Space-time dependent impulse response of a subcritical cylindrical reactor

In this paper, a new formulation of the spatial dependent impulse response of a subcritical reactor in a cylindrical geometry is proposed. An expression of the transfer function between a point source at the center of coordinates and the flux at a given point (r,z) is obtained by solving: by means of Laplace transform, the one group diffusion equation. In this transfer function, variables r and p (p being the Laplace variable) remain linked within a modified Bessel function. Taking the inverse Laplace transform is done by two different ways: - using the Mellin-Fourier method which separates variables r and t. This method makes it possible to establish that there is identity between the classical formulation and the new one. - using an inverse Laplace transform which keeps variables r and t linked. This method requires to approximate the inverse Laplace transform of the end factor. It is then possible to replace the radial harmonics modes series of the classical expression by a single function. This new formulation seems to be of particular interest when dealing with reactors of large size and lifetime. It is also interesting each time the harmonics play an important role. (author)