Stochastic Processes in a Subcritical Nuclear Reactor in the Presence of a Fission Source

The forward Kolgomorov equation is written for the case of a subcritical reactor monitored by two detectors and excited by a fission source located inside a fission chamber (an arrangement currently in use to measure reactivities). The marginal distribution of neutrons is shown to be given by the negative binomial distribution with an amplified correlation as compared to the case of a photoneutron source. The amplification allows the definition of an equivalent factor D_eq for the Diven factor, which makes possible the application of formulas originally derived for interpretation of noise measurement in the presence of a photoneutron source to the case of a fission source. The ratio of the correlations measured under the successive presence of both kind of sources allows the direct measurement of the effective delayed fraction, β_ef. The factor D_eq is proven to be consistent with a derivation based on the Schottky prescription for the noise source.