The Degenerate Kernel Technique and Neutron Thermalization Calculations in Asymptotic Reactor Theory

The substitution of a K-term degenerate kernel expansion (DKE) for the true scattering kernel in the inscattering term for neutron thermalization calculations has been shown to recast the solution of the original speed dependent Fredholm integral operator equation into that of a speed-independent K × K matrix operator equation, which is well suited for numerical calculations: A DKE has been constructed that rapidly converges pointwise to the true scattering kernel, preserves the total scattering cross section, and contains the correct speed structure to yield accurate solutions in neutron thermalization calculations. This DKE was employed in the numerical solution of the steady-state, time-moment, time-eigenvalue, and time-dependent neutron thermalization problems within the framework of asymptotic reactor theory. A detailed numerical investigation of the DKE approximation to the free proton gas and polyethylene scattering kernels indicated that accuracy consistent with a 32 discrete speed mesh point treatment was obtained by employing a 10-term DKE. This implies that the degenerate kernel technique reduces the size of the matrix operator equations to be solved to ∼ ⅓ the size required by a discrete ordinate approach, hence implying considerable computer cost reductions in neutron thermalization calculations.