Solution of the one-speed neutron transport equation in anisotropic scattering medium with a Pomraning-Eddington approximation approach

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Abstract In this work, a combined modified K-integral approach and Pomraning-Eddington approximation to solve the neutron transport equation for general anisotropic scattering law is presented. This combined approach leads to the establishment of general expressions of the even e(x, μ) and odd o(x, μ) functions of the angular variable μ. Both functions are slowly varying in x. Furthermore, these expressions can be reduced to those reported in literature. In addition, the parameters such as <?CDATA ${D}_{p}={\int }_{-1}^{1}{\mu }^{2p}e(x,\mu )d\mu $?> D p = ∫ − 1 1 μ 2 p e ( x , μ ) d μ and <?CDATA ${d}_{p}={\int }_{-1}^{1}{\mu }^{2p+1}o(x,\mu )d\mu $?> d p = ∫ − 1 1 μ 2 p + 1 o ( x , μ ) d μ with p = 1, 2, … are obtained without any integral calculus and the variables we used α 1, α 2, r 1 and r 2 verify the relation <?CDATA $\left({\alpha }_{1}\tfrac{{r}_{2}}{{r}_{1}}-{\alpha }_{2}\tfrac{{r}_{1}}{{r}_{2}}\right)=0$?> α 1 r 2 r 1 − α 2 r 1 r 2 = 0 . As application, diffusion lengths are calculated for linear scattering and the neutron heat fluxes are evaluated graphically for four-parameter scattering phase function.

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