A collision probability method for one-dimensional space-time nuclear reactor kinetics.

A collision probability method has been developed for the modeling of nuclear reactor kinetics in one dimension in space and in time. The method is an integral transport method which is capable of solving general nuclear kinetics problems over an unlimited time interval and an infinite number of collision generations. The time dependent collision probability method is derived by first Laplace transforming the integro-differential form of the time dependent neutron transport equation. The resulting Laplace transformed equation involving a complex total cross section is then integrated by standard means to obtain the integral form of the neutron transport equation. The Laplace transform is then inverted to obtain an integral equation for the scalar flux involving a purely real total cross section in one-dimensional slab geometry in space and in time. The integral equation is discretized using a flat flux approximation in both space and time to obtain a linear system of algebraic equations for the advanced-time discrete scalar fluxes in terms of the discrete scalar fluxes for the previous time steps. The discrete scalar fluxes are coupled to each other through approximate, but highly accurate time dependent collision probabilities which are obtained by analytically integrating the integral transport kernel over space and time. Although in theory the scalar flux at each point in space is coupled to every other point in space and to every point in time previous to the time step being solved, because of the exponential nature of the time dependent integral transport kernel the discrete integration may be truncated after a reasonable number of terms in both space and time. By assuming isotropic scattering in the lab frame of reference and utilizing transport corrected total and scattering cross sections, the scattering source may be approximated as the product of the transport corrected scattering cross section and the scalar flux without resorting to higher order scattering moments. The time dependent collision probability method has been used to simulate both one energy group time dependent neutron transport benchmark problems and multiple energy group prompt critical nuclear reactor kinetics problems. On the former, the method has demonstrated the capability to accurately reproduce analytic solutions on relatively moderate grids in space and time. On the latter, the method produces results with generally slightly higher amplitudes and integrated energy delivered than an equivalent diffusion theory code.PhDApplied SciencesNuclear engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129458/2/9513389.pd