The neutron transport equation can be expressed in a form identical to that of the diffusion equation in the elementary theory of diffusion. The kinetic equation expressed in such a form is defined as the kinetic diffusion equation. The kinetic diffusion equation in a one-dimensional planar geometry is derived and physical validation is given for the parameters in the equation. The physical meaning of the parameters is illustrated for the numerical solution of Milne’s problem. It is shown that the diffusion equation in the elementary theory of diffusion is a particular case of the kinetic diffusion equation. The criteria of realizability of this particular case are determined. The kinetic diffusion equation can be extended to other geometries, including multidimensional.
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V. V. Seliverstov, “Diffusion form of the transport equation and the kinetic diffusion method (application to one-dimensional planar geometry),” At. Énerg., 86, No. 1, 16–27 (1999).
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Translated from Atomnaya Énergiya, Vol. 114, No. 6, pp. 308–315, June, 2013.
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Seliverstov, V.V. Kinetic diffusion equation in neutron transport theory. At Energy 114, 381–390 (2013). https://doi.org/10.1007/s10512-013-9728-5
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DOI: https://doi.org/10.1007/s10512-013-9728-5