The difference may be well expressed by following example:
The number of neutrons (the neutron population) in the core at time zero is 1000 and k∞ = 1.001 (~100 pcm).
Calculate the number of neutrons after 100 generations. Let say, the mean generation time is ~0.1s.
To calculate the neutron population after 100 neutron generations, we use following equation:
N1=N0.1.001 = 1001 neutrons after one generation
N2=N0.1.001.1.001 = 1002 neutrons after two generations
N3=N0.1.001.1.001.1.001 = 1003 neutrons after three generations
N50=N0. (k∞)50 = 1051 neutrons after fifty generations.
N100=N0. (k∞)100 = 1105 neutrons after hundred generations.
If we consider the mean generation time to be ~0.1s, so the increase from 1000 neutrons the 1105 neutrons occurs within 10 seconds.
It is obvious the infinite multiplication factor in a multiplying system is a measure of the change in the fission neutron population from one neutron generation to the subsequent generation.
- k∞ < 1. If the multiplication factor for a multiplying system is less than 1.0, then the number of neutrons is decreasing in time (with the mean generation time) and the chain reaction will never be self-sustaining. This condition is known as the subcritical state.
- k∞ = 1. If the multiplication factor for a multiplying system is equal to 1.0, then there is no change in neutron population in time and the chain reaction will be self-sustaining. This condition is known as the critical state.
- k∞ > 1. If the multiplication factor for a multiplying system is greater than 1.0, then the multiplying system produces more neutrons than are needed to be self-sustaining. The number of neutrons is exponentially increasing in time (with the mean generation time). This condition is known as the supercritical state.