Statistical Theory of Fission Chains and Generalized Poisson Neutron Counting Distributions

Prasad, M. K.; Snyderman, N.J.

doi:10.13182/nse11-86

Cited by 20 publications

(28 citation statements)

References 9 publications

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“…We conclude this discussion on numerical methods by mentioning other methods which have been developed to compute the neutron number probability distributions. Work by Prasad and Snyderman (2012) developed a recursive point model for subcritical systems regarding the time-asymptotic neutron number probability distribution of neutrons which escape a multiplying medium and are therefore available for detection. Additionally, Abate and Whitt (1992); Williams (2016); Chambers et al (2016) have used numerical inversion of the generating function transform to obtain the neutron number probability distributions.…”

Section: Introductionmentioning

confidence: 99%

Diffusion theory model of the neutron number probability distribution in a subcritical multiplying assembly

Saxby

Prinja

Eaton

2017

Annals of Nuclear Energy

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The probability distribution of neutron numbers in a symmetric subcritical reflected fissile sphere is numerically obtained using a one-speed diffusion approximation to the underlying backward Master equation. Employing an accurate space-time discretisation scheme, the coupled but closed system of equations for the number probabilities is sequentially solved as a function of position and time of an injected neutron. This solution is then used to construct the corresponding distributions for a random intrinsic source of arbitrary multiplicity. Numerical results clearly demonstrate the importance of including spatial dependence in the neutron number probability distributions, which show complex spatial behaviours that cannot be encapsulated in a point model system. This is especially evident in the case of the multi-region model where the presence of a reflector is seen to alter the approach to steady state of the number probabilities, while the material interface has a significant effect on the magnitude of the probabilities, both locally and globally.

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Section: Introductionmentioning

confidence: 99%

Diffusion theory model of the neutron number probability distribution in a subcritical multiplying assembly

Saxby

Prinja

Eaton

2017

Annals of Nuclear Energy

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“…These count distributions b n (T) can be used to determine the strength F s of the spontaneous fission sources in the object, the efficiency ϵ of the liquid scintillator array, and multiplication M of fissile material [7]. We will show that these count distributions can also be used to determine the rate of neutrons from the (α,n) reactions.…”

Section: Moment Equations With Different Nuclear Data and Efficienciementioning

confidence: 95%

“…For time-gated fast neutron counting, the time dependent second and third moments of the random time gate distribution b n ðTÞ are a generalization of the formulas given by Prasad-Snyderman [7]. Normalizing by the count rate:…”

Section: Moment Equations With Different Nuclear Data and Efficienciementioning

confidence: 99%

Distinguishing Pu metal from Pu oxide and determining α-ratio using fast neutron counting

Verbeke

Chapline

Sheets

2015

Nuclear Instruments and Methods in Physics Research Section A:

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a b s t r a c tWe describe a new method for determining the ratio of the rate of (α,n) source neutrons to the rate of spontaneous fission neutrons, the so-called α-ratio. This method is made possible by fast neutron counting with liquid scintillator detectors, which can determine the shape of the fast neutron spectrum. The method utilizes the spectral difference between fission spectrum neutrons from Pu metal and the spectrum of (α,n) neutrons from PuO 2 . Our method is a generalization of the Cifarelli-Hage method for determining k eff for fissile assemblies, and also simultaneously determines k eff along with the α-ratio.Published by Elsevier B.V.

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“…Each neutron created by the spontaneous fission is capable -with probability p -of causing a subsequent fission, and by extension, a fission chain with a neutron multiplicity distributed according to P n . The generating function for the distribution P Sn was shown to be [5] …”

Section: Neutron Time Interval Distributionsmentioning

confidence: 99%

On the Time Interval Distribution Between Neutron Counts in a 3He Proportional Counter with Detector Dead Time

Walston¹

2012

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For materials where a spontaneously fissioning isotope (e.g.238 U or 240 Pu) initiates fission chains which propagate within a quantity of fissile material (e.g.235 U or 239 Pu), the neutrons are not generated according to a Poisson process because a single random event -the spontaneous fission of a radioactive nucleus -can generate many neutrons. We propose a perturbative theory to correct the time interval distribution between neutron counts for materials that spontaneously generate fission chains to accommodate the detector dead time inherent in 3 He proportional counters. We also propose a perturbative correction for multi-element detectors where the dead time applies only to neutrons counted within a single element.

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Statistical Theory of Fission Chains and Generalized Poisson Neutron Counting Distributions

Cited by 20 publications

References 9 publications

Diffusion theory model of the neutron number probability distribution in a subcritical multiplying assembly

Diffusion theory model of the neutron number probability distribution in a subcritical multiplying assembly

Distinguishing Pu metal from Pu oxide and determining α-ratio using fast neutron counting

On the Time Interval Distribution Between Neutron Counts in a 3He Proportional Counter with Detector Dead Time

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