n_N and n₀ are the number of neutrons following the first N generations and are proportional to the average neutron density, average neutron flux and total power of the reactor. Thus, we can write the following:

P = P₀ . e ^N·DK

If DK is positive, we have more fissions than necessary to maintain the chain reaction. The neutron density will increase and we will have more neutrons available to cause other fissions. That is to say: density increases, the fission rate increases and, consequently, the power level increases.

THE EFFECT OF NEGATIVE REACTIVITY CHANGES

The same expression as before is applied, except for the sign. For example, if k_eff = 0.997, the DK reactivity will be:

 DK = -0.003

 and the neutron population will, thus, decrease.

That is to say:

n_N = n₀ . e^N.DK

n_N = n₀·e^{500·(-0.003)}

n_N = n₀ . e^-1.5

n_N = n₀ . 0.22  Þ 

What this signifies is that neutron density, the neutron population, neutron flux and reactor power will have diminished by 22% following 500 generations.

EXAMPLE PROBLEM 1

EXAMPLE PROBLEM 2