SPACE SOLAR POWER REVIEW T Volume 3, Number 1, 1982 • • £
SPACE SOLAR POWER REVIEW Published under the auspices of the SUNSAT Energy Council Editor-in-Chief Dr. John W. Freeman Space Solar Power Research Program Rice University, P.O. Box 1892 Houston, TX 77001, USA Associate Editors Dr. Eleanor A. Blakely Lawrence Berkeley Laboratory Colonel Gerald P. Carr Bovay Engineers, Inc. Dr. M. Claverie Centre National de la Recherche Scientifique Dr. David Criswell California Space Institute Mr. Leonard David PRC Energy Analysis Company Mr. Hubert P. Davis Eagle Engineering Professor Alex J. Dessler Rice University Mr. Gerald W. Driggers L-5 Society Mr. Arthur M. Dula Attorney; Houston, Texas Professor Arthur A. Few Rice University Mr. I.V. Franklin British Aerospace, Dynamics Group Dr. Owen K. Garriott National Aeronautics and Space Administration Professor Norman E. Gary University of California, Davis Dr. Peter E. Glaser Arthur D. Little Inc. Professor Chad Gordon Rice University Dean William E. Gordon Rice University Dr. Arthur Kantrowitz Dartmouth College Mr. Richard L. Kline Grumman Aerospace Corporation Dr. Harold Liemohn Boeing Aerospace Company Dr. James W. Moyer Southern California Edison Company Professor Gerard K. O'Neill Princeton University Dr. Eckehard F. Schmidt AEG—Telef unken Dr. Klaus Schroeder Rockwell International Professor George L. Siscoe University of California, Los Angeles Professor Harlan J. Smith University of Texas Mr. Gordon R. Woodcock Boeing Aerospace Company Dr. John Zinn Los Alamos Scientific Laboratories Editorial Assistant: Edith R. Mahone Editorial Office: John W. Freeman, Editor-in-Chief, Space Solar Power Research Program, Rice University, P.O. Box 1892, Houston, TX 77001, USA. Published Quarterly. (ISSN 0191-9067)
0191 -9067/82/010001-01 $03.00/0 Copyright ® 1982 SUN SAT Energy Council EDITORIAL Ben Bova's new book, The High Road, makes a compelling case for a stronger U.S. space program. The book is important because it speaks to a general audience. It carries the argument for space to the American people in a very forceful way. In the book, Bova deplores the lack of commitment and follow-through following the Apollo program. He examines the fallacy of the “Politics Scarcity" and how the “we can't afford it syndrome” becomes a self-fulfilling prophecy. He demonstrates how the space program has paid for itself many times over. But the real message of The High Road is the necessity for commitment and determination. Space can give this country a new beginning, but human “will” must make it happen. That “will” must transcend political winds. Two ways in which this can happen are through a greater private enterprise interest in space and through private foundation support for space research. Two new U.S. initiatives have recently emerged aimed at this goal. These are the establishment of Space Services Inc. and The Space Foundation. Space Services Inc. has set itself the ambitious goal of developing its own launch vehicle system for commercial use. The Space Foundation is supporting the industrialization of space by providing graduate student fellowships and thesis awards for space utilization related graduate research. The first of these awards were made to eight students in Houston, Texas, October 27, 1981. These two initiatives are bold symbols that the American “will” is alive and well. Again, the follow-through must continue. John W. Freeman Editor-in-Chief
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0191 -9067/82/01 OOO3-O5$O3.00/0 Copyright ® 1982 SUNSAT Energy Council LETTER TO THE EDITOR To the Editor: The paper “Space Settlements and Extraterrestiral Resources — What Benefits to SPS Construction' ' (1) constitutes one of the first of many works which will focus on the benefits of using nonterrestrial materials (NTM's) to construct systems in space supportive of a wide range of human and human directed activities. The topics to be explored are clearly at least as vast as those related directly or indirectly to industrial activities on Earth and will profit from the work of many people from this period of time onward. At the end of these comments, we have appended a reference list of recent work relevant to studies on space industry, space solar power systems (SPS), and space habitation. Portions of the compilation were conducted by Mr. P. Puzo under contract to the California Space Institute. An annotated bibliography is available from the California Space Institute on these and other entries. Mr. Woodcock explores in this paper some of the interactions between the costs of providing habitats in deep space for workers producing SPS and the costs of constructing SPS. We raise several points of disagreement with the contentions of the paper and direct the reader's attention to several problem areas which we feel are of economic significance to industrial systems in space using solar energy and NTM's. In particular, we feel that several of the references (2,3) consider in greater detail the development of evolutionary strategies for the growth of space industries. Mr. Woodcock challenged the general results of a recent study conducted by the General Dynamics Corporation with respect to the construction of SPS from lunar materials (4). The study ground rules stated that the NASA/Johnson Space Center reference SPS program, derived primarily from Boeing data, was to be used without modification as the basis for lunar resource utilization (LRU) comparison with corresponding Earth baseline studies. Second, the most cost effective LRU concepts were to be defined and compared to the exiting Earth baseline. Thus, the LRU study had no control over the Earth-baseline case. The LRU study assumed a great deal more automation than the Earth baseline. Increased automation does indeed give LRU an unfair advantage but the study personnel felt this approach was philosophically correct. It was also required that all facilities were to be deployed from Earth. No use of lunar materials would be made in the construction of any portions of the facilities of production either on the Moon or in space. Woodcock contends the costs of producing parts by LRU were 6 times less than for terrestrial production. This contention is not correct. In comparing the cost to produce satellites both RDT&E and actual production costs must be considered. In the Earth baseline, production costs include an allocation of facilities cost through
overhead. Conversely, in the LRU options, facilities costs are a part of RDT&E. To obtain a proper comparison facilities, RDT&E and production costs must be added. The results are compared in Table 1. Woodcock indicates that nonrigorous techniques were used in the estimation of labor costs in the LRU study. This is not the case. The so-called “grass roots” technique was used only in the estimating of salaries of space workers. The primary LRU study estimating technique, like Woodcock's, was the use of cost estimating relationships based on historical data. The question of labor union activities in affecting labor rates is only one of many factors which may contribute to obtaining efficient space manufacturing costs. The primary issue is not less salary per worker but the fact that there are fewer workers in the space-based scenarios than for the terrestrially supported scenarios. The LRU study used 1500 people in space. The terrestrial model had many thousands (over 500,000) on Earth and approximately 500 to 1000 in space, in some cases. The LRU study does not imply that space workers will work for less than Earth workers. Salaries are a primary economic factor in space operations only if many more workers are required in space for the LRU approach than are required in space for the terrestrial baseline models. The Woodcock approach to determining “realistic” space manufacturing costs is to back out the labor assuming that the labor content does not change from Earth to space. The immediate question is Why bother backing out the labor if you have the costs already? Woodcock himself maintains that worker salaries are not a primary economic factor, so what is the objective of this particular discussion? The second question is How can one assume that the labor content does not change from Earth to space? The LRU study assumed that LRU manufacturing must be more automated than Earth based, thus the labor content is less. Using his method, it would take 82,000 workers for the LRU scenario. The LRU scenario employs a total of 1500-2000 space workers. The LRU economic analysis included a sensitivity study which Mr. Woodcock failed to mention. It took into account LRU cost variations (including personnel requirements) and their effect on the earth baseline comparison. The requirement for 82,000 space workers, however, was not one of the variations considered. New approaches toward the manufacture of SPS using NTM's should offer many advantages for space production. This was one of the major results of a study by the Massachusetts Institute of Technology (5). The needs to design systems elements to
simultaneously be of very high efficiency of operation, low specific mass (for example kW/kg), adaptable to launch from Earth onboard a rocket, able to be packaged, unpacked, and assembled and so on, can be relaxed or circumvented by space manufacturing. The weightlessness and vacuum of space permit considerable simplifications in the design, embodiment and operation of systems for the high volume fabrication than can be conducted on Earth. We note that Woodcock is already assuming the use of lunar derived oxygen for use as propellant. The rate of mass processing and the type required is not appreciably different from that associated with construction of SPS's from NTM's. Large space structures considered to date (including SPS) are extremely redundant in both basic units of construction and in assembly operations. It seems very likely that manufacturing systems with a high degree of redundancy or parallelism can be used. The first complete production units may be rather small, perhaps compatible with deployment in a few shuttle missions. If significant fractions of the manufacturing systems can be produced from lunar materials then growth may be decoupled from labor, production, and investment considerations on Earth. The MIT study supports the possibilities of parallelism and considerable flexibility of output products of initial small space manufacturing facilities (SMF). There are terrestrial analogues to the high levels of automation production assumed in the LRU and MIT studies. Current automated production facilities can be used to assess whether the LRU study estimate for space workers is reasonable. The Nissan (Datsun) Assembly Plant at Zama, Japan, is 97% automated. It produces automobiles, which are more complicated than SPS components, at a rate of 8.2 metric tons/day-worker. To build one 10 GW SPS per year requires manufacturing of 374 tons/day of components, based on LRU study assumptions of 112,200 ton SPS mass and 300 working days per year. This requires 46 workers each producing 8.2 tons/day. Obviously additional in-space personnel will be required for such functions as materials processing, stock production, detail parts manufacturing, facility maintenance, and service. Except for maintenance and services, these can and should also be highly automated. The LRU study estimated 1400 SMF personnel. It is estimated that 540 workers were required for SPS final assembly based on Boeing's estimate. The LRU study used Boeing's estimate for final assembly personnel and facilities weight and cost. Thus 860 inspace personnel remain for manufacturing SPS components and subassemblies. This is a factor of 18 more than the 46 required for existing highly automated, complicated production processes and seems to be a very conservative estimate. The Woodcock model that requires the transport into space of more than 82,000 personnel and the need for construction of very large initial habitats does not appear to be justified. As previously noted, Woodcock contends that habitat construction paces the economic development of SPS construction using NTM's because of the large number of workers (more than 82,000). He then proposes an evolutionary development of habitats which eventually leads to large constructs made in part from NTM's. We note that this scenario is not intrinsically different from that explored in Ref. 1 except that in the production of one 10 GW SPS each year the SMF could be constructed of assemblies of modified shuttle propellant tanks which are encased in several meters of lunar soil for radiation protection of the crews. There is not a requirement for the immediate production of large monolithic habitats are argued by Woodcock. However, this early SMF or others like it could be adapted to manufacture such habitats. It seems clear at this time that major investments (tens of billions of dollars) will be required to bring economically beneficial space industries into existence. One of
the points which O'Neill (3) made with respect to SPS construction using NTM's was that the system must grow at a reasonably rapid rate using internal resources. This point still seems generally valid and should be subjected to much more analysis. At least one generalized model of growth via NTM's has been developed (6). One aspect of growth via NTM's is mass multiplication (7). This means that the total of all mass brought from Earth (reagents, equipment, support facilities, transportation fluids, etc.) should be significantly less than the total mass of NTM's processed by the system over its life. Ideally one would like an infinite ratio. That is, produce all goods from space resources and bring nothing from Earth. However, this is very likely not necessary for commerce in cis-lunar space and in fact the use of lunar resources may sharply decrease the cost of Earth to space transportation and allow a much greater materials commerce between cis-lunar space and the Earth than is generally anticipated. Woodcock notes that the use of lunar materials or nonterrestrial materials in general is not in the “main stream” of space industrialization research and planning. We vigorously disagree and assure the reader we are not overcome with dejection in the face of such rejection. Rather, we expect a flow of progress in NTM's interest which will shift the river banks of the main stream. We feel even Mr. Woodcock is getting into the swim (or drink) with us and welcome others to join. Naturally the water will have to be made in part from lunar and other NTM's. David R. Criswell Visiting Research Physicist California Space Institute (UC-San Diego) Edward H. Bock General Dynamics Corp. Convair Division, San Diego, CA REFERENCES 1. G.R. Woodcock, Space Settlements and Extraterrestrial Resources—What Benefits to SPS Construction, Space Solar Power Review (to be published). 2. U.S. National Aeronautics and Space Administration, Space Resources and Space Settlements, John Billingham er al., eds., NASA Special Publication 428, Technical Information Branch, Washington, DC, 1979. 3. American Institute of Aeronautics and Astronautics, Space-Based Manufacturing from Nonterrestrial Materials, Gerard K. O'Neill, ed., Progr. Astronaut. Aeronaut. 57, 1977. 4. General Dynamics Corporation, Convair Division, Lunar Resources Utilization for Space Construction: Final Report, Edward H. Bock, Study Manager, Contract No. NAS9-15560, 1979. 5. Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Extraterrestrial Processing and Manufacturing of Large Space Systems, NASA Contractor Report 161293, NASA, Washington, DC, 1979. 6. A.H. Goldberg and D.R. Criswell, The Economics of Bootstrapping Space Industries — Development of an Analytic Computer Model, Space Solar Power Review 3, 73-94, 1982. 7. R.D. Waldron et al.. Role of Chemical Engineering in Space Manufacturing, Chem. Eng. 86, 80-94, 1979. 8. American Astronautical Society, The Future United States Space Program, Proceedings of the 25th AAS Anniversary Conference, Adv. Astronaut. Sci. 38, 1979. 9. U.S. Department of Energy and U.S. National Aeronautics and Space Administration, Final Proceedings of the Solar Power Satellite Program Review, DOE/NASA, Washington, DC, 1980. 10. U.S. National Aeronautics and Space Administration, Radiation Energy Conversion in Space, Kenneth W. Billman, ed., Prog. Astronaut. Aeronaut. 61, 1978. 11. American Institute of Aeronautics and Astronautics, Proceedings of the Fourth Princeton/AIAA Conference on Space Manufacturing, J. Grey and C. Krop, eds., AIAA, New York, 1979.
12. American Institute of Aeronautics and Astronautics, Proceedings of the Princeton/AIAA/NASA Conference on Space Manufacturing Facilities (Space Colonies), J. Grey, ed., AIAA, New York, 1975. 13. American Institute of Aeronautics and Astronautics, Proceedings of the Third Princeton/AIAA Conference on Space Manufacturing Facilities, J. Grey, ed., AIAA, New York, 1977. 14. American Institute of Aeronautics and Astronautics, Technical Committee on Space Systems, Space Transportation Systems 1980-2000, AIAA Aerospace Assessment Series, Vol. 1, 1978. 15. S.R. Taylor, Lunar Science: A Post-Apollo View, Pergamon Press, New York, 1975. 16. K.A. Ehricke, Lunar Industries and Their Value for the Human Environment on Earth, Acta Astronaut. 1, 585-682, 1974. 17. U.S. House Committee on Science and Technology, Subcommittee on Space Science and Applications, International Space Activities 1979, U.S. Government Printing Office, Washington, DC, 1979. 18. U.S. National Aeronautics and Space Administration, Handbook of Lunar Materials, R.J. Williams and J.J. Jadwick, eds., NASA Reference Publication 1057, NASA, Scientific and Technical Information Office, Washington, DC, 1980. 19. U.S. National Aeronautics and Space Administration, Space Settlements: A Design Study, F. Johnson and C. Holbrow, eds., NASA Special Publication 413, NASA, Scientific and Technical Information Office. Washington. DC, 1977. 20. U.S. National Aeronautics and Space Administration, Summer Workshop on Near-Earth Resources, J.R. Arnold and M.B. Duke, eds., NASA Conference Publication 2031, NASA, Washington, DC, 1978. 21. U.S. National Aeronautics and Space Administration, Extraterrestrial Materials Processing and Construction; Final Report, D.R. Criswell, Program Director, NASA, Washington, DC, 1978. 22. U.S. National Aeronautics and Space Administration, Extraterrestrial Materials Processing and Construction; Final Report, D.R. Criswell. Program Director, NASA, Washington, DC, 1980.
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0191 -9067/82/010009-21 $03.00/0 Copyright ® 1982 SUN SAT Energy Council METEOROLOGICAL EFFECTS ON LASER PROPAGATION FOR POWER TRANSMISSION R. E. BEVERLY III Consulting Physicist 1891 Fishinger Road Columbus, Ohio 43221 Abstract — Potential mitigation techniques which can minimize the deleterious effects of inclement weather on space-to-Earth power transmission using lasers have been examined, including the choice of laser wavelength, propagation zenith angle, receptor-site elevation, and the potential of laser hole boring. An extensive series of propagation calculations have been performed to estimate the attenuation due to molecular absorption and aerosol absorption and scattering. All commonly encountered meteorological conditions have been modelled, including haze, fog, clouds, rain, and snow. Spectral windows at 2 and 11 gm were identified which permit the highest transmission efficiency for low- and high-elevation receptor sites, respectively, under various meteorological conditions. A new method of hole boring is proposed which is environmentally innocuous and which meets safety standards imposed for accidental specular or diffuse reflection of the beam within the atmosphere and the concomitant random-pointing hazard. A repetitively-pulsed (~ 100 pulses/sec), high peak-power-density (~ 105 W/cm2) laser beam is superimposed on the low-power-density, continuous-wave primary beam resulting in shattering of the obscuring aerosol but with a beam having a combined average power density of only — 10 W/cm2. INTRODUCTION Lasers are presently being evaluated as an alternate power beaming technique to microwaves for space-to-Earth power transmission. Although preliminary studies (1) indicate that laser power transmission has the advantages of negligible environmental damage and small land requirements associated with the receptor sites, meteorological conditions influence the transmission efficiency to a much greater extent than with microwaves. With proper selection of laser wavelength, clear-air propagation can be very efficient; however, haze, fog, clouds, and rain can severely attenuate the beam. This study investigates potential mitigation techniques which may minimize this effect by a judicious choice of laser operating parameters. In particular, the influence of laser wavelength and receptor elevation on transmission efficiency under realistic meteorological conditions is examined. The viability of hole boring through obstructing aerosol formations is quantitatively evaluated consistent with safety and environmental concerns. Finally, laser operating conditions are recommended which will afford the largest receptor power availability for typical mid-latitude sites. Research supported by Rockwell International Corporation, Space Operations and Satellite Systems Division (NASA/MSFC Prime Contract No. NAS 8-32475).
PROPAGATION CHARACTERISTICS UNDER VARIOUS METEOROLOGICAL CONDITIONS Physical Mechanisms The attenuation of laser radiation passing through the Earth's atmosphere is termed linear attenuation if the processes responsible are independent of the beam intensity. In general, molecular scattering, molecular absorption, aerosol scattering, and aerosol absorption contribute to linear attenuation. Beam attenuation and spreading due to turbulence, another linear mechanism, are negligible for space-to- Earth power transmission (1). If the attenuation depends on the beam intensity, however, the propagation is termed nonlinear. For example, estimates for the onset of thermal blooming are given in Ref. (1); if the molecular and aerosol absorption coefficients are sufficiently small, gross beam wander and self-induced spreading will not occur. Another nonlinear mechanism is aerosol droplet vaporization. With sufficiently large laser power densities, hole boring through various types of meteorological formations may be affected with a concomitant increase in transmission efficiency. Mitigation Techniques A number of high transparency spectral “windows” are present for which laser radiation will propagate from space to Earth with only minimal attenuation due to molecular absorption. During periods of heavy cloud cover or precipitation, however, a severe loss in transmission efficiency will occur because of aerosol absorption and scattering. The transmission efficiency may be improved during adverse meteorological conditions by [1] selection of a wavelength region which minimizes the effects of aerosol absorption and scattering, 12] increasing the elevation of receptor sites, [3] using a vertical propagation path (zenith angle 0 = 0°) rather than line- of-sight propagation from a satellite in geosynchronous equatorial orbit (0 — 50°), and [4] by hole boring, i.e., vaporization of the aerosol droplets within the beam path. Wavelength Selection. Preliminary information (2, 3, 4) indicates that operation in the spectral region around 11 /im may reduce the attenuation caused by light fog and light cloud cover. This phenomenon occurs for two reaaons: [1] the real part of the complex refractive index of water has a minimum at about 12 ^im and [2] the aerosol size distribution of certain fogs and clouds decreases more steeply than (particle radius)-2 above 7-10 p.m radius, thus reducing the scattering and absorption coefficients. Receptor Elevation. The selection of receptor sites at high elevation can reduce the deleterious effects of haze and can mitigate the problems caused at lower elevations (river valleys, coastal regions, etc.) by many types of advection and radiation fogs. In addition, if water vapor is an important molecular absorber for a specific laser line, high elevation receptor sites can “get above” a large fraction of the humid air in the lower troposphere and result in improved transmission efficiency. The clear-air transmission efficiency (considering molecular absorption only) is, unfortunately, undesirably low everywhere in the ll-/am window except for high- elevation receptor sites. Alternately, we have identified an extremely high- transmission region around 2 pm in which molecular absorption is negligible concurrent
with a minimum in the aerosol absorption coefficient of water based droplets. Zenith Angle. The space-to-Earth transmission efficiency for all linear attenuation mechanisms and a propagation zenith angle 8 scales as exp(-secd). If molecular absorption is strong, for example, operation at a propagation zenith angle of 0° rather than 50° results in a significant improvement in the transmission efficiency. If the laser wavelength is properly optimized, however, vertical propagation does not afford a significant improvement in the power availability (all meteorological conditions considered) and cannot be justified in terms of the increased cost and complexity of the required space hardware. Hole Boring. Using hole-boring models applicable to the range of laser-beam parameters of interest for power transmission, we have estimated the power densities necessary to affect aerosol clearing under various meteorological conditions. Laser hole boring through certain types of hazes, fogs, and clouds may be possible consistent with safety and environmental concerns. In particular, all but the thickest cirriform clouds and all stratiform clouds with the exception of nimbostratus can be penetrated without the need for weapon-quality beams. For lasers operating in the ll-/zm window, cw power densities of 100-200 W/cm2 are required. Because of the small aerosol absorption coefficient in the 2-ju.m window, hole boring at these wavelengths using a cw beam alone will be ineffective. A train of short-duration pulses superimposed on the “main” cw beam will, however, affect penetration under these circumstances. Several other physical mechanisms must be considered in conjunction with hole boring. Intensity fluctuations can be induced by temperature and water-vapor gradients within the beam path (5,6) and gross refractive bending of the beam can be enhanced under certain conditions by droplet vaporization (7-12). For laser power transmission, intensity fluctuations which do not result in significant beam spreading should be of no concern. We have examined the regime in which refractive bending occurs and found that severe distortion should be negligible for the power densities and beam diameters under consideration here. Another phenomena which has been recently considered is droplet recondensation in a laser-vaporized path. Overheating of the particles produces local supersaturation, resulting in the production of a large number of fine particles which may attenuate the beam and limit its penetration (13-15). This effect is pronounced at higher radiation intensities, for larger particles, and at lower temperatures. Again, for conditions anticipated here, this effect should not occur. Propagation Calculations—Aerosols Models. Aerosol scattering, absorption, and extinction coefficients and differential scattering cross sections were calculated for haze, advection and radiation fogs, various types of clouds, and rain and snow distributions at various precipitation rates. These calculations require detailed properties of the various aerosols, such as composition, size distribution, particle concentration, and complex index of refraction as a function of wavelength.Literature sources for distribution and concentration data are listed as results are presented. Index of refraction data are given in Ref. (16). For the calculations involving haze, absorption and scattering coefficients for the various aerosol models were taken directly from the work of Shettle and Fenn
(17). For most types of fogs and precipitation, it is a good approximation to assume that the particles consist of pure water. For clouds, which consist of nuclei surrounded by condensed water, this assumption may not be valid. In the Mie scattering regime, scattering, absorption, and extinction coefficients and differential scattering cross sections are calculated using the code hsphr (18). The code is restricted to spherical particles but does have provisions for heterogeneous compositions in which a spherical nucleus of radius «0 and complex index of refraction n0 is surrounded by a second material having a concentric radius a and complex index of refraction n. Theoretical treatments of the Mie problem are well documented in the literature and will not be repeated here. The method adopted here is the classical numerical treatment given by van de Hulst (19). The code was checked against the concentric sphere calculations of Kerker et al. (20) with excellent numerical agreement. The visibility or, more precisely, meteorological range as used in this study is defined by Koschmieder's relation, where ^sc is the aerosol scattering coefficient at 0.55 /rm, chosen because the peak sensitivity of the human eye occurs at this wavelength. The use of /3SC instead of /3ex (extinction coefficient) implies that the absorption coefficient (/3„) is small enough to neglect at visual wavelengths, a good assumption except for polluted air. From the foregoing relation, it is evident that the transmittance for a path length equal to Rm is 0.02. Haze. The atmospheric transmission efficiency for hazy conditions was calculated using representative aerosol models selected from the work of Shettle and Fenn (17). Results of calculations performed for hazy conditions (Rm = 5 km) are shown in Fig. 1. The aerosol models employed for each atmospheric layer are given in the figure insert. These curves show little fine structure as would be expected, since molecular absorption has been neglected. We can conclude that selection of a laser wavelength shorter than about 2 ptm is undesirable for propagation through haze. Furthermore, Rayleigh (molecular) scattering becomes significant at shorter wavelengths, scaling as X-4, and visible lasers would suffer attenuation due to this mechanism as well as because of haze aerosol extinction. The transmission efficiency as a function of altitude for propagation at a zenith angle of 50° under clear (Rm = 23 km) and hazy (Rm = 5 km) conditions is shown in Fig. 2. Clearly, receptor siting at elevations h > 1 km is desirable to partially mitigate the effects of haze. Thus, siting in basin or valley areas subject to weather inversions is undesirable, especially if the site is subject to urban pollution. Fog. We have taken the Mie calculations of Pinnick et al. (21,22) for four liquid water contents W (g/m3) of fog and replotted the extinction data as functions of wavelength. The fog particle-size measurements judged to be reliable were chosen to represent a wide range of conditions ranging from maritime and continental advection fogs (23, 24, 25) to inland radiation fogs (25, 26, 27, 28). These calculations are shown in Figs. 3 and 4. Error bars, if used, simply denoted the range of calculated /3ex for the various size distributions given by the respective authors. These figures show that laser operation at a wavelength around 11 /rm may be effective in partially mitigating the effects of light fog as has been confirmed experimentally (29,30). The minimum scatter in these data around 11 pun is in conformance
Fig. 2. Space-to-Earth transmission efficiency as a function of receptor-site elevation (aerosol extinction only). Fig. 1. Transmission efficiency for space-to-Earth propagation to sea level under hazy atmospheric conditions; molecular absorption is omitted to permit consideration of aerosol extinction alone.
Fig. 3. Calculated extinction coefficients for International Code 2 (Rm = 0.5 km) and Code 6 (Rm = 10 km) fogs. with the fact that the explicit details of the size distributions have less influence on /3n (21,22). As the water content increases, accompanied by a decrease in visibility, the minimum in /3ex near 11 pun disappears and the extinction coefficient is nearly flat with wavelength. Clouds. Using the Mie scattering code hsphr, /3„, /3SC, and and the forward and backward angular scattering coefficients, k{ and kb, were calculated for representative middle- and low-level cloud types. Two particle compositions were modelled: [1] homogeneous particle polydispersions of pure water and [2] heterogeneous particle polydispersions consisting of nuclei of fixed radius surrounded concentrically by liquid water. Hence, the thickness of the liquid water shell varies according to the particle size distribution while the diameter of the nuclei remain constant. Nuclei
Fig. 4. Calculated extinction coefficients for International Code 1 (R,„ — 0.1 km) and Code 5 (R,„ = 3 km) fogs. models used in the heterogeneous areosol calculations were taken from Nilsson (16). Comparisons were made between homogeneous (water mode) and heterogeneous particle (accumulation mode and coarse particle mode) models for two cloud types, cumulus and cumulonimbus, which are representative of cloud distributions having only small particles (a < 20 gm) and those having a significant fraction of larger particles with a > 20 gun (31). The presence of nuclei strongly influences the behavior at shorter wavelengths, whereas negligible differences exist between calculated coefficients at wavelengths longer than about 5 gtm. The extinction coefficient as a function of wavelength for A s 9 gun is relatively constant for homogeneous (water mode) particle calculations. For particle distributions with small-diameter nuclei (accumulation mode), however, the extinction coefficient decreases with decreasing wavelength for 2 s X < 5 gun. When the nuclei diameter increases, as with the coarse
Fig. 5. Calculated extinction coefficients for representative stratiform (solid curves) and middle-level (dashed curves) clouds. Particle distribution data were taken from the following references: altostratus, stratocumulus, and nimbostratus (Yamamotoet al. (32)]; altocumulus [Lewis (33)]; stratus I and II [Carrier et al. (34)]. particle mode, the extinction coefficients at shorter wavelengths increase in magnitude to values comparable to the water mode. Note that observational measurements do not show a decrease in jBex with decreasing wavelength as predicted by the accumulation mode, which may result from the assumption of constant-diameter nuclei. In addition, cloud-particle size distributions for a < 2 jim are not well defined due to the lack of adequate in situ measurement techniques. Since such small particles largely determine the absorption/scattering behavior at shorter wavelengths, calculational errors may be significant. Because of the uncertainties inherent in the heterogeneous particle models (especially at shorter wavelengths), we have shown the results of calculations for clouds
Fig. 6. Calculated extinction coefficients for clouds with marked vertical extent. Particle distribution data were taken from the following references: cumulus humulis I and II IWarner (35)]; cumulus congestus and cumulonimbus (Carrier et al. (34)). using the water mode only. The assumption that cloud particles are homogeneous and composed entirely of pure water is perfectly acceptable in the middle- and far-infrared spectral regions and is subject to question only for UV, visible, and nearinfrared wavelengths. A significant reduction in ;8ex occurs around 11 /am for clouds in which the large particle distribution decays more rapidly than a 2. This effect is particularly noticeable in calculations for altostratus, stratocumulus, and stratus clouds as shown in Fig. 5. Clouds characterized by a greater proportion of larger particles, e.g., nimbostratus and cumulonimbus (Figs. 5 and 6) show little improvement in /3ex at 11 jam. Alternately, operation at a laser wavelength near 2.25 jam may offer improved transmission through thin clouds because of a minimum in pn. Operation at even shorter wavelengths is undesirable because of the increased attenuation due to haze and molecular scattering. Tabulated absorption and extinction coeffi-
Fig. 7. Measured (36-40, 42, 43) and calculated (41) transmissivities of cirriform clouds for X = 11 /im. cients for the two spectral windows of interest are given in Ref. (31). Statistical variations in the particle distributions and concentrations can result in up to a factor of 3 difference in the predicted value of /3ex as illustrated by the curves labelled cumulus humulis I and II in Fig. 6. For example, particle concentrations, N„, for cumulus clouds range from about 100 cm'3 to greater than 400 cm-3. All of the thicker cloud types (especially cumuliform types, Fig. 6) are highly attenuating and are impenetrable unless hole boring at very high intensities is employed. Those cloud types which are characteristically thinner, such as middle and stratiform types, can be partially transparent, as shown by observational measurements (31). Calculation of the transmission efficiency through such formations should use forward-scattering corrections since Mie scattering from cloud particles is predominately in a forward direction. While this correction may result in a change in the transmission efficiency of perhaps 20%, this effect is unimportant compared with statistical uncertainties inherent in any model developed to predict the temporally- dependent laser power received at terrestrial sites.
Ice Clouds. Ice clouds forming at high altitudes contain predominantly nonspherical crystals and, hence, the Mie scattering code hsphr is unsuitable for calculating extinction and absorption coefficients. For example, cirriform clouds are composed mainly of hexagonal-column crystals several hundred micrometers long at a concentration of 0.1 to 1 cm 3. To estimate the transmissivity through these cloud types, we relied upon existing observational measurements and the rather limited number of available theoretical treatments. A number of authors have measured the transmissivity of various cloud types at different wavelengths. Few, however, have simultaneously measured the cloud thickness so that /3ex can be estimated. For those instances where the cloud thickness is known, we have plotted the transmissivity at 11 gm as a function of cloud thickness for various cirriform clouds in Fig. 7. The upper curve is a least-squares fit to the measurements of Kuhn and Weickmann (39) for cirrus clouds. Cirrus-cloud measurements of other references are in close agreement with this curve. The theoretical calculation of Liou (41) is for randomly-oriented ice cylinders having a mean length of 200 gm, a mean radius of 30 gim, and a mean concentration of 0.05 cm'3. This gives a frozen water density of 0.0283 g/m3. Because Liou did not attempt to incorporate a size distribution model into his calculations, this theoretical estimate must be taken only as a rough approximation to the transmissivity properties of an actual cirrus cloud. Denser cirriform clouds, such as cirrostratus, are more opaque to infrared radiation even though their average thickness is generally less than for cirrus clouds. Unlike many water-based cloud types occurring at lower altitudes, dense cirriform clouds may attenuate more strongly at 11 gm than at shorter wavelengths (36, 40, 44), although this effect amounts to a difference in transmissivity of perhaps 20% at most. Rain. For large, homogeneous, and spherical droplets such as rain, light absorption and extinction can be approximated by geometrical optics (19): Equation 2 was derived assuming hralX > 1 and (n' - 1) < 1, which holds for most rains with the exception of fine mists. The absorption efficiency factor is likewise given by
where N(a) is the scatterer size distribution with lower and upper radius limits a, and a2, respectively. Rensch and Long (30) have taken the Laws-Parsons rain particle distribution and calculated )3ex and pa as functions of the rainfall rate, R (mm/h). For the present study, we have employed the Marshall-Palmer distribution given by N(D) = Noexp(-AD) , (9) where D is the drop diameter (mm), N(D) dD is the number of drops per unit volume in the size increment from D to D + dD (m 3 mm '), and A is a parameter which depends upon the type and intensity of precipitation (mm-1). Three separate distributions, taken from the work of Joss et al. (45) and representative of different types of precipitation, were used in the numerical calculations. Fig. 8. Calculated (this work, 30) and measured (29) extinction and absorption coefficients for rain.
Calculational results for a wavelength of 11 /rm are shown in Fig. 8. Because of the large particle diameters in the rain distributions, Qex and Qa rapidly converge to values of 2 and 1, respectively, as we integrate from a, to a2. For R > 0.1 mm/h, therefore, the present results are effectively independent of wavelength for wavelengths in the infrared, and depend only upon the explicit details of the particle distribution. Observational measurements, however, show distinct differences between the total attenuation coefficient for different wavelengths, partly due to differences in molecular absorption. Few measurements of the attenuation of laser radiation due to rain have been performed; Chu and Hogg (29) made observations at 0.63, 3.5, and 10.6 gm during periods of rainfall largely free of accompanying fog. They observed greater attenuation at 10.6 gm than at the shorter wavelengths, and we have plotted their data in Fig. 8. The curve labelled is a least-squares fit to their experimental data and represents total attenuation due to all processes. The curve labelled is the estimated extinction coefficient, found by subtracting the molecular absorption and clear-air background aerosol attenuation from Because the relative humidity during the summer showers reported by Chu and Hogg approaches 100%, the molecular absorption coefficient was calculated at 10.6 /zrn using the code laser and the tropical summer atmospheric model. We notice that the corrected extinction curve thus obtained is in good agreement with theoretical predictions using the continuous rainfall particle distribution. Wilson and Penzias (46) found values of ^/R in the range 2.3-2.8 x 10 2 km-1 mm ' h for/? < 50 mm/h, in good agreement with our theoretical predictions without any correction. Obviously, the range of and /?„ observed at a particular rainfall rate is due to variations in the particle distributions. Snow. Little theoretical or observational data of laser propagation in snow exists. Observational measurements taken by Chu and Hogg (29), Wilson and Penzias (46), Soklov (47), and Nakajima et al. (48) show severe attenuation for moderate precipitation rates, and preliminary measurements indicate that the attenuation at 10.6 gon is significantly greater than at 0.63 and 3.5 gun. We have estimated the value of /3n and /3a as functions of the snowfall rate R using two models. In the equivalent liquid-drop model, Sekhon and Srivastava (49) found that the particle distribution of melted snow crystals is given by Here, D is the liquid drop diameter (mm) and R is the melted snowfall rate (mm/h). In the second model, called the aggregate snowflake model, we use the actual particle size distribution which can also be represented in the Marshall-Palmer functional form. To obtain the snowflake diameter, the relationship between particle masses in the liquid and ice-crystal forms is used: where p is the density, D is the particle diameter, and the subscripts L and i denote liquid and ice forms, respectively. Passarelli (50) found that 3, from which we obtain
Fig. 9. Calculated (this work) and measured (29, 47) extinction and absorption coefficients for snow. If the liquid-drop particle distribution given in Eq. 10 is modified by Eq. 13, we have an approximate relation giving the actual snowflake particle size distribution. We expect that the equivalent liquid-drop model will underestimate and /3a because the particle diameters are too small, whereas the aggregate snowflake model will overestimate these coefficients because the actual snowflake distribution is approximated by spherical particles composed of liquid density water. The results of calculations, shown in Fig. 9 for a wavelength of 11 jam, bound the experimental measurement of Chu and Hogg (29) and Sokolov (47) as would be intuitively expected. At low snowfall rates, the aggregate snowflake model more closely estimates the measured extinction coefficients of Sokolov, whereas at higher snowfall rates, the aggregate snowflake model clearly overpredicts observed behavior and the equivalent liquid-drop model establishes a lower bound for the estimates. In general, the attenuation and forward scattering properties of snow appear to be between those of rain and dense fog.
Propagation Calculations — Molecular Absorption Calculational Models. Molecular absorption is calculated for a given laser wavelength X by the computer code laser (51). Absorption line parameters for atmospheric molecular species are taken from the AFGL line-parameter compilation (52). The average molecular absorption coefficient for each of 32 atmospheric layers is calculated for the following atmospheric models: U.S. standard, tropical, midlatitude summer, mid-latitude winter, subarctic summer, and subarctic winter. Transmission Efficiencies. The transmission efficiency for space-to-Earth propagation was calculated for a number of laser lines in the 2, 9, and 11 gm spectral regions. The 2 and 11 gun regions were chosen because they may afford an improvement in transmission through various meteorological aerosols. The 9 gm region was chosen because the laser lines of certain isotopic species of CO2 may offer higher transmission efficiencies than their naturally occurring counterpart, 12C16O2; 12C16O2 is uniformly distributed in the atmosphere and its strong absorption lines should be avoided by selection of alternate laser wavelengths. All calculations are for propagation to receptor site elevations of 0.0, 0.5, and 3.0 km for a zenith angle of 50°. The spectral region from 2.100 to 2.315 gem offers an excellent high-transparency window with relatively few strong absorption features. Calculated transmission efficiencies of all laser lines examined in this spectral region exceed 99.9% for all site elevations and are insensitive to seasonal variations. Since the individual windows between absorption features are wide (in many cases > 10 cm '), there is hope that a scalable, high-power laser operating at a wavelength in one of these windows can be developed. The transmission efficiency of several mid-rotational P- and /?-branch laser lines of the isotopic-species l2CIKO2 laser operating on the 10°0—*02°0 band are given in Table 1. Operation of a CO2 laser in this mode results in a significant improvement in the transmission efficiency compared with operation on “standard” lines of the 00°l-»10°0 band of 12Cl6O2; seasonal variations, however, are pronounced and the highest (average) annual transmission efficiency to typical receptor sites (h = 0.5 km) is only 87.7% for the 9.124-gim line. Because of the potential importance of the 11-gim region, the interval from 10 to 12 gm was closely examined for high transparency windows. This spectral region is
characterized by a profuse number of absorption lines which are highly pressure broadened in the lower troposphere. Windows which were at least 1.0 cm-1 wide with edges at least 1.0 cm 1 from a major absorption line were selected for detailed calculations, hitran spectral plots (53) were particularly useful in this search, although their transmission efficiencies cannot be used in the present study because they are for 10-km horizontal paths. If a known (high-power) laser line exists within a window, this wavelength was used in the LASER-code calculation; for those windows for which no laser line could be identified, the central wavelength was used. The transmission efficiencies for all windows identified in this manner are given in Table 2. For comparison, calculations are also shown for the “standard” 10.6-/zm CO2 laser line, which is totally unsuitable for space-to-Earth power beaming. Most of the absorption occurs in the lower troposphere and seasonal variations in the transmission efficiency are again pronounced. The highest annual transmission efficiency to typical receptor sites is 82.3% for the 10.916-/zm line. High-elevation operation (A = 3.0 km) increases this value to 96.3%. Indeed, power transmission in the 9 and 11 gm regions is probably limited to high-elevation sites. The examination of the 10 to 12 spectral region was exhaustive and we believe that no high-transparency window was overlooked. Therefore, laser operation at any other wavelength in this region or pressure detuning of “standard” high-power laser lines will not result in transmission efficiencies greater than those given here. HOLE BORING For a laser beam to penetrate an aerosol layer of thickness Szc moving with a lateral wind velocity v, Harney (54) showed that the aerosol vaporization time zr must satisfy the following inequality as a minimum requirement: where ZE is the time required for the droplet to shrink to some arbitrary fraction of its
original radius during exposure to a constant intensity /, Jis the beam diameter, and the absorption coefficient /?„ and water content W are related by Qa is the Mie absorption factor, N„ is the total particle concentration, p is the droplet density, and ac is the mode radius, i.e., the radius corresponding to the maximum number of particles. Numerical solution of the approximate equation for the evaporation rate was obtained by Kuzikovskii and Khmelevitsov (55) allowing for the nonlinear dependence of the temperature on water-vapor concentration for laser intensities I ~ 102—104 W/cm2. The parameterized relationship of the vaporization time tv and instantaneous droplet radius a was expressed as In Eqs. 16 and 17, t„ is in sec, I is in W/cm2, and X and ac are in gm. The complex index of refraction is n = n' - ik. For the droplet to be ineffectual in attenuating the beam, we require that the particle be reduced in size until a = 0.01X. It is more convenient to specify meteorological aerosols in terms of their liquid-water/ice path lengths, p (g/cm2), so that where v is in m/sec, d is in m, ac and X are in p.m, p is in g/cm2, p is in g/cm3, and / is in W/cm2. Qa, given previously by Eq. 6 for the large-radius approximation, is not valid for cloud and fog droplets. As an analytic convenience, we use the Shifrin approximation [see Gordin and Strelkov (56)] given by
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