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six factor formula : ウィキペディア英語版
six factor formula
The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium. The formula is
k = \eta f p \varepsilon P_ P_


| 1.65
|-
| f
| The thermal utilization factor
| Probability that a neutron that gets absorbed does so in the fuel material.
| f = \frac
| 0.71
|-
| 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 \left( -\frac N_i I_}} \right)
| 0.87
|-
| \varepsilon
| The fast fission factor (Epsilon)
|
\tfrac}

| \varepsilon \approx 1 + \frac\frac P_}
| 1.02
|-|
|-
| P_
| The fast non-leakage probability
| The probability that a fast neutron will not leak out of the system.
| P_ \approx \mathrm \left( -^2 \tau_ \right)
| 0.97
|-|
|-
| P_
| The thermal non-leakage probability
| The probability that a thermal neutron will not leak out of the system.
| P_ \approx \frac^2}
| 0.99
|-
|}
The symbols are defined as:
*\nu, \nu_f and \nu_t are the average number of neutrons produced per fission in the medium (2.43 for Uranium-235).
*\sigma_f^F and \sigma_a^F are the microscopic fission and absorption cross sections for fuel, respectively.
*\Sigma_a^F and \Sigma_a are the macroscopic absorption cross sections in fuel and in total, respectively.
*N_i is the number density of atoms of a specific nuclide.
*I_ is the resonance integral for absorption of a specific nuclide.
*
*I_ = \int_ dE' \frac \frac.
*\overline is the average lethargy gain per scattering event.
*
*Lethargy is defined as decrease in neutron energy.
*u_f (fast utilization) is the probability that a fast neutron is absorbed in fuel.
*P_ is the probability that a fast neutron absorption in fuel causes fission.
*P_ is the probability that a thermal neutron absorption in fuel causes fission.
*^2 is the geometric buckling.
*}^2 = \frac is the age to thermal.
*
*\tau = \int_ dE'' \frac \frac^2 + \Sigma_t(E') \right )}.
*
*\tau_ is the evaluation of \tau where E' is the energy of the neutron at birth.
==Multiplication==
The multiplication factor, k, is defined as (see Nuclear chain reaction):
k = \frac}

If k is greater than 1, the chain reaction is ''supercritical,'' and the neutron population will grow exponentially.

If k is less than 1, the chain reaction is ''subcritical,'' and the neutron population will exponentially decay.

If k = 1, the chain reaction is ''critical'' and the neutron population will remain constant.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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