The method of subgroups for considering the resonance structure of the cross sections in neutron calculations (part 1)

Nikolaev, M.N.; Игнатов, А. А.; Isaev, N. K.; Khokhlov, V.F.

doi:10.1007/bf01338769

Cited by 37 publications

(7 citation statements)

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“…The more accurate treatment utilizes probability tables to account for the fine-scale variability of the cross sections in the URR. The probability table method [Nikolaev, et al, 1970;Levitt, 1972] divides the range of total cross section values into discrete bands. The probability tables consist of band-averaged total and partial cross sections, and the probabilities that the total cross section lies within each band.…”

Section: The Unresolved Resonance Rangementioning

confidence: 99%

The Physical Models and Statistical Procedures Used in the RACER Monte Carlo Code

Sutton¹,

Brown²,

Bischoff³

et al. 1999

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Section: The Unresolved Resonance Rangementioning

confidence: 99%

The Physical Models and Statistical Procedures Used in the RACER Monte Carlo Code

Sutton¹,

Brown²,

Bischoff³

et al. 1999

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“…The subgroup methods [1][2][3] have been used in reactor calculation as a convenient tool to treat the resonance selfshielding effect. The basis of the method is to use multiple averaged cross sections (subgroup cross sections) and the probabilities (subgroup probabilities) according to the level of total cross section, and the self-shielding effect of each 'subgroup' can be treated independently.…”

Section: Introductionmentioning

confidence: 99%

“…The method is especially important because of the capability of treating the location dependence of the self-shielding effect. [4][5][6] In order to determine the subgroup parameters, two methods, the fitting method 1) and the moment method 7) are widely used.…”

Section: Introductionmentioning

confidence: 99%

A Generalized Approach to Optimize Subgroup Parameters

Yamamoto

2004

Journal of Nuclear Science and Technology

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The comparison of the two subgroup methods, the fitting method and the moment method, was made. It was proved that the both methods are identical under a special condition for the background cross section. More detailed analysis was done from the actual derivation process of the two methods and a generalized formulation was shown that is applicable to the both methods. It became clear that the moment method is regarded as a modified version of the fitting method with a flexible weighting function. It was also concluded that the two methods are identical when the parameter of the moment method takes a specified value (I¼1).Two optimization procedures were proposed to obtain the best subgroup parameters by the use of the least square fitting. One of the methods enables to reduce the error in effective cross section from 6 to 2%.

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“…In recent years, the subgroup methods [1][2][3][4] have been widely applied to reactor calculations in order to treat the resonance effect of heavy elements contained in nuclear fuel. The basis of the method is to use multiple averaged cross sections (subgroup cross sections) and the probabilities (subgroup probabilities) according to the level of total cross section, and the self-shielding effect of each 'subgroup' can be treated independently.…”

Section: Introductionmentioning

confidence: 99%

A Complement Proposal for Optimization of Subgroup Parameters

Yamamoto

Takeda

2006

Journal of Nuclear Science and Technology

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A new theory and methodology to optimize subgroup parameters were established by the use of Chebyshev approximation. The optimization of the fitting method was realized by the minimax approximation provided by the Remes algorithm. As for the moment method, a new definition for moments was proposed to cure the poor reproducibility of effective cross section by the original moment method. The new moment method uses transformed Chebyshev polynomials as orthogonal bases. This method is mathematically stable and the efficiency was verified by a numerical example. It was also shown that use of preconditioning can furthermore enhance the efficiency. The first dominant term of the new moments can be approximated by old moment definition with ¼À0:1{À0:6, including the case with ¼À1=2. This fact can explain the efficiency of the reservation of half-integer moments in the reproducibility of effective cross section that was mentioned by Unesaki.

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The method of subgroups for considering the resonance structure of the cross sections in neutron calculations (part 1)

Cited by 37 publications

References 0 publications

The Physical Models and Statistical Procedures Used in the RACER Monte Carlo Code

The Physical Models and Statistical Procedures Used in the RACER Monte Carlo Code

A Generalized Approach to Optimize Subgroup Parameters

A Complement Proposal for Optimization of Subgroup Parameters

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