Six factor formula
Encyclopedia
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
The symbols are defined as :
):
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.
Nuclear engineering
Nuclear engineering is the branch of engineering concerned with the application of the breakdown as well as the fusion of atomic nuclei and/or the application of other sub-atomic physics, based on the principles of nuclear physics...
to determine the multiplication of a nuclear chain reaction
Nuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...
in a non-infinite medium. The formula is
| Symbol | Name | Meaning | Formula | Typical Thermal Reactor Value |
|---|---|---|---|---|
 |
Reproduction Factor (Eta) | The number of fission neutron Neutron The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of... s produced per absorption in the fuel. |
 |
1.65 |
 |
The thermal utilization factor | Probability that a neutron that gets absorbed does so in the fuel material. |  |
0.71 |
 |
The resonance escape probability | Fraction of fission neutrons that manage to slow down from fission to thermal energies without being absorbed. |  |
0.87 |
 |
The fast fission factor (Epsilon) |  |
 |
1.02 |
 |
The fast non-leakage probability | The probability that a fast neutron will not leak out of the system. |  |
0.97 |
 |
The thermal non-leakage probability | The probability that a thermal neutron will not leak out of the system. |  |
0.99 |
The symbols are defined as :
, 
and 
are the average number of neutrons produced per fission in the medium (2.43 for Uranium-235Uranium-235- References :* .* DOE Fundamentals handbook: Nuclear Physics and Reactor theory , .* A piece of U-235 the size of a grain of rice can produce energy equal to that contained in three tons of coal or fourteen barrels of oil. -External links:* * * one of the earliest articles on U-235 for the...
).
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 nuclideNuclideA nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....
.
is the resonance integral for absorption of a specific nuclideNuclideA nuclide is an atomic species characterized by the specific constitution of its nucleus, i.e., by its number of protons Z, its number of neutrons N, and its nuclear energy state....
.
.
(often referred to as worm-bar or squigma-bar) 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 bucklingGeometric and Material BucklingIn a nuclear reactor, criticality is achieved when the rate of neutron production is equal to the rate of neutron losses, including both neutron absorption and neutron leakage. Geometric buckling is a measure of neutron leakage, while material buckling is a measure of neutron production minus...
.
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 reactionNuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...
):
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
- Critical massCritical massA critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The...
- Nuclear chain reactionNuclear chain reactionA nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...
- Nuclear reactorNuclear reactorA nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...
- Four factor formula