km, is incident at the top of the atmosphere (15 km in the present investigation). Ionospheric interactions with the beam are neglected, being outside of the scope of the present study. Photon paths are traced through the cloud until they are absorbed or scattered either back out of the atmosphere or to the surface. The total number of photon paths is chosen so that about 25,000 photons are scattered to the surface, allowing adequate statistics of surface power density levels. A uniform distribution of photons is assumed in most cases with a uniform power level across the beam of 12.7 mW/cm2, Actual beam configurations are dependent upon the required sidelobe suppression and beam frequency. In many cases it may be expected that up to 5% of the total beam power will fall outside of the 5 km-in-diameter rectenna. The results in this section examine several important microwave beamed power parameters as well as beam interaction with various rain cloud shape and attenuation parameters. First, the transmission efficiencies and surface power densities are computed as a function of beam frequency. Second, the effect of cloud temperature is discussed. Third, calculations as a function of beam nadir angle are presented. Fourth, the effect of cloud size on surface power densities is examined. Last, the effect of various drop size distributions upon transmission losses and surface power densities are compared. The drop size distribution is assumed as a first approximation to be vertically and horizontally homogeneous. Unless otherwise noted, beam nadir angle has been selected to be 0°, and rain cloud dimensions are 7 km in vertical extent and 24 km on a side. Clouds of this arbitrary size structure are used as a basis for later comparison with other cloud shapes. Cumulonimbus clouds are generally smaller than 24 km in diameter, while nimbostratus clouds are generally less than 7 km in vertical extent. A. Beam Frequency The Rain M drop size distribution (Table 2) arbitrarily has been chosen for the preliminary set of calculations presented in Table 4a. The effect of various beam frequencies from 2.45 to 10 GHz is examined at beam nadir angle of 0°. At 2.45 GHz, all but 84 MW of the total 10 GW of beamed-power propagates directly through the rain cloud without absorption or scattering. Of this loss to the beam, about 8 MW is scattered to the surface, 0.7 MW is scattered back to space, and 75 MW is absorbed by the cloud. The greatest loss to the beam power at all frequencies is absorption by drops within the cloud. The attenuation of the beamed- power increases rapidly with increasing frequency. Doubling the frequency from 2.45 to 5 GHz at this particular cloud optical depth increases beam attenuation to approximately 1.0 GW (or 10% of the total beamed-power); at 7 GHz the loss has increased to 2.2 GW, while at 10 GHz the loss is 4.1 GW (or 41% of the total beamed-power). It is generally assumed that beam transmission efficiencies of about 85% are acceptable for the SPS concept to be feasible, so that total attenuation losses of about 15% to the beam power are tolerable. Greater losses would make the proposed system efficiencies too low to be economically competitive with alternative energy approaches. Therefore, the previous discussion indicates that beam frequencies of up to about 5 GHz may be tolerable for conditions of medium-to-heavy rainfall rates. Much larger attenuation losses to the microwave beam may be experienced for very heavy rainfall conditions and at higher frequencies. However, cloud bodies with very large rainfall rates are generally fast moving and short lived.
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