Abstract
Targets designed for medical radionuclide production typically contain a foil that separates the accelerator vacuum from the target material and which must retain its integrity while being heated by 30 μA beams. The heat flow equation is solved in order to determine the radial temperature distribution across this foil and its dependence on different materials of various thickness. All three forms of heat transfer, radiation, forced convection and conduction, are considered in this mathematical treatment. The resulting nonlinear differential equation is solved by the method of successive approximations to determine a temperature distribution that is proven to converge arbitrarily close to the exact solution. In addition, an upper limit is given for the maximum error in the distribution after a finite number of iterations. These results are used to calculate the amount of convective cooling that must be incorporated into a target foil design.
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