The value of the product in equation 1 is of the order of 107 m2, making it evident that the required antennas are truly enormous structures and will inevitably be very costly. The only hope, therefore, of providing electricity at a reasonable cost per kilowatt is to generate a very large amount of power. It is the purpose of this analysis to show that the cost per kilowatt can be minimized and to determine the unique conditions which lead to this minimization. There are two reference or baseline SPS systems that have been studied in considerable detail, either of which may be used as a model on which a cost function may be based. The older of the two is the klystron-powered reference system which has evolved over several years of study (1). The second is the recently defined magnetron-powered system (2, 3, 4), which makes abundant use of the klystron system study results but uses magnetron tubes instead of klystrons for converting the d.c. solar power into microwave power at a frequency of 2450 MHz. We have chosen the magnetron-powered system for this study because its design is based on certain exact microwave relationships that will be given in the next section. MICROWAVE RELATIONSHIPS It proves convenient to express the microwave transmission characteristics of the system in terms of the two quantities ST and SR, which are the power densities at the centers of the spacetenna and rectenna, respectively. The reason for this is that both these quantities are constrained. There is an upper limit on ST, the density at the center of the spacetenna, which is imposed by the need to get rid of waste heat generated by the d.c. to RF converter tubes, at the same time maintaining temperatures on the spacetenna at some safe level. In the case of SR, the limit is actually imposed by the ionosphere and not by any mechanism within the rectenna itself. Heating of the ionosphere by the power in the beam can create nonlinearities in that medium with serious implications for RF communications over a wide range of frequencies. The total power radiated by the spacetenna is proportional to its area and to the central power density, ST. If ohmic efficiency is r)H, then The constant K, called the aperture power coefficient, is dependent on the illumination function/}/), where/(r) is the electric field distribution, normalized such that /(0) = 1, and r is normalized radius in the circular aperture of the spacetenna. We assume that either the rectenna is in the far-field of the spacetenna or that the latter is focused on the former so that diffraction-limited conditions prevail in the focal plane. Then the power density at the beam peak in the center of the rectenna is
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