Complex problems arising in the collision probability theory for neutron transport

Several comprehensive but time consuming neutronic codes are available for performing nuclear reactor and fuel cycle evaluations. In addition, simple models utilizing collision probability theory are used to perform similar tasks with reasonable accuracy. However, the current collision probability theory treats the heterogeneous reactor configurations with a two region unit cell model. This model does not address several important reactor parameters including spatial self-shielding effects and simultaneous use of different reactor fuels within a reactor core. This dissertation studies the fidelity of expanding the collision probability theory to address the stated shortcomings through analyzing two problems. Problem 1 analyzes the effects of self-shielding. The cylindrical fuel region is divided into several sub-regions and an overall equivalent escape probability from the entire fuel region is developed based on the identified neutron transmission and escape probabilities within each fuel sub-region. The multiplication factor and radioisotopic inventory results based on modified V:BUDS (Visualize: Burnup, Depletion, Spectrum) code are in good agreement with benchmark scenarios for a reactor unit cell. The accurate multiplication factor calculation allows more accurate studies on the maximum fuel burnup and radionuclide inventories of interest in nuclear non-proliferation studies. Problem 2 analyzes the effects of simultaneous use of different fuels within a fuel lattice where the zero neutron leakage assumption across the unit cell boundaries is not valid. The developed methodology expands capabilities of the collision probability theory to a supercell model that allows existence of two different fuels. The radioisotopic inventory results for different fuels obtained from the modified V:BUDS code are in excellent agreement with the benchmark problems. These accurate results may be used in general fuel cycle and transmutation studies within power reactors.