are integrated over the area of the main lobe of the untapered pattern, it is seen that the n = 2, n = 3, and "ideal" cases actually put more power into the untapered main lobe area than the untapered beam does, and the n = 4 case places nearly as much. Thus, the broadening of the main lobe does not appear to be a problem. For strict safety thresholds, the total area occupied by the exclusion zones decreases substantially if the beam is tapered. For a safety threshold of 0.01 mW/cm2, the maximum reduction of total exclusion zone area occurs in the n = 4 case. Although the total main lobe area of the system increases by 72%, this is of little consequence, since the total 83.8% capture area is 54% smaller than in the untapered case. For the 0.1 mW/cm2 case, there is no advantage in going to tapers higher than n = 2. As the safety threshold is increased, the exclusion boundary falls within the main lobe; as the main lobe broadens with increasing taper, the exclusion zone area increases. These cases are denoted by asterisks in Table 3. Note also that for a safety threshold of 1.0 mW/cm2, the total exclusion zone area is larger than in the untapered case. For the 5.0 and 10.0 mW/cm2 cases, the total relative areas of the exclusion zones for the tapers considered range from 1.12 to 1.18. Thus, beam tapering is actually disadvantageous for high safety thresholds, at least from the point of view of total exclusion zone area. An additional constraint on beam tapering is the effect on the peak intensity at the transmitting antenna. From Equation la, it can be seen that this is proportional to nPt. Since P, is divided by N in the re-scaled cases, the peak intensity at the transmitting antenna varies as n/N (assuming Dt is held constant). If it is desirable to hold this intensity at or below its original value, then tapers greater than n = 5 should be avoided. Note that for the "ideal" case, the peak beam intensity is proportional to As before, N can be found by setting this expression equal to 1. 1 The peak intensity at the transmitting antenna will thus be greatly reduced in this case. Although the relative area of the main lobe is given as 2.04 in Table 3, in practice, it can be considered to be the same as that for the n = 2 case. Furthermore, the "ideal" case has a smaller total exclusion zone area than the n = 2 case for the 0.01 mW/cm2 threshold, but not for the higher thresholds shown in Table 3. Thus, the choice of taper will, to some extent, depend on safety requirements. Note that Dt is assumed to remain constant at 1128 meters (area = 1 km2) in the re-scaled system. If the reference system has a solar collector area on the order of 50 km2, then the re-scaled system will have an area of about 50/N km2, or as little as 3 km2. While it may seem impractical to retain the 1 km2 transmitting antenna size for so little (relatively speaking) collector area, recent work on thin film
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