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Transport Solutions to the One-Dimensional Critical Problem

George J. Mitsis

Nuclear Science and Engineering

Volume 17 / Number 1 / September 1963 / Pages 55-64


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The new method of Case for treating the one-velocity transport equation is applied to a uniform, one-dimensional multiplying medium. The method leads to exact expressions for the neutron distribution and criticality conditions. These expressions depend on expansion coefficients which are shown to satisfy a Fredholm integral equation. The results of diffusion theory with the exact Milne problem extrapolation distance are shown to correspond to the zeroth-order approximation of the Neumann series solution to the Fredholm equation.

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