Authors & Affiliations
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
The paper analyzes the transformation of the continuous and discrete spectrum of a one-velocity neutron transport equation using the example of the discrete ordinate method. It is shown how, with such a discretization, the region of the continuous spectrum is filled with individual eigenvalues, the discrete part is more and more accurately described depending on the order of the Gauss quadrature.
Known analytical solutions for an infinite medium with an external source constructed in the space of generalized functions with integration over the continuum of eigenfunctions are compared with so-lutions obtained in the form of expansions on the systems of finite-dimensional eigenfunctions of the ordinate method. The calculations performed for two subcritical systems with the parameter C=0.9 (breeding medium with K∝≈0.9) and C=0.5 (weakly breeding medium) with an isotropic and directed neutron source.
Calculations have shown that the use of complete systems of eigenfunctions and eigenvalues makes it possible to analyze the accuracy of deterministic calculations of neutron fluxes, in particular the accuracy of asymptotic and transition parts, which is important for many problems of neutron physics.
neutron transport equation, matrix representation, system of eigenvalues and eigenvectors, asymptotic and transient solution
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