One-dimensional fast neutron spectrum calculations based on the new continuous slowing down model

Recent works in application of the continuous slowing down theory to fast reactor spectrum calculations have successfully demonstrated its usefulness, in the representation of fine spectra and in the extreme reduction of computation time. However, these works are restricted to the space-independent neutron spectra. In this paper, an extension to space-dependent problems has been attempted with the use of a new continuous slowing down model typical of the Greuling-Goertzel equation derived by authors. The numerical treatments, in space-dependent problems, consume surprisingly much time to obtain the results corresponding to the fine or ultra fine group spectra. Therefore, the analytical treatments have been carried out as follows. The continuous slowing-down equation is based on the one-dimensional diffusion equation for multi-region reactors in plane geometry. This new equation is solved by applying the Laplace transformation on a space variable. As compared with the Age-diffusion equation, the rigorous inversion of this Laplace transformed equation is very difficult to solve analytically in general. The authors here propose that the expression of this inversion could be described by means of an infinite number of Age-like solutions, which use the age defined by the second moment on the space of the Greuling-Goertzel diffusion equation. Thus, the analytical approach is easily realized. After some manipulations, the continuous slowing-down equation is transformed into the integral equation of the lethergy u for the unknown flux and current at the outermost boundaries of a reactor. The flux and current in a region are determined with the aid of the transfer matrix, as in the case of the Lie-series method