## Abstract

The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with
More>>

## Citation Formats

Ceder, M.
Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method).
Sweden: N. p.,
2002.
Web.

Ceder, M.
Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method).
Sweden.

Ceder, M.
2002.
"Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)."
Sweden.

@misc{etde_20248917,

title = {Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)}

author = {Ceder, M}

abstractNote = {The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with the beginning of an incoming pulse. The Feynman-alpha method has been elaborated for such a case recently. The other method can be called stochastic pulsing. It means that there is no synchronisation between the detector time gate start and the source pulsing, i.e. the start of each measurement is chosen at a random time. The analytical solution to the Feynman-alpha formula from this latter method is the subject of this report. We have obtained an analytical Feynman-alpha formula for the case of stochastic pulsing by two different methods. One is completely based on the use of the symbolic algebra code Mathematica, whereas the other is based on complex function techniques. Closed form solutions could be obtained by both methods; however the results obtained by complex analysis are significantly more compact. The results show that the stochastic pulsing gives a variance-to-mean curve that is smoothly regular with a simple periodic oscillation. It consists of a Feynman-curve corresponding to a stationary source, plus an infinite sum of periodic sine functions squared. Thus the traditional smooth Feynman-alpha expression is given as the lower envelope of the pulsed curve. Such a solution is suitable for the determination of the subcritical reactivity by fitting a curve to the local minima of the variance-to-mean curve from experimental data, or even to the complete curve. These results are in contrast with the case of the so-called deterministic pulsing, where no simple closed form solution is available, and where the relationship between the traditional and pulsed Feynman-alpha formula is more indirect.}

place = {Sweden}

year = {2002}

month = {Mar}

}

title = {Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)}

author = {Ceder, M}

abstractNote = {The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with the beginning of an incoming pulse. The Feynman-alpha method has been elaborated for such a case recently. The other method can be called stochastic pulsing. It means that there is no synchronisation between the detector time gate start and the source pulsing, i.e. the start of each measurement is chosen at a random time. The analytical solution to the Feynman-alpha formula from this latter method is the subject of this report. We have obtained an analytical Feynman-alpha formula for the case of stochastic pulsing by two different methods. One is completely based on the use of the symbolic algebra code Mathematica, whereas the other is based on complex function techniques. Closed form solutions could be obtained by both methods; however the results obtained by complex analysis are significantly more compact. The results show that the stochastic pulsing gives a variance-to-mean curve that is smoothly regular with a simple periodic oscillation. It consists of a Feynman-curve corresponding to a stationary source, plus an infinite sum of periodic sine functions squared. Thus the traditional smooth Feynman-alpha expression is given as the lower envelope of the pulsed curve. Such a solution is suitable for the determination of the subcritical reactivity by fitting a curve to the local minima of the variance-to-mean curve from experimental data, or even to the complete curve. These results are in contrast with the case of the so-called deterministic pulsing, where no simple closed form solution is available, and where the relationship between the traditional and pulsed Feynman-alpha formula is more indirect.}

place = {Sweden}

year = {2002}

month = {Mar}

}