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UBC Theses and Dissertations

Mathematical modeling of dynamical response of medical cyclotron targets Jahangiri, Pouyan


The focus of this thesis is to understand the dynamical behavior of fluid targets under proton beam bombardment. Although the reactor-based beam-matter interaction has different applications, the motivation of this work stems from nuclear medicine, i.e. maximizing the yield of radioisotopes for medical diagnoses. This can be improved through increases in heat transfer rates to the cooling fluids. To do so, there is a need to understand the transport mechanisms in the targets during bombardment, an area which is relatively unexplored. In this thesis, we build upon the work of Wojciechowski et al. [64] and Peeples et al. [42–45] and develop a system of equations based on the conservation laws. The complexity of the model is reduced to something which is tractable through volume-averaging technique. Our modeling effort is presented in four different yet complementary studies. In the first and second studies, the model is validated against the pressure-rise of a gas target and is expanded to describe the final response of a liquid target at steadystate. Excellent agreement is achieved in all cases. In the third study, transient behavior of a liquid target is examined. In what we consider unique findings, selfsustained oscillatory behaviors were observed and captured by the model. In the last study, we seek the further limits of the model through a linear stability analysis. The existence, uniqueness, and stability of steady-state points are challenged and the conditions leading to an oscillatory behavior are identified. Finally, this work is the necessary first step in a larger research program to design cyclotron targets.

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