:<\/p>\n
\nof thermal neutrons absorbed in the fuel. The reproduction factor is shown below.<\/p><\/div><\/div>