The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium.

Six-factor formula: [1]
Symbol Name Meaning Formula Typical thermal reactor value
Thermal fission factor (eta) neutrons produced from fission/absorption in fuel isotope 1.65
Thermal utilization factor neutrons absorbed by the fuel isotope/neutrons absorbed anywhere 0.71
Resonance escape probability fission neutrons slowed to thermal energies without absorption/total fission neutrons 0.87
Fast fission factor (epsilon) total number of fission neutrons/number of fission neutrons from just thermal fissions 1.02
Fast non-leakage probability number of fast neutrons that do not leak from reactor/number of fast neutrons produced by all fissions 0.97
Thermal non-leakage probability number of thermal neutrons that do not leak from reactor/number of thermal neutrons produced by all fissions 0.99

The symbols are defined as:[2]

  • , and are the average number of neutrons produced per fission in the medium (2.43 for uranium-235).
  • and are the microscopic fission and absorption cross sections for fuel, respectively.
  • and are the macroscopic absorption cross sections in fuel and in total, respectively.
  • is the number density of atoms of a specific nuclide.
  • is the resonance integral for absorption of a specific nuclide.
    • .
  • is the average lethargy gain per scattering event.
    • Lethargy is defined as decrease in neutron energy.
  • (fast utilization) is the probability that a fast neutron is absorbed in fuel.
  • is the probability that a fast neutron absorption in fuel causes fission.
  • is the probability that a thermal neutron absorption in fuel causes fission.
  • is the geometric buckling.
  • is the diffusion length of thermal neutrons.
    • .
  • is the age to thermal.
    • .
    • is the evaluation of where is the energy of the neutron at birth.

Multiplication

The multiplication factor, k, is defined as (see nuclear chain reaction):

k = number of neutrons in one generation/number of neutrons in preceding generation
  • 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.

See also

References

  1. Duderstadt, James; Hamilton, Louis (1976). Nuclear Reactor Analysis. John Wiley & Sons, Inc. ISBN 0-471-22363-8.
  2. Adams, Marvin L. (2009). Introduction to Nuclear Reactor Theory. Texas A&M University.
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