percentage of powers in the main beam, are obtained forthose systems optimized for minimum sidelobes. That is, the systems constrained to 0.01 mW/cm2 asymptotically reach 98.5% efficiency while the 0.03 mW/cm2 systems approach only 97% efficiency. (These efficiencies are for perfect antennas with no phase, amplitude, or failure errors.) The optimized systems usually achieve higher efficiencies than the 10 dB Gaussian reference system. The relative sizes and performance characteristics for five configurations are summarized in Fig. 11. The first column has the 10 dB Gaussian reference system for comparison. Each of the next three systems have superior performance with lower costs, smaller rectennas, and 0.01 mW/cm2 sidelobe levels. The choice between these systems would have to be made after the actual ionospheric and thermal limits are known. CONCLUSIONS AND RECOMMENDATIONS It is recommended that the 10 dB Gaussian reference configuration be replaced with an optimal taper system. The optimal taper systems have many advantages — lower electricity costs, smaller rectennas, higher transmission efficiencies (and hence, less RFI effects), larger transmit powers, and lower sidelobe levels (0.01 mW/cm2). Since the exact ionospheric and thermal limits are not presently known, a conservative choice might be the /0 = 32 mW/cm2, To = 23 kW/m2, and 50 = 0.01 mW/cm2 single beam system which is given in column 2 of Fig. 10. REFERENCES 1. Satellite Power System: Concept Development and Evaluation Program, Reference System Report, DOE/ER-0023, October, 1978. 2. Solar Power Satellite System Definition Study — Phase II, Vol. II: Reference System Description, Boeing Aerospace Co. (Contract NAS 9-15636), NASA CR-160443, 1979. 3. L.M. Duncan and W.E. Gordon. lonosphere/Microwave Beam Interaction Study, Rice University, Contract NAS9-15212, September 1977. 4. Microwave Power Transmission System Studies — Vol. II. Raytheon Company (Contract NAS 3-17835), NASA CR-134886, 1975. 5. G. Goubau and F. Schwering, On the Guided Propagation of Electromagnetic Wave Beams, Ire Trans. Antennas Propagat. AP-9, May 1961. 6. S. Silver, Microwave Antenna Theory and Design, MIT Radiation Lab Series, McGraw-Hill, 1949. 7. C.E. Mack and H.G. Moyer, Optimization of Antenna Pairs for Microwave Power Transmission, Space Solar Power Rev. 1, 221, 1980. 8. R. Fletcher and M.J.D. Power, A Rapidly Convergent Descent Method for Minimization, Computer J. 6, 163-168, 1963. 9. I.L. Johnson, The Davidson-Fletcher-Powell Penalty Function Method: A Generalized Iterative Technique for Solving Parameter Optimization Problems, NASA-TN D-8251, March 1976. 10. C.M. Rush et al.. Performance of VLF, LF, and MF Telecommunication Systems in a Simulated Satellite Power System Environment Ascertained by Experimental Means, Radio Sci. 16, 219-239, 1981.
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