For SPS (using D = I km, w = 1 E-4 km or 10 cm), L = 10,000 km or less than 'A the operating distance. Therefore R > 3L and the coherent microwave power of a given SPS beam would extend in a lobe-like (Fraunhofer) diffraction pattern across the entire hemisphere of Earth. The angular width of the main power beam of an antenna is approximately 5 = w/D which for the SPS parameters above gives s = 1 E-4 radians. The minimum beam diameter (d) at a range R is given by d = sR which gives d = 3.6 km at geosynchronous (SPS) range (36,000 km). Because the moon is 10 times farther from Earth than geosynchronous orbit a lunar antenna would have to be 10 km across rather than 1 km to send the energy of one of its beams into a spot 3.6 km across. However, for a 10 km antenna on the moon the transition distance, L, to the far field is L = 1,000,000 km. The Earth would be in the near field of the lunar antenna (R < 0.4L) and there would be little power in diffraction lobes outside the main portion of a power beam. See Steinberg (34) for a discussion of large phased arrays which can be composed of non-periodic radiators, produce geometric optic beams in the near field and be focused. To a first approximation the segmented lunar antenna can be modeled as a set of non-periodic radiators. The number (N) of radiators will be in the millions. Any one power beam will have the angular width given above. The average intensity of stray power of a given beam will be \/N of the intensity of that beam. Very large segmented antennas on the moon seem possible. The moon is an old body with very little internal energy. Horizontal and vertical ground motions evoked over large areas by deep moonquakes are the order of 1 to 10s of nm (21). Deep moonquakes are small and release the order of 1 million joules of energy per year or an average of 0.03 watts of power (12). It has been shattered to great depths by meteorite impacts and does not propagate coherent seismic waves as does Earth. Solid body tides of the entire moon are likely to be the greatest distortions. These tides are regular, predictable in their distortion and their effects can be eliminated electronically. Antennas 100 km or more across appear worthy of consideration. They would occupy only a small fraction of the visible disk of the moon and accommodate growth of the associated power systems adequate to power all foreseeable terrestrial needs. For a 100 km diameter antenna L = 100,000,000 km would pertain. The Earth and associated microwave reflectors would be well within the near field. A shared, oversized antenna aperture affords many methods for controlling multiple beams and the characteristics of any given beam such as diffraction limit, side lobe levels, position of beam center line, depth of field, and location of the focal region. The oversized array on the moon and the microwave reflectors in space can use all the modern techniques of phased array electronics and geometric optics to control the many separately directed beams simultaneously projected by each segmented array on the moon (17). Thus, both small and large receivers on Earth or in space can be equally efficient in the reception of power. A 100 km diameter lunar antenna operating with 10 cm microwave would have a minimum spot size at Earth of approximately 400 m. Most rectennas would be 2 or more times larger. A few hundred of MW of power could be received by a rectenna only a km across. Note that 1 MW/cm2 is the same as 10 MW/km2 or 0.01 GW/km2. The SPS base line was to operate at 23 MW/cm2 or 230 MW/km2 at the center of the beam. Because the SPS power beam operated in the far field most of the power was carried near the intense center of the beam. Thus, the rectenna received most of its power near its center and much less in the bulk of its peripheral area. The LPS, especially when orbital reflectors are introduced, can illuminate the rectenna more uniformly. More power can be pumped into a given field of antennas by approx-
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