What is criticality in a Nuclear reactor?

Let us assume that a reactor is producing 1 Watt of power steadily as a result of 3.1 x 10^10 fissions per second.

The number of Neutrons available for fission at any time remains same during criticality condition. When the chain reaction is maintained steady, the power level is steady and the reactor is said to be critical.

If the power is increasing or decreasing, the rate of neutron production is not constant.

The neutron multiplication factor, K, based on the neutron cycle is used to keep track of neutron production.

K = number of neutrons in a generation / number of neutrons in preceding generation

For instance, consider 100 neutrons, which is our first generation.

If K=1, there will be 100 neutrons at beginning of second generation, 100 at third generation and so on. Fissions continue at the same rate as at the beginning.

If K>1, say 1.05, the 100 neutrons of first generation produce 100 x 1.05 = 105 neutrons at the beginning of next generation.

After 100 generations, the number of neutrons present would be 13150 i.e.100 x (1.05)^100.

The power would be increasing and is said to be super critical. In this case the power increased 131 times in about one tenth of a second. This is too fast to control and in practice multiplication factor is never allowed to become so large.

If K<1, the neutron population decreases with time and power decreases and reactor is said to be subcritical.



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