A response-based time-dependent neutron transport method

An efficient response-based solution to the time-dependent neutron transport equation in a semi-infinite slab is derived. The solution is based on polynomial expansions of the source terms and neutron flux in the time domain. The expansion coefficients of the flux solution are computed in terms of response functions, which are special cases of Green’s functions for arbitrary in-volume and surface sources. The resulting response equation, which is a convolution integral equation in time, is reduced to a linear algebraic system of equations in the expansion coefficients. Two example problems are solved using the response-based method, and the extension of the method to general (finite, heterogeneous) problems is discussed.