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**Harvard**

Kitamura, Y., Pázsit, I., Yamamoto, A. och Yamane, Y. (2007) *Calculation of higher moments of the neutron multiplication process in a time-varying medium*.

** BibTeX **

@article{

Kitamura2007,

author={Kitamura, Yasunori and Pázsit, Imre and Yamamoto, A and Yamane, Yoshihiro},

title={Calculation of higher moments of the neutron multiplication process in a time-varying medium},

journal={Annals of Nuclear Energy},

issn={0306-4549},

volume={34},

issue={5},

pages={385-395},

abstract={The zero-power reactor noise theory in a steady neutron multiplying medium was extended recently to a medium randomly varying in time to bridge the fields of the zero-power and the power reactor noise. For a time-varying medium in which the transition probability randomly fluctuates, only the use of the probability generating function technique based on the forward master equation approach is practical. However, with the forward master equation approach, the treatment of the joint moments of the neutron number and the medium state leads to a closure problem. Recently, the capability of the moment calculation technique for such cases was extended such that the closure problem could be solved exactly. The present paper describes and demonstrates this closure-free moment calculation technique in a time-varying binary multiplying medium, in which the medium state has two possible realizations. In addition to the first two moments of the neutron number N alone (irrespective of the medium state η), the joint moments of Nn and ηm, i.e., <Nnηm>, were also obtained in a compact form for n = 1, 2 and arbitrary values of m, without a closure assumption. It was found that, for even m values, the asymptotic values of Nn and ηm are uncorrelated, whereas, for odd m values, they are negatively correlated, namely, their covariance is less than zero. The first two moments of the neutron number theoretically obtained were verified by the Monte Carlo technique. A perfect agreement was found between the Monte Carlo and the theoretical solutions. The closure-free moment calculation technique demonstrated in the present paper is expected to be applicable to various other problems related to the birth-and-death process with fluctuations of the transition probability, in which a closure problem occurs.},

year={2007},

keywords={Neutron fluctuations, zero power reactor noise, time-varying system, joint moments, master equations},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 41965

A1 Kitamura, Yasunori

A1 Pázsit, Imre

A1 Yamamoto, A

A1 Yamane, Yoshihiro

T1 Calculation of higher moments of the neutron multiplication process in a time-varying medium

YR 2007

JF Annals of Nuclear Energy

SN 0306-4549

VO 34

IS 5

SP 385

OP 395

AB The zero-power reactor noise theory in a steady neutron multiplying medium was extended recently to a medium randomly varying in time to bridge the fields of the zero-power and the power reactor noise. For a time-varying medium in which the transition probability randomly fluctuates, only the use of the probability generating function technique based on the forward master equation approach is practical. However, with the forward master equation approach, the treatment of the joint moments of the neutron number and the medium state leads to a closure problem. Recently, the capability of the moment calculation technique for such cases was extended such that the closure problem could be solved exactly. The present paper describes and demonstrates this closure-free moment calculation technique in a time-varying binary multiplying medium, in which the medium state has two possible realizations. In addition to the first two moments of the neutron number N alone (irrespective of the medium state η), the joint moments of Nn and ηm, i.e., <Nnηm>, were also obtained in a compact form for n = 1, 2 and arbitrary values of m, without a closure assumption. It was found that, for even m values, the asymptotic values of Nn and ηm are uncorrelated, whereas, for odd m values, they are negatively correlated, namely, their covariance is less than zero. The first two moments of the neutron number theoretically obtained were verified by the Monte Carlo technique. A perfect agreement was found between the Monte Carlo and the theoretical solutions. The closure-free moment calculation technique demonstrated in the present paper is expected to be applicable to various other problems related to the birth-and-death process with fluctuations of the transition probability, in which a closure problem occurs.

LA eng

DO 10.1016/j.anucene.2007.02.005

LK http://dx.doi.org/10.1016/j.anucene.2007.02.005

OL 30