Diffusion approximation

A method for solving the kinetic equation of neutron (or other particles, quanta) transport. It is based on the concept of the density of a neutron flow (an unknown function of the coordinates of the inspected point and of the components of the velocity and time vector) in the form of the first two terms of the expansion into spherical functions, which depend on the angular coordinates of the neutron velocity vector. In a single-velocity stationary problem it leads to a diffusion equation.

The diffusion approximation is applicable away from sources and boundaries of domains having various properties, and yields solutions the form of which coincides with the asymptotic part of the solutions of transport equations. For improved forms of the diffusion approximation see Diffusion methods.

#### References[edit]

[1] |  S. Glastone, "The elements of nuclear reactor theory" , v. Nostrand (1954)

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[2] |  G.I. Marchuk, "Methods of calculation of nuclear reactors" , Moscow (1961) (In Russian)

#### Comments[edit]

The diffusion approximation is also applied in wave propagation and scattering problems, where the ratio of the volume occupied by the particles to the total volume of the medium is large. The method has been successfully used in the analysis of the optical fibre oximeter of blood. The use of the so-called Henyey–Greenstein formulas as an approximation for the phase function makes it possible to describe scattering from blood cells and clouds in an elegant way.

See also Neutron flow theory; Transport equations, numerical methods.

#### References[edit]

[a1] |  A. Ishimaru, "Wave propagation and scattering in random media" , 1–2 , Acad. Press (1978)

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[a2] |  B. Davison, "Neutron transport theory" , Oxford Univ. Press (1957)
[a3] |  K.M. Case, P.F. Zweifel, "Linear transport theory" , Addison-Wesley (1967)