Complex Buckling Modes in Asymmetric Cell Lattices

Hughes, R. P.

doi:10.13182/nse79-a19960

Cited by 7 publications

(3 citation statements)

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“…The critical buckling and the k eff are both real in a critical buckling search calculation in a symmetric unit cell. For an asymmetric cell, however, the buckling that is parallel to the direction having asymmetry must be complex in order to obtain a real-valued k eff (Hughes, 1979). If we persisted in the real-valued buckling in an asymmetric cell, k eff would have to be complex (Tommasi, 2015).…”

Section: Monte Carlo Methods For Complex-valued Buckling In An Asymmetmentioning

confidence: 99%

Monte Carlo method for solving a B1 equation with complex-valued buckling in asymmetric geometries and generation of directional diffusion coefficients

Yamamoto

Sakamoto²

2018

Annals of Nuclear Energy

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Direction-dependent diffusion coefficients generated using a Monte Carlo method that explicitly solves a heterogeneous B 1 equation are validated in this paper. The validation is conducted by comparing the direction-dependent neutron leakage using directional diffusion coefficients with the results of a neutron transport calculation. This paper develops a new method for critical buckling search calculation to solve a heterogeneous B 1 equation for an asymmetric unit cell in which the critical bucking has a complex value. A complex-valued critical buckling can be searched using the differential operator sampling method for estimating the sensitivity coefficients of k eff with respect to the buckling. In an asymmetric unit cell, the neutron flux and the neutron current also have complex values. The real part of the neutron flux obtained by a critical buckling search calculation represents the neutron spectrum in the center portion of the finite geometry composed of the unit cells.

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Section: Monte Carlo Methods For Complex-valued Buckling In An Asymmetmentioning

confidence: 99%

Monte Carlo method for solving a B1 equation with complex-valued buckling in asymmetric geometries and generation of directional diffusion coefficients

Yamamoto

Sakamoto²

2018

Annals of Nuclear Energy

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show abstract

“…Then the functional dependence of these maxima on the abscissas is fitted using pre-determined shapes (z mid is the abscissa of the core midplane, i.e. 14 cm here): For the core built from symmetric cells, a pure cosine shape Y ¼ cos B r ðz À z mid Þ ½ ; For the core built from asymmetric cells, a ''cosine with drift'' (Hughes 1979) …”

Section: -Cell Slab Coresmentioning

confidence: 99%

“…Furthermore, they give an example of a 1D slab core made of repeating dissymmetric unit cells where a sinusoidal macroscopic flux shape cannot be established. (Larsen and Williams, 1978) show the possibility of a neutron ''drift'' in a privileged direction within an asymmetric heterogeneous medium, and (Hughes, 1979) shows that k can be real (at least at second order iñ B) in an asymmetric cell, provided thatB itself is complex-valued.…”

Section: Introductionmentioning

confidence: 99%