## Subcritical Reactor Dynamics

Dynamics tests may be used to determine the degree of subcriticality in a subcritical reactor. The method for performing and interpreting this type of measurement may be deduced by considering the kinetics equations for a subcritical reactor with a source (space-independent model):

6

dn/dt = [(p — P)/]n + £ А, с, + S (5.4.1)

;= і

dCJdt = Pi/An — A, C; (5.4.2)

where S is the source strength. A subcritical reactor can be perturbed by modulating the source or by modulating the reactivity. The pertinent transfer functions are

We note that these two transfer functions differ only by a gain factor. The shapes of the frequency response functions are identical.

Figure 5.7 shows the frequency responses for various levels of subcriticality. The high-frequency break is due to a pole with a value (P — p0)/A. A frequency response measurement using a source modulation or a reactivity modulation around the fixed subcritical reactivity can be used to determine (P — p0)/A by identifying the break frequency. If p and A are adequately known, p0 can

then be determined. We also note that the phase shift in the range 0.001 to 1 rad/sec is quite sensitive to the subcritical reactivity for subcriticalities of less than a few dollars. This suggests that low-frequency measurements can be used to determine the subcritical reactivity by relating the phase shift to subcriticality.

The frequency response has been measured in research reactors using the source-modulation technique. This requires the use of a pulsed neutron

source. It is not usually feasible to use this technique in power reactors, and other techniques for measuring subcritical reactivity have been developed. These are the random-noise technique (3-5), the source-multiplication technique (5), and the inverse-kinetics technique (5).