Some properties of fluctuations of the neutron field in a nuclear reactor

Gomin, E. A.; Gorodkov, S. S.

doi:10.1007/bf01125743

Cited by 6 publications

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“…The value of σ Φ depends on the shape of the core [6]. For a large cylindrically symmetric core, C σ = 0.147 for reflection of the boundary and 0.085 for absorption, which is close to Eqs.…”

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 78%

“…But it should be remembered that the errors in neighboring cells are matched (see Fig. 1) and formula (6) works only under the conditions of (1) and (2).…”

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 98%

“…Formula (6) actually predicts the average error σ Φ of the fluxes for many variants of a single calculation with different sets of random numbers. Two Monte Carlo calculations may seem to be insufficient to confirm it convincingly.…”

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 99%

“…In the second place, it is asserted in [4][5][6] that the random variance of the cell parameters within the technological tolerances results in a large reactor in a systematic deformation of the neutron field, described by a smooth function of the coordinates. Figure 1 illustrates the deviation corresponding to this assertion, and systematic for Monte Carlo calculations, of Φ i from F in our calculation.…”

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 99%

“…The problem of this effect was investigated in [4][5][6]. The root-mean-square difference of the fluxes in the cells σ Φ as a result of the effect of the technological tolerances σ K for individual cells is determined by the formula [4] (3)…”

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 99%

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Fast assessment of the error in the neutron distribution in a large reactor in Monte Carlo calculations

Gorodkov

2007

At Energy

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It is suggested that there is a close analogy between the statistical error of local characteristics in a MonteCarlo calculation of a large reactor and random deviations of the multiplication properties of these cells from a nominal value within technological tolerance limits. It is well-known that the latter result in global and strongly correlated deformations of the neutron field which are especially noticeable in large reactors. The scale of the deformations, or the statistical error, of the neutron field is determined by a formula obtained from an analysis of the influence of technological tolerances. Model Monte Carlo calculations confirm that this analogy is correct.The efficiency of computers and the possibilities of programs for performing neutron-physical calculations by the Monte Carlo method have reached a high level. These advances make possible Monte Carlo calculations of large reactors on a larger scale. Analysis of the results of such calculations has raised several questions [1][2][3]]. An answer to one of them, concerning the statistical error of the neutron fluxes, is proposed in the present paper.We note that in the terminology used by specialists reactors whose core size is much greater than migration length of neutrons in the core are said to be large. Specifically, S >> M 2 , where S is the area of a horizontal section of the core and M 2 is the migration area of neutrons in the core. It is this ratio that is responsible for the feature which is undesirable in Monte Carlo calculations. In addition, it is assumed in the discussions below that the core consists of elements with transverse section of the same size. In light-water reactors (VVÉR, PWR), such elements are called fuel assemblies, and in reactors with graphite (RBMK) or heavy water (CANDU) coolant they are called cells. We shall use the latter term below. The area S cell of the transverse cross-section of a cell is close to M 2 , i.e., S cell~ M 2 .(1)This means that most neutrons created in a cell are also absorbed in it. We shall denote by N cell the number of cells in the core. On this basis N cell >> 1.We note that in reactors the dominant ratio of the neutron generation operator differs from 1 by the ratio ~M 2 /S, which under conditions (1) and (2) is much less than 1 -the cases studied in [1].Let us consider a two-dimensional reactor with a square core consisting of identical cells. This simplification will not result in loss of generality of the conclusions drawn below, but it will make it possible to drop details which are not important in this case. We shall assume that the reflection boundary condition holds at the core boundary, and we shall calculate such a reactor by the Monte Carlo method with N h histories. This means that an idea of the properties of the reactor will be

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Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 78%

“…But it should be remembered that the errors in neighboring cells are matched (see Fig. 1) and formula (6) works only under the conditions of (1) and (2).…”

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 98%

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 99%

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 99%

Section: Reactor In Monte Carlo Calculationsmentioning

confidence: 99%

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