r = distance from antenna center in meters, and scale factor in meters. It follows that the waste heat flux radiated towards the structure at the center of the antenna is given by: It is interesting to observe that for a given power transmission the maximum waste heat flux is independent of This can be attributed to the fact that increasing requires increasing the power level per converter. The end result being that the waste heat per unit area remains constant (assuming constant converter efficiency). Figure 3.3-27 presents the waste heat flux at the center of the antenna as a function of the scale factor p. Two curves are shown: one for a microwave converter efficiency of 85% and the other for an efficiency of 70% which is now considered representative of the klystron performance rather than 75%. For values up to about 600 meters, exhibits a strong influence on the maximum waste heat flux. The maximum flux values that can be tolerated by three candidate materials are shown as 36 00 , 3600, and 8100 w/m for aluminum, graphite/epoxy and polyimide composites, respectively. These values establish minimum values for the scale factor p, i.e., they impose a constraint on the shape of the Gaussian distribution. For example, considering an efficiency of 70% and an aluminum structure, Fig. 3. 3-27 shows that the microwave converters will have to be spaced according to p 1100 meters, which produces a fairly flat Gaussian distribution, nearly a uniform distribution. Figure 3. 3-28 shows the waste heat profile across the antenna surface for three values of p. It clearly illustrates the effect that p has on the waste heat profile; smaller values of p producing profiles with greater waste heat concentrations at the center and lower waste heat concentrations at the perimeter, which in turn leads to greater differences in column and beam temperatures between the center and the perimeter.
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