Reactivity is a measure of the departure of a reactor from criticality. The reactivity is related to the value of k_eff. Reactivity is a useful concept to predict how the neutron population of a reactor will change over time.

EO 1.8Given the number of neutrons in a reactor core and the effective multiplication factor, CALCULATE the number of neutrons present after any number of generations.

EO 1.9DEFINE the term reactivity.

EO 1.10 CONVERT between reactivity and the associated value of k_eff,

EO 1.11 CONVERT measures of reactivity between the following units:

EO 1.12 EXPLAIN the relationship between reactivity coefficients and reactivity defects.

Application of the Effective Multiplication Factor

When k_eff remains constant from generation to generation, it is possible to determine the number of neutrons beginning any particular generation by knowing only the value of k_eff and the number of neutrons starting the first generation. If N_o neutrons start the first generation, then neutrons start the second generation. Equation (3-4) can be used to calculate the number of neutrons after the completion of "n" generations.

Example:

The number of neutrons in the core at time zero is 1000 and k_eff = 1.002. Calculate the number of neutrons after 50 generations.

Solution:

Use Equation (3-4) to calculate the number of neutrons.

Reactivitv

If there are N_o neutrons in the preceding generation, then there are N_o(k_eff) neutrons in the present generation. The numerical change in neutron population is (N_ok_eff -N_o). The gain or loss in neutron population (N_ok_eff -N_o), expressed as a fraction of the present generation (N_ok_eff), is shown below.

This relationship represents the fractional change in neutron population per generation and is referred to as reactivity (p). Cancelling out the term N_o from the numerator and denominator, the reactivity is determined as shown in the equation below.

From Equation (3-5) it may be seen that p may be positive, zero, or negative, depending upon the value of k_eff.The larger the absolute value of reactivity in the reactor core, the further the reactor is from criticality. It may be convenient to think of reactivity as a measure of a reactor's departure from criticality.

Example:

Calculate the reactivity in the reactor core when k_eff is equal to 1.002 and 0.998.

Solution:

The reactivity for each case is determined by substituting the value of k_eff into Equation (3-5).