Celsius will generate 5.5 times as much microwave power as one operating at 100 degrees Celsius. It follows, therefore, that a device that is both highly efficient and which can feed heat into its allowed heat disposal area at a high temperature has a great advantage over a moderately efficient device operated at a low temperature. It may be of interest to apply this tube to a scenario in which the transmitting antenna is radiating 7 gigawatts of power to produce 5 gigawatts of DC power output at the rectenna on the ground. The average radiated power density over the 785,000 square meter antenna ( one kilometer in diameter) is then 8.9 kW/m2. However, the distribution of transmitted power over the face of the antenna to reduce sidelobes will approach that of a truncated gaussian for which the peak to average power may be about 3. The corresponding peak radiated power density at the center of the antenna is then 27 kW/m2. Now, if figure 3 is examined it is noted that 27 kW/m2 is near 32 kW/m2 radiated power density that requires both high efficiency of the microwave generator (85%) and high radiating temperature of 300°C (573 Kelvin). It is also desirable that the conversion device be cooled by direct passive radiation into space rather than being indirectly connected to the heat radiator with a liquid or vapor cooling system. Active cooling systems have a reliability disadvantage because of the danger of being punctured by passing debris which would create a vapor which could be ionized by the microwave or high voltage DC power and cause electrical loss and breakdown. Theoretical Study of Magnetron Directional Amplifier Radiation Cooling During the NASA/DOE sponsored study of the Solar Power Satellite in the 1977 to 1980 time period, the magnetron with its high efficiency, mechanical simplicity, and ability to behave as a phase-locked amplifier with added external circuitry was evaluated as a candidate for the microwave generator in the Solar Power Satellite [1], This study, in combination with studies of a slotted waveguide array, produced a design of a radiating module like that shown in Figure 1. As shown in Figure 1, the magnetrons with their circular radiators are thermally isolated from the front of the radiating module so that solid state sensing and control devicescan be placed on the front of the array. This allows the tubes and their radiators to be operated at high temperature on the back side of the array although the radiators can radiate effectively from one face only. The earliest studies on the microwave generator tube for the SPS quickly zeroed in on pyrolytic graphite (also referred to as "pyrographite") as a preferred material for the radiator [1,4]. In the range of 100 degrees to 300 degrees Celsius the annealed or heat-treated pyrolytic graphite has a heat a conductivity twice that of copper as shown in Figure 4 and it has a density of only 2.0 as contrasted to 8.9 for copper. Further it has a natural emissivity of 0.92 and a negligible vapor pressure at the intended operating temperature. It was also assumed that for purposes of data computation the radiator was radiating into deep space with a temperature of near 0 degrees Kelvin.
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