Comments on the stochastic characteristics of fission chamber signals

Abstract

a b s t r a c tThis paper reports on theoretical investigations of the stochastic properties of the signal series of ionisation chambers, in particular fission chambers. First, a simple and transparent derivation is given of the higher order moments of the random detector signal for incoming pulses with a non-homogeneous Poisson distribution and random pulse heights and arbitrary shape. Exact relationships are derived for the higher order moments of the detector signal, which constitute a generalisation of the so-called higher order Campbelling techniques. The probability distribution of the number of time points when the signal exceeds a certain level is also derived. Then, a few simple pulse shapes and amplitude distributions are selected as idealised models of the detector signals. Assuming that the incoming particles form a homogeneous Poisson process, explicit expressions are given for the higher order moments of the signal and the number of level crossings in a given time interval for the selected pulse shapes.

Campbelling-type theory of fission chamber signals generated by neutron chains in a multiplying medium

“…To this end we will use an extended version of the formalism applied in [10] to account for the statistics of the incoming particles.…”

“…Although the signal of the detector at any given time is the sum of the signals of all previous random detections, the starting point is, just as in [10], to specify the properties of the detector signal after the detection of one neutron. In [10], from these, it was immediately possible to write down a backward master equation for the probability distribution of the detector signals, due to the independence of the detection events.…”

“…In [10], from these, it was immediately possible to write down a backward master equation for the probability distribution of the detector signals, due to the independence of the detection events. In the present case, it will not be possible to directly specify the probability of the arrival of the neutrons at the detector; we can only specify the probability (intensity) of the source neutron emission and hence write down a master equation for the probability distribution of the detector signal for one source neutron.…”

“…Regarding the formalism, the usual derivation of the traditional and higher order Campbell relationships is either heuristic [2][3][4], or rather involved [7,8]. Recently a rather transparent and effective formalism was suggested by the present authors by using the backward master equations [9,10]. The formalism can easily be extended from the case of independent incoming events to the case when the incoming neutrons were generated in a subcritical multiplying medium driven with an external source.…”

“…The formalism can easily be extended from the case of independent incoming events to the case when the incoming neutrons were generated in a subcritical multiplying medium driven with an external source. This is made by combining the backward master equation for the detector signal, proposed in [10], with the backward master equations of neutron branching in a subcritical multiplying medium [1]. This will ensure that the temporal correlations between the detection events will correspond to a measurement in a reactor core during start-up, or in a safeguards measurement in e.g.…”