Diffusion approximation

A transport closure in which a current is proportional to the negative gradient of a scalar field. It discards detailed angular dependence and becomes unreliable where a nearly isotropic local distribution cannot be assumed. Effective coefficients and boundary modelling must match the physical application.

A diffusion approximation for a scalar neutron flux, with one prescribed energy group. Its terms balance current loss, absorption, nuclear fission production and a source. A solution also requires appropriate boundary conditions.

The positive separation parameter in $-{\nabla }^2\varphi =B_g^2\varphi$ for a specified fundamental spatial mode and boundary conditions. The corresponding material parameter must match it for a source-free steady solution.

The coefficient in $\mathbf{J}=-D\nabla \varphi$ for the scalar neutron flux convention. It has dimensions of length, unlike a particle-density diffusion coefficient with dimensions length squared per time. For a single fixed speed $v$, the corresponding density diffusion coefficient is $vD$.