The An method and the spherical-harmonics approximation in neutron transport theory

Abstract

The work presented in this paper completes the theoretical analysis that concerns the use of the A n approximate method in solving the monokinetic neutron transport equation. The method has been devised from the integral form of the transport equation and is connected to a proper approximation of the transport kernel which may be accomplished by means of a general integration formula. It is prove that under a suitable chois of the A n approximation parameters, namely referring to the classical Gauss-Legendre integration technique, the system of space second-order differential equations which constitute the method may be cast into a form perfectly equivalent to the P N model, for any geometry. On the other hand, when used to describe plane geometry systems only, the A n method may be seen to be always equivalent to the discrete ordinate one.