Analysis of Cluster Geometries Using the DP1 Approximation of the J_± Technique

The J_± technique is an approximation of the collision probability (CP) method in which a probability matrix is associated with each homogeneous region, and then, these regions are coupled using an interface current technique. The main advantages of the J_± technique are its speed and the fact that the probability matrix associated with each region is completely decoupled from its environment. Previous work using the DP0 approximation of the J_± technique has been carried out for cluster geometries. Here, the DP1 approximation is investigated, and in addition to the uniform angular flux contribution, linearly anisotropic contributions are also considered. For cluster geometries, this results in an approximation for the angular fluxes of the form ψ(r_s,Ω) = a + b(Ω.N), where a and b are expansion coefficients to be determined, Ω is the neutron angular direction, and N is normal at surface s. A surf ace fractioning correction is also introduced to remove the diffraction effect that arises when using the J_± method in two-dimensional geometries. The results obtained by means of the DPI approximation are now very close to those of the CP method.