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I will be conducting research in nuclear engineering, specifically in neutronics. For the design and analysis of reactor cores, knowledge of the neutron flux is necessary to predict the reactor power and temperature distributions. Generally, radiation transport codes employ either deterministic or Monte Carlo methods. While Monte Carlo solution methods have certain advantages (such as modeling of secondary particle transport), deterministic codes are generally more efficient. In addition, they are better suited for examining small changes in the flux as parameters are varied. Monte Carlo codes always have a statistical uncertainty which tends to obscure small changes. For these reasons, deterministic codes are useful tools and will continue to be developed.
Within the class of deterministic methods, one can solve either the Boltzmann transport equation or the diffusion equation. The transport equation is a detailed mathematical statement of local balance of the angular neutron flux as a function of time, space, angle, and energy. Using Fick's Law, also known as the diffusion approximation, one obtains a simpler equation which lacks angular functional dependence. The diffusion approximation has limitations, many of which are encountered in a typical reactor core. With current implementations, solving the transport equation on an entire reactor core is too computationally intensive to be practical. Therefore, while designers may use transport-based codes for fuel rod or fuel assembly calculations, diffusion codes are standard for core-level calculations. With more efficient solution methods, the errors inherent in diffusion codes would be eliminated.
The advancement of transport computational methods has mirrored the rapid increase in computer memory and speed. However, as clock speeds plateau, the methods must be adapted and improved if efficiency gains are still to be achieved. One avenue is implementing efficient parallel algorithms. Another important option is continuing to seek creative new methods.
J.M. Hykes and J.D. Densmore. Non-analog Monte Carlo estimators for radiation momentum deposition. Journal of Quantitative Spectroscopy and Radiative Transfer, 110:1097-1110, September 2009.
Joshua M. Hykes, Yousry Y. Azmy, Steven H. King, Jesse J. Klingensmith, and Sebastian Schunert. Verifi cation and validation of deterministic radiation transport numerical methods, codes, and nuclear data for estimating radiation dose to patients during CT scan. In International Conference on Mathematics, Computational Methods & Reactor Physics. American Nuclear Society, May 2009.
George L. Mesina, Joshua Hykes, Donna Guillen. Streamlining the RELAP5-3D Code, International Topical Meeting on Nuclear Reactor Thermal Hydraulics, October 2007.
Guillen, Donna Post, George L. Mesina, Joshua M. Hykes. Restructuring RELAP5-3D for Next Generation Nuclear Plant Analysis, 2006 American Nuclear Society Annual Meeting, Reno, NV.
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