Talk:Four factor formula
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The four-factor formula, also known as Fermi's four factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in an infinite medium. The formula is[1] k_{\infty} = \eta f p \varepsilon Symbol Name Meaning Formula \eta Reproduction Factor (Eta) The number of fission neutrons produced per absorption in the fuel. \eta = \frac{\nu \sigma_f^F}{\sigma_a^F} f The thermal utilization factor Probability that a neutron that gets absorbed does so in the fuel material. f = \frac{\Sigma_a^F}{\Sigma_a} p The resonance escape probability Fraction of fission neutrons that manage to slow down from fission to thermal energies without being absorbed. p \approx \mathrm{exp} \left( -\frac{\sum\limits_{i=1}^{N} N_i I_{r,A,i}}{\left( \overline{\xi} \Sigma_p \right)_{mod}} \right) \epsilon The fast fission factor \frac{\mbox{total number of fission neutrons}}{\mbox{number of fission neutrons from just thermal fissions}} \varepsilon \approx 1 + \frac{1-p}{p}\frac{u_f \nu_f P_{FAF}}{f \nu_t P_{TAF} P_{TNL}}
The six factor formula defines each of these terms in much more detail. Multiplication
The multiplication factor, k, is defined as (see Nuclear chain reaction): k = \frac{\mbox{number of neutrons in one generation}}{\mbox{number of neutrons in preceding generation}}
If k is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.
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