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From transport to diffusion through a space asymptotic approach. (English) Zbl 1196.82105

Summary: The spatially asymptotic theory is a useful approach to the neutron transport model for nuclear reactor physics applications. For steady-state problems the transport equation is taken in an infinite medium and it is treated by the Fourier transform. A formal solution is thus obtained for any assumption on the order of anisotropy, leading to the \(B_N\) formulation. In the case of isotropic emissions the Green function of the problem can be given an explicit expression by the inverse Fourier transformation, leading to the solution that can also be obtained by Case method.
The analysis of the kernel of the solution in the Fourier space can give important physical information on the transport phenomenon. Lower order models can be derived by giving an approximate formulation to the exact kernel, and thus somewhat allowing a distortion of the rigorous physical transport features. A study of the eigenvalues of various models can give an important insight on the physical limits of approximations introduced.
Within the asymptotic approach an optimization strategy allows to evaluate diffusion theory parameters for realistic system calculations. A discussion on the performance yielded by various definitions is carried out by comparisons of the numerical results for a two-dimensional system. The results presented evidence the impossibility to have a general formulation of diffusion parameters capable to perform satisfactorily in all physical situations.

MSC:

82C70 Transport processes in time-dependent statistical mechanics
82D75 Nuclear reactor theory; neutron transport
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