{"id":13612,"date":"2017-02-01T16:48:12","date_gmt":"2017-02-01T16:48:12","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=13612"},"modified":"2022-10-20T07:50:13","modified_gmt":"2022-10-20T07:50:13","slug":"nuclear-fission-chain-reaction","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/","title":{"rendered":"Nuclear Fission Chain Reaction"},"content":{"rendered":"
A nuclear fission chain reaction<\/strong> is a self-propagating sequence of fission reactions in which neutrons released in fission produce additional fission in at least one other nucleus. The chain reaction<\/strong> can take place only in the proper<\/strong> multiplication environment<\/strong> and only under proper conditions<\/strong>.<\/div><\/div>\n

The fission process may produce 2, 3, or more free neutrons<\/a><\/strong> that are capable of inducing further fissions<\/strong> and so on. This sequence of fission events is known as the fission chain reaction<\/strong>, and it is important in nuclear reactor physics<\/a>.<\/p>\n

The chain reaction<\/strong> can take place only in the proper<\/strong> multiplication environment<\/strong> and only under proper conditions<\/strong>. Suppose one neutron causes two further fissions. In that case, the number of neutrons in the multiplication system will increase in time, and the reactor power (reaction rate<\/a>) will also increase in time. To stabilize such a multiplication environment, it is necessary to increase the non-fission neutron absorption<\/a> in the system (e.g.,, to insert control rods<\/a><\/strong>). Moreover, this multiplication environment (the nuclear reactor<\/a>) behaves like an exponential system, which means the power increase is not linear, but it is exponential<\/strong>.<\/p>\n

\"Nuclear<\/a>
The\u00a0nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions.<\/figcaption><\/figure>\n

On the other hand, if one neutron causes less than one<\/strong> further fission, the number of neutrons in the multiplication system will decrease in time, and the reactor power (reaction rate) will also decrease in time. It is necessary to decrease the non-fission neutron absorption in the system (e.g.,, to withdraw control rods<\/strong>) to sustain the chain reaction<\/strong>.<\/p>\n

There is always a competition<\/strong> for the fission neutrons in the multiplication environment. Some neutrons will cause further fission reaction<\/strong>, some will be captured<\/strong> by fuel or non-fuel materials, and some will leak out<\/strong> of the system.<\/p>\n

It is necessary to define the infinite and finite multiplication factors<\/strong> of a reactor to describe the multiplication system. The method of calculations of multiplication factors was developed in the early years<\/strong> of nuclear energy. It is only applicable to thermal reactors<\/strong>, where the bulk of fission reactions occurs at thermal energies. This method puts into context all the processes associated with the thermal reactors (e.g.,, neutron thermalization, neutron diffusion, or fast fission) because the most important neutron-physical processes occur in energy regions that can be clearly separated from each other<\/strong>. In short, the calculation of the multiplication factor gives a good insight into the processes that occur in each thermal multiplying system.<\/p>\n

<\/span>Fast vs. Thermal Flux Spectrum<\/div>
\n
\"thermal<\/a>
The spectrum of neutron energies produced by fission varies significantly with certain reactor designs. thermal vs. fast reactor neutron spectrum<\/figcaption><\/figure>\n<\/div><\/div>
<\/span>Six Factor Formula - Fast Reactors<\/div>
For fast reactors<\/strong><\/a>, in which neutrons cause the fission with a very broad energy distribution, such an analysis is inappropriate. The neutron flux<\/a> in fast reactors has to be divided into many energy groups<\/strong>. Moreover, in fast reactors, neutron thermalization is an undesirable process, and therefore the four-factor formula does not make any sense. The resonance escape probability is insignificant because very few neutrons exist at energies where resonance absorption is significant. The thermal non-leakage probability does not exist because the reactor is designed to avoid the thermalization of neutrons.<\/div><\/div><\/div>\n
\n

Infinite Multiplication Factor – Four Factor Formula<\/h2>\n

In this section, the infinite multiplication factor<\/strong>, which describes all the possible events in the life of a neutron and effectively describes the state of an infinite multiplying system, will be defined.<\/p>\n

The necessary condition for a stable, self-sustained fission chain reaction<\/strong> in a multiplying system (in a nuclear reactor<\/a>) is that exactly every\u00a0fission <\/a>initiates another fission<\/strong>. The minimum condition is for each nucleus undergoing fission to produce, on average, at least one neutron that causes fission of another nucleus. Also, the number of fissions occurring per unit time (the reaction rate<\/a>) within the system must be constant.<\/p>\n

This condition can be expressed conveniently in terms of the multiplication factor<\/strong>. The infinite multiplication factor is the ratio of the neutrons produced by fission<\/strong> in one neutron generation<\/a> to the number of neutrons lost through absorption<\/strong> in the preceding neutron generation. This can be expressed mathematically, as shown below.<\/p>\n

\"Multiplication<\/a><\/p>\n

The\u00a0infinite multiplication factor<\/strong><\/a> in a multiplying system measures the change in the fission neutron population<\/a> from one neutron generation to the subsequent\u00a0generation.<\/p>\n