ing by raindrops within the biologically sensitive levels (3= 10 ju.W/cm2). For lower levels of exposure below the Soviet safety standard, power density levels due to scattering outside of the rectenna may exceed those due to the beam geometry. At a beam frequency of 7 GHz, surface power densities within the rectenna region show an inversion of the normal situation, with the lower rainfall rate producing the largest surface scattered power densities. This is due to the fact that multiple scattering within the cloud becomes more significant with increasing drop size and increasing beam frequency. Increasing photon path lengths, along with extremely strong drop absorption, causes this behavior. However, at larger distances from the rectenna, the largest rainfall rates produce the largest surface power density levels. Similar behavior is also found at larger frequencies (10 GHz). VI. CONCLUSIONS The present investigation calculates surface power density levels, for a microwave beam propagated through various sized clouds, (a) at frequencies ranging from 2.45 to 10 GHz, (b) for beam nadir angles ranging from 0° to 60°, and (c) for a wide range of raindrop size distributions ranging from light rain to extremely heavy rainfall rates of 150 mm/h. Scattered surface power density levels outside of the rectenna remain below the Soviet exposure standard (10 /u.W/cm2) at frequencies of 2.45 and 3.3 GHz, even for extremely heavy rainfall rates. However, exposure levels outside of the rectenna may reach 100 gW/cm2 at higher frequencies for heavy rainfall rates. Therefore, from the point of view of public health and safety, the scattering of microwaves by rain clouds is not a serious problem even at larger frequencies. Exposure levels due to scattering are often smaller than those due to antenna sidelobe characteristics. Cloud shape (and orientation with respect to beam position) becomes increasingly important at large beam nadir angles. For increasing cloud width, the peak surface power density decreases, while shifting away from beam center. The effect of increased beam nadir angle is to lower transmission efficiency of the beam while increasing surface scattering. The position of large drop concentrations within the cloud may also significantly affect surface power density levels outside of the collecting rectenna. Increasing the level of scattering within the cloud decreases power density levels near the rectenna, but strongly increases those levels at greater distances from the receiver. While there appear to be no severe environmental restrictions due to scattering of the microwave beam, the total transmission efficiency may be strongly reduced by higher beam frequencies, by large beam nadir angles and by large raindrops. In order for the microwave beamed power concept to be feasible, total system efficiencies of about 60% are required. Of this total, it is estimated that transmission losses no larger than about 10%^15% can be tolerated. Beam losses due to scattering are much smaller than beam losses due to raindrop absorption. Doubling beam transmission frequency from 2.45 to 5 GHz at moderate rainfall and at a beam nadir angle of 0° in a 7 km thick cloud increases transmission loss by about an order of magnitude, from about 1% to about 10%. Increasing beam nadir angle to 45° at 5 GHz increases beam loss to about 14%. Much larger losses occur for higher frequencies, for larger beam nadir angles, and for larger rainfall rates. Acknowledgements — The authors extend their thanks to S. Wunch who typed the manuscript, Judy Sorbie who drafted the figures, and to P. Martin who proofread the manuscript and made many helpful suggestions.
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