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The Campbell theorem, relating the variance of the current of a fissionchamber (a "filtered Poisson process") to the intensity of the detection eventsand to the detector pulse shape, becomes invalid when the neutrons generatingthe fission chamber current are not independent. Recently a formalism wasdeveloped by the present authors [1], by which the variance of the detectorcurrent could be calculated for detecting neutrons in a subcritical multiplyingsystem, where the detection events are obviously not independent. In thepresent paper, the previous formalism, which only accounted for promptneutrons, is generalised to account also for delayed neutrons. A rigorousprobabilistic analysis of the detector current was performed by using the samesimple, but realistic detector model as in the previous work. The results ofthe present analysis made it possible to determine the bias of the traditionalCampbelling techniques both qualitatively and quantitatively. The results showthat the variance still remains proportional to the detection intensity, and isthus suitable for the monitoring of the mean flux, but the calibration factorbetween the variance and the detection intensity is an involved function of thedetector pulse shape and the subcritical reactivity of the system, whichdiverges for critical systems.

Theory of fission detector signals in reactor measurements - detailed calculations