Akcasu, A. Ziya

Neutron diffusion in a randomly inhomogeneous multiplying medium with random phase approximation

Neutron diffusion in a randomly inhomogeneous multiplying medium is studied. By making use of a random phase assumption we show that the average neutron density approximately satisfies an integral equation in Fourier space, which is solved using Kummer functions. We used multi-dimensional formulation. In the case of one dimension, we obtain the result of Rosenbluth and Tao for the mean total density for large t. In the three-dimensional case, a closed form of solution is derived for the mean total neutron density. Its asymptotic behavior is also investigated for large t.