Neutron transport and diffusion in inhomogeneous media. I
Edward W. Larsen · Journal of Mathematical Physics · 1975
The asymptotic solution of the neutron transport equation is obtained for large near-critical domains D which possess a cellular, nearly periodic structure. A typical mean free path in D is taken to be of the same order of magnitude as a cell diameter, and these are taken to be small (of order ε) compared to a typical diameter of D. The solution is asymptotic with respect to the small parameter ε. It is a product of two functions, one determined by a detailed cell calculation and the other obtained as the solution of a time dependent diffusion equation. The diffusion equation contains precursor (delayed neutron) densities, equations for which are derived. The coefficients in the diffusion equation, which are determined using the results of the cell calculation, differ from those now used in engineering applications. The initial condition for the diffusion equation is derived, and the problem of determining the boundary condition is discussed.