Benchmark criticality calculations for one speed neutron transport

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Benchmark criticality calculations for the two canonical problems of a critical slab and a sphere with isotropic scattering have been carried out using three different computational techniques. These approaches include the X-function and Neumann iteration, F[N subscript] method, and discrete ordinate methods. It is found that to the orders of the approximations considered here, the critical half thickness and critical radius values obtained through the three approaches are consistently accurate from 9 to 12 significant figures, and agree amongst themselves. The accuracy for the corresponding values for neutron density using X-function, and discrete ordinate method (the only two explored for the density computations) is 9 to 10 figures. In several instances, the results constitute an improvement on the previously reported benchmark results in literature. Our computational techniques have yielded highly accurate benchmark results for the critical half thickness of the slab and the critical radius of a sphere and also for neutron density. These results could be used as new benchmark values for future criticality analysis. In addition to the calculations described above, the standard Monte Carlo code, (MCNP5) has been verified against our results for the case of a critical sphere. Converged keff [eff is subscripted] and neutron density values using MCNP5 are compared with our suggested benchmark values from DO method. It is found that the neutron density values obtained by MCNP5 show a significant deviation from our suggested benchmark values using the above three methods at lower c values (or for larger spheres).