The Collided Flux Expansion Method for Time-Dependent Neutron Transport

The neutron transport equation for a localized isotropic burst of neutrons in plane geometry can be represented as an infinite set of equations. Kholin has solved these equations, expressing the neutron density in terms of an infinite series of integrals. These integrals are evaluated numerically by either a recursion relation or a Chebyshev-Gauss quadrature approximation. The neutron density found by this method serves as an analytic “benchmark” to which other solutions to the time-dependent transport equation can be compared. A new closed form of the solution is also derived.