On a comparative analysis of the solutions of the kinetic neutron diffusion equation by the Hankel transform formalism and the spectral method

• We derived an analytical solution to the kinetic diffusion.
• We established a new approach of diffusion equation in a cylindrical coordinates.
• The solution for 6 delayed neutrons was founded using the spectral method.
• We apply the usual eigenfunctions for cylindrical coordinates, Bessel functions.
• We presented a comparison between integral transform and spectral method solution.

In the present work we discuss the kinetic neutron diffusion equation in homogeneous cylinder geometry. We construct solutions unaffected by a numerical artifact, known as stiffness of the equation system, for two energy groups, one and six precursor concentrations, respectively. Upon applying the Hankel transform in the diffusion equation one obtains a generalized system for the fast and thermal, and the precursor concentrations of delayed neutrons. The Hankel Transform together with the Parseval identity indicate a natural orthogonal basis that is convenient to expand solutions for extended problems in zero order Bessel functions. A direct comparison of results obtained by integral transform techniques against the results from spectral theory validate this procedure. We show numerical results for the one precursor group case as well as the six precursor group case and show consistency of the results.