First-order numerical optimization of fission-chamber coatings using natural uranium and thorium

Presently, fission chamber technology utilizes neutron-sensitive coatings often composed of radioisotopes that are becoming increasingly difficult to obtain. Using only natural uranium and thorium, a maximized stable device lifetime in a constant neutron flux can be obtained by optimizing the regenerative fission chamber coating. A system of coupled differential equations was developed by considering neutron-induced fission, neutron absorption, and radioactive decay of 17 radioisotopes spanning the product family tree from ²³²Th to ²⁴¹Pu. By solving the system of coupled differential equations, the interaction rate of the regenerative fission chamber coating can be found as a function of time (or total fluence) in a constant neutron flux. The Kansas State University (KSU) TRIGA Mark II nuclear reactor was used as a basis to study the effectiveness of mixed fission chamber coatings over time. By varying the initial composition of the fission chamber coating, an optimal composition of ²³²Th and natural uranium is capable of maintaining stable device operation (<;5% deviation from initial response) under a constant neutron flux of 2.2 × 10¹³ n cm^-2 s^-1 up to a total neutron fluence of 7.65 × 10²² n cm^-2, corresponding to over 110 years.