A rigorous weight function for neutron kinetics equations of the quasi-static method for subcritical systems

The purpose of the present work is to develop an efficient solution method to solve the time dependent multi-group diffusion equations for subcritical systems with external sources using the quasi-static method. Usually, the k-eigenfunction for an adjoint criticality equation is used as a weight function to derive a one-point neutron kinetics equation for the amplitude function in the quasi-static method. It is shown that the use of this k-eigenfunction introduces a first order error due to the change of the flux, when the systems are not close to the critical state. It is shown also that the use of the ω-eigenfunction for the adjoint time dependent equation as the weight function can eliminate such first order error resulting from ignoring the term of first order change of the shape function to solve subcriticality problems, and it gives more accurate results than the use of conventional k-eigenfunctions of the critical adjoint equation.