21  National Academy of Sciences, National Academy of Engineering and Institute of Medicine, Policy  Implication of Greenhouse Warming: Mitigation, Adaptation, and the Science Base (National  Academy Press, Washington, D.C., 1992).

22 Since space-deployed scatterers could in principle last indefinitely, they have a several dozen-fold  advantage in time-integrated mass budget relative to stratospherically-deployed ones, which must be  re-constituted twice per decade. This durability-in-service saving trades off interestingly, albeit not  compellingly, against the present ~104-fold disadvantage in cost of transportation to deployment-site.

Space-launch service costs will have to decrease to a few dozen dollars per pound in order to become  competitive for present purposes. High-acceleration payload launchers are potentially of interest, as  scatterer payloads are likely to be very acceleration-tolerant – and perhaps can be segmented into quite  modest sizes and masses, as well.

23  Positioning a sunlight-shade or Snell's Law-refractor (i.e., a 1-D Fresnel phase plate) composed of  1014 gms of lunar glass near the Earth-Sun interior Lagrange point (L1) has been suggested in Early JT,   Space-Based Solar Shield To Offset Greenhouse Effect, J. Brit. Interplanet. Soc., 42, 567-9 (1989). The  present proposal positions a metallic small-angle-scatterer of sunlight of comparable area but ~105-fold  smaller mass Sunward of L1. A system of this type likely would be assembled quite close to the Earth,  e.g., in LEO, and then rapidly ''flown'' into its deployment location as a solar sail, exploiting its very  small mass-to-optical cross-section and its active radiation momentum management capabilities.

24  The total areal size of such a scattering system must remain the same as scattering systems deployed in close  proximity to the Earth, but its total mass potentially may be much more modest, as it must scatter sunlight only  through ~102-fold smaller angles. In particular, the conducting elements of the scattering units need carry only  ~102-fold smaller currents, so that they can be of 102-fold smaller cross-sectional area (for a given optical  electric field strength, which is effectively constant for all scattering system deployments in ~1 AU sunlight),  and thus can have 102-fold smaller mass. The mass of such a scattering system can be estimated by noting that  the total area must be ~1% of the Earth’s disc, while it must have good metallic conductors of ~3 x10-11 cm2   cross-sectional area (~600 Å thick by ~1000 Å in transverse width) spaced every 100l/2~3 x 10-3 cm in both  transverse dimensions. If the density of the conductor is taken to be 3 gm/cm3 (e.g., Al), then the mass density  is ~ 1.2x10-7 gm/cm2, and the total mass is just this density times the 1% of the Earth’s disc area of ~1.2x1018  cm2 which is to be sun-shaded, or ~1.2x1016 cm2: ~1.4x109 gms. The total mass of the ideal scattering system  thus is ~1.5x109 gm or 1,500 ton – plus whatever overhead mass is required to deploy and operate these  (literally) diaphanous scattering screens; the actual scattering system has about twice this mass – ~3400 tons –  for reasons which are discussed below.  The possibilities of incrementing or decrementing terrestrial insolation in manners which are both geographically  and spectrally selective by use of such a distant scattering system seem obvious.

25  The momentum carried by sunlight, while very small, is assuredly not negligible: at 1 AU, it amounts to ~4x10-5 dynes/cm2. Over a day, this accumulates to ~3 dyne-sec/cm2 and, over a year, to ~103 dynesec/ cm2 of impulse fluence. If exactly backscattered (toward the sun), only radial momentum is gained by the scattering unit; however, if deflected at any angle <p, it will also impart angular momentum to the scatterer: the Poynting-Robertson effect. Since scattering units typically have an areal mass <<10-3 gm/cm2,  they can undergo many gee-sec of acceleration even during a day, and thousands of gee-second annually (i.e.,  can see Dv of >>10 km/sec). Such velocity changes in essentially all orbits of interest are almost invariably  intolerable, and either deployment or operational means must be devised to avoid them.

Unwanted angular momentum may be readily jettisoned by time-varying the orientation of a relatively very  small reflector capable of scattering sunlight through a high mean angle. However, the radial momentum

imparted by sunlight must be sustained for intervals as long as a half-year, until the Earth’s orbital motion

about the sun will dissipate it; in most cases-of-interest, this is a very long time-interval over which to tolerate  radial momentum absorption. However, if the scattering unit is deployed sunward of the Earth’s orbit but  quasi-orbits the sun at the same angular rate as does the Earth (so as to continually shadow-shield the  designated fraction of the Earth), then it may in principle sink as large fraction as may be desired of the

incident sunlight’s radial momentum into the solar gravitational field, i.e., it may position itself closer to the  Sun than the L1 point so as to sink the scattered radiation's radial momentum into the solar gravitational field;  the smaller its areal mass density, the more Sunward of L1 it must position itself. Now the radial radiation  momentum flux is ~4x10-5 dynes/cm2, only 5x10-5 of which is deposited on the scatterer as it deflects the  incident sunlight by 10-2 rad, so that the mass density corresponding to deposited radiation radial momentum balancing the gravitational ‘deficiency’ is ~1.5x10-7 gm/cm2. This is only a few times greater than the areal  mass density of the ideal scattering system positioned at L1. Thus, by moving ~1% inward from L1 – and  increasing the total area of the scattering system by ~2-fold, in order to continue to shadow the Earth while  moving further Sunward from it, we can simultaneously sink the residual radial momentum of the scattered  sunlight into the solar gravitational field and maintain the desired shading of the Earth.  Residuals in both radial and angular momentum flux from solar gravitation and from the Poynting-Robertson  effect, respectively, are probably best sunk by sunlight retroreflection action performed by a relatively small area (i.e., 0.3%) of high-angle reflector. However, this necessarily will have a ~50X greater areal mass-density  than does the small-angle-scattering screens of greatest interest, so that a ~15% overhead cost is thereby  incurred by the scattering system.

26  Trepte CR and Hitchman MH, Tropical stratospheric circulation deduced from satellite aerosol data, Nature 355, 626-8 (1992); Trepte CR, Veiga RE, and McCormick MP, The Poleward Dispersal of Mount  Pinatubo Volcanic Aerosol, J. Geophys. Res. 98, 18563-73 (1993); Grant WB et al, Use of volcanic  aerosols to study the tropical stratospheric reservoir, J. Geophys. Res. 101, 3973-88 (1996).

27  See, e.g., Taylor KE and Penner JE, Response of the climate system to atmospheric aerosols and greenhouse gases, Nature 369, 734-7 (1994); Chuang CC, et al, An Assessment of the Radiative Effects of  Anthropogenic Sulfate, J. Geophys. Res. 102, 3761-78 (1997); and Intergovernmental Panel on Climate  Change, Climate Change 1995: The Science of Climate Change , JT Houghton, et al, eds. (Cambridge  Univ. Press, Cambridge, 1996).

28  See, e.g., Dyson FJ and Marland G, Technical fixes for the climatic effects of CO2. Workshop on the  Global Effects of Carbon Dioxide from Fossil Fuels. USDoE Report CONF-770385 (USDoE, Washington  DC, 1979); Budyko MI, The Earth's Climate: Past and Future. (Academic Press, New York, 1982);  Broecker WS, How to Build a Habitable Planet (Eldigio Press, Palisades, NY, 1985).

29 In this approach, advantage is taken of the stronger Rayleigh scattering of the shorter wavelengths of optical  sunlight as compared to those of terrestrial thermal emissions. A performance-optimized scattering system of  present interest consists of a world-wide, ultra-thin cloud of dielectric particles, each of 0.05-0.1 mm diameter, deployed in the Earth’s stratosphere. The Rayleigh scattering cross-section S of a particle of volume V whose  polarizability a=3(e-1)/4p(e+2) for photons of angular frequency w is S = (8p/3)(w/c)4a2V2. [See, e.g.,  Landau LD and Lifshitz EM, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).] For such a spherical particle whose diameter is equal to a quarter-wavelength of 0.5 mm radiation which has a dielectric  coefficient e~1.7 (e.g., a water-rich microdrop of refractive index ~1.3), S may be estimated to be ~5x10-12  cm2. Thus, ~1028 of these particles, uniformly distributed in the stratosphere, would be required to scattershield  the 5x1018 cm2 of terrestrial surface with optical density 10-2 at the sub-solar point. (While only the  bluer portion of the visible spectrum, l£0.5 mm, would be scattered with this cross-section, the effective scattering in the earlier half of local morning and the latter half of local afternoon in the tropics and all day at  higher latitudes is considerably greater than this value, due to the greater atmospheric path traversed by  incident sunlight, so that the net required energetic effect of panchromatic scattering is attained, in first  approximation). Each of these scattering particles may be estimated to have an average mass of ~10-15 gm  (i.e., be ~0.12 mm in diameter and of unit density), so that the required quantity of them would imply a total  mass of the scattering system of ~1013 gms, or 10,000,000 tons. A mean stratospheric lifetime of each scattering particle of 5 years would imply a required injection rate of 2x106 tons annually, or a time-averaged  injection rate of 60 kg/second, which is feasible to maintain e.g., with highly parallel exercising of existing fine-aerosol-dispersion technology.

30 E.g., Brady BB, Fournier EW, Martin LR and Cohen RB, Stratospheric Ozone Reactive Chemicals Generated by Space Launches Worldwide. Aerospace Report No. TS-94(4231)-6. (The Aerospace  Corporation, El Segundo, CA, 1994).

31  Because of the strong dependence of the Rayleigh scattering cross-section on e, [(e-1)/(e+2)]2, when e is  not much greater than unity, it would be more somewhat mass-efficient to deploy alumina microspheres,  instead of SO2/SO3/H2SO4 ones: the significantly greater density of alumina (~3.5 gm/cm3) is more than  compensated by its greater dielectric coefficient, 3.10. (Alumina, like sulfate, is ubiquitous in the terrestrial  biosphere, and its stratospheric injection seemingly poses no significant environment issues. However, its  refractory character makes it more challenging to deploy, at least in some modes. A notable exception might  be a high-average-power combustor of aluminum powder deployed at a high-altitude, near-equatorial groundsite,  one whose carefully-engineered exhaust-stream could hydrodynamically penetrate the overlying tropopause and inject £0.1 mm-diameter alumina particles into the mid-stratosphere with high mass-efficiency. ) Worth noting in passing is the fact that the annual tonnages of either sulfur or aluminum oxides presently  proposed for stratospheric deployment are tiny compared to the quantities of these materials which are either  naturally lofted into the atmosphere (e.g., by dust storms) or are already injected by human activities (e.g., burning of fossil fuels of all types).

32Absorption of solar photons with thermal (quasi-isotropic) re-radiation of the absorbed energy may be reasonably mass-efficient in some circumstances, e.g., when using photoelectric-effect (bound-free) absorbers.

For instance, the photoelectric cross-section of good metals just above the work-function-edge for near-optical  radiation is ~3x10-17 cm2, and is ~3x10-18 cm2 at three times this photon energy (i.e., a 107- and 108-fold reduction below the line-center bound-bound resonant cross-section, corresponding to the relative final-state  phase-space volumes of the two types of transitions). For scattering unit design purposes, an effective  photoelectric cross-section of 10-17 cm2 is a reasonable estimate (taking into account finite solar spectral  width requirements and considering that the solar spectral intensity falls rapidly above even the lowest-energy  single-element photo-edge, that of Cs metal at a photon wavelength ~0.37 mm), and assuming that all photons  with energies above the photo-edge interact with this cross-section. Likewise, note that a multiple alkalimetal  alloy system can lower this photoedge to an effective 2 eV threshold (e.g., as the tri- and quad-alkalimetal- alloy photocathodes of commercial photodetection devices routinely do). A sheet of this material of a  few dozen atoms thicknesses – ~100 Å – would then represent an extinction length for blue-green photons, and  would have a mass-density of £3x10-6 gm/cm2. Then, assuming that scattering units comprised of such 10-6  cm-thick sheeting would absorb half the incident solar spectrum and that the corresponding scattering system would sun-shield 0.01 of the Earth’s disc continuously, the minimum mass-budget of an efficiently implemented scattering system comprised of such ultra-thin sheets of photoelectric absorber/thermal re-radiator would be (2)(10-2)(1.2x1018 cm2)(3x10-6 gm/cm2)~7x1010 gms ~ 70,000 tons. If deployed either in the  atmosphere or in LEO, individual scattering units could be effective only £50% of the time, so that ³140,000  tons would be required to fully implement such a scattering system.

The constituent materials of every efficient photoelectric absorber for solar-spectrum radiation inherently are  readily oxidizable, particularly in the highly (photo)reactive upper atmosphere, so that only LEO deployment  of such systems appears feasible – unless ³two-fold mass penalties are paid for protective jacketing, e.g., SiO. In addition to having a relatively large mass budget for a space-deployed system, such an absorption/reradiation module in space would have the active momentum-management requirements characteristic of any space-based scattering system; this additional complexity would trade off against the multi-decade lifetimes  (and thus far lower annualized costs) implicit in LEO deployment.

33  The scattering system of this approach is comprised of a set of single-layer screens which scatter incident  sunlight through ~p/2 rad, and whose conducting elements must be ~1 skin-depth in longitudinal extent, or  ³200 Å, by ~300 Å in transverse width, spaced at £3x10-5 cm distances in both dimensions; packaging mass for protection against stratospheric oxidation would be comparatively small, if metal having a thin protective  oxide, such as Al, is used. Such a high-angle scattering system would have electrically conducting ‘wire’ elements massing a total of ~15,000 tons; averaging random orientation and diurnal availabilities drives this up by ~2p, to ~90,000 tons. (Overhead mass for deployment and operation would, of course, be additional,  although, in fractional terms, it would be smaller, as the scattering screens would be much stronger, due to  their thicker conducting members.)

34  Thin-walled helium-filled balloons are routinely employed to lift multi-ton payloads to 30-50 km altitudes,  and maintain them there for multi-day intervals (limited mostly by the durability-against-photooxidation of the balloon's plastic wall). It thus seems entirely reasonable to consider ultra-thin metallic-walled balloons, partially inflated with a suitable lifting-gas, e.g., H2, as sunlight-backscattering ‘stratostats’, for they can be expected to have very long stratosphere residence times (probably limited by micrometeoritic puncture-rates).  A wall thickness of ~0.02 mm of e.g., Al, is ~1 skin-depth at the 8x1014 Hz frequencies characteristic of midvisible solar radiation and thus suffices to (predominantly) backscatter the blue end of the incident solar spectrum; however, it is £0.2 skin-depth at 2-3x1013 Hz and thus is nearly transparent to Earth thermal emissions in the 8-14 mm wavelength atmospheric pass-band. Each of these balloons thus constitutes a ‘micro anti-greenhouse’: it passes space-directed low-frequency photons emitted by the Earth but reflectively backscatters-into-space the high-frequency ones incoming from the Sun.

Since the thickness of the balloon's metallic wall is determined by electrodynamic skin-depth considerations,  the balloon diameter is selected so as to position it at the desired stratospheric altitude when it is fully  expanded, subject to the constraint that it must be buoyant at the launch-site altitude. An Al wall thickness  of 0.02 mm, a balloon radius of 4 mm, a fully-inflated volume of 0.25 cm3, a mass of 10-5 grams and an optical scattering cross-section (between ~0.25 and ~1 mm wavelength) of 0.5 cm2 correspond to a balloon  deployment altitude of 25 km. (Likely different choices of deployment altitude involve £2-fold adjustment of the balloon diameter while keeping its wall thickness invariant.) Since it is required to scatter-shield  ~5x1016 cm2 (recalling that 1% of the Earth’s total area is to be so sun-shielded), ~1017 of these ‘‘selflofting  blue-UV chaff’’ objects will be required, with an associated mass of ~1012 grams, or 1,000,000 tons.

If they are deployed uniformly over a 50 year interval (i.e., quickly compared to a doubling-time of  atmospheric CO2), then ~2x1010 grams/year – ~6x107 balloons/sec, or 108 cm2/sec, or 1 hectare/sec of  these scatterers – must be created and deployed. (Newspaper printing-press technology seems a particularly likely basis for ‘printing’ these balloons on a H2-loaded Al bilayer-sandwich substrate. High-circulation major newspapers print ~106 copies of a ~10-2 hectare-area newspaper daily, for a round-the-clock mean rate of  ~0.1 hectare printed per second; the peak printing rate is ~0.3 hectare/sec. Thus, the time-averaged balloon  creation-and-deployment rate is comparable to the peak output rate of a large newspaper printing-facility.)

This deployment rate will require 4.5x107 lbs/year of Al-as-foil (at a current annual cost of £$40 M for ingot, likely a few times this for mass-produced ultra-thin foil), and a ~15-fold lower mass of several-fold cheaper H2 gas: ~1,500 tons. These ‘‘self-lofting blue-UV chaff’’ balloons constitute one of the lowest-technology approaches, in that, once created and released at ground-level, they self-deploy and automatically-operate. The feedstream requirement is only ~1% of the current total annual production of aluminum metal. Since 6% (by mass) of the Earth’s crust is Al, the quantity of ultra-thin Al foil drifting down from the skies during the mid-21st century wouldn’t discernibly impact the environment, the more so as such very thin foils would photooxidize to the hydrated oxide quite rapidly in the wet troposphere: at ~290oK, Al exposed to dry oxygen forms a stable oxide  layer of 10-30 Å thickness, but wet oxidizing atmospheres can form >1 mm hydrated oxide layers on bulk Al in a matter of hours – and hydrated AlOx films crumble to powder very rapidly. (It therefore should be feasible to deploy such ‘‘self-lofting blue-UV chaff’’ from desert sited-factories – or from high-latitude ground-sites – and have them quickly rise into the stratosphere intact, while they would invariably be wet-oxidized into invisiblyfine hydrated alumina dust during their slow, end-of-life descent through the troposphere, obviating ''littering'' concerns raised in connection with return-to-Earth of far larger, non-optimized balloons). It's obviously feasible to employ a metallic overcoating of the required thickness applied to an appropriate thickness of a stronger dielectric, e.g., a modern plastic film such as polyaramid or polybenzoxazole, in order to gain durability. (The metallic overcoating would then serve its sunlight-scattering function and would also protect the super-strength plastic film from stratospheric photochemical damage. )

This particular insolation-scattering solution has a much less pronounced dispersion than does the Rayleigh  scattering one: it only scatters more strongly with the half-power of the photon frequency (rather than the