Reactor Theory (Nuclear Parameters) DOE-HDBK-1019/2-93
Reactivity Coefficients and Reactivity Defects
The amount of reactivity (r) in a reactor core determines what the neutron population, and
consequently the reactor power, are doing at any given time. The reactivity can be effected by
many factors (for example, fuel depletion, temperature, pressure, or poisons). The next several
chapters discuss the factors affecting reactivity and how they are used to control or predict
To quantify the effect that a variation in parameter (that is, increase in temperature, control rod
insertion, increase in neutron poison) will have on the reactivity of the core, reactivity
coefficients are used. Reactivity coefficients are the amount that the reactivity will change for
a given change in the parameter. For instance, an increase in moderator temperature will cause
a decrease in the reactivity of the core. The amount of reactivity change per degree change in
the moderator temperature is the moderator temperature coefficient. Typical units for the
moderator temperature coefficient are pcm/oF. Reactivity coefficients are generally symbolized
by ax, where x represents some variable reactor parameter that affects reactivity. The definition
of a reactivity coefficient in equation format is shown below.
ax D r
If the parameter x increases and positive reactivity is added, then ax is positive. If the parameter
x increases and negative reactivity is added, then ax is negative.
Reactivity defects (Dr) are the total reactivity change caused by a variation in a parameter.
Reactivity defects can be determined by multiplying the change in the parameter by the average
value of the reactivity coefficient for that parameter. The equation below shows the general
method for relating reactivity coefficients to reactivity defects.
Dr = ax Dx
The moderator temperature coefficient for a reactor is -8.2 pcm/oF. Calculate the
reactivity defect that results from a temperature decrease of 5oF.
D r aT D T
The reactivity addition due to the temperature decrease was positive because of the
negative temperature coefficient.