An Analytical Solution of the Neutron Diffusion Equation in Toroidal Coordinates

抄録

Analytical solutions of the neutron diffusion equation in the non-separable toroidal coordinate system are useful for analyses of diffusion phenomena described in the toroidal coordinate, though the solutions have not been obtained yet. By using the method developed by Weston, the problem of solving the partial differential equation in the three variables in which only one variable is separable is reduced to solving a recurrent set of ordinary differential equations in one variable. Thus, analytical solutions are obtained for the neutron diffusion equation in the toroidal coordinate. These solutions form a complet set of the solutions, satisfying the condition for representing the diffusion from a point source when the fundamental length in the toroidal coordinate d approaches zero.
As an example of applications of the solutions, the monoenergy neutron flux which takes a given value around the axisymmetrical toroidal neutron source is evaluated with high accuracy, without using the approximation of the expansion with respect to the inverse aspect ratio.