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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 = 1, the chain reaction is critical and the neutron population will remain constant. In an infinite medium, neutrons cannot leak out of the system and the multiplication factor becomes the infinite multiplication factor, =, which is approximated by the four-factor formula.
The "Six-factor formula" is the neutron life-cycle balance equation, which includes six separate factors, the product of which is equal to the ratio of the number of neutrons in any generation to that of the previous one; this parameter is called the effective multiplication factor k, also denoted by K eff, where k = Є L f ρ L th f η, where ...
The multiplication factor is sometimes calculated with a simplified four-factor formula, which is the same as described above with and both equal to 1, and is used when an assumption is made that the reactor is "infinite" in that neutrons are very unlikely to leak out of the system.
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0
The average number of neutrons that cause new fission events is called the effective neutron multiplication factor, usually denoted by the symbols k-effective, k-eff or k. When k-effective is equal to 1, the assembly is called critical, if k-effective is less than 1 the assembly is said to be subcritical, and if k-effective is greater than 1 ...
A numerical measure of a critical mass depends on the effective neutron multiplication factor k, the average number of neutrons released per fission event that go on to cause another fission event rather than being absorbed or leaving the material. A subcritical mass is a mass that does not have the ability to sustain a fission chain reaction ...
Reactivity (denoted ρ or ΔK/K) is related to the effective neutron multiplication factor (k eff), the average number of all neutrons from one fission that cause another fission. [2] ρ = k eff - 1 / k eff But in nuclear physics, it useful to talk about the reactivity contributed by just the prompt neutrons. This is the reactivity in ...