Paper IAA-95-IAA.4.1.102 Presented at the 46th International Astronautical Congress, October 1995, Oslo, Norway Small Laser-propelled Interstellar Probe Geoffrey A. Landis Ohio Aerospace Institute NASA Lewis Research Center 302-1 21000 Brookpark Road, Cleveland, OH 44135 U.S.A. Background: Cost of Interstellar Flight Recent reviews of interstellar flight have underscored the immense cost of even a small interstellar probe. Mileikowsky (1994), for example, calculates the cost of a 1000 kg interstellar flyby probe traveling at 0.3 times the speed of light. Analyzing the laser-pushed lightsail propulsion system proposed by Forward (1984), 65,000 GW must be supplied to the laser for 900 hours. At a capital cost of $2/W, the electrical generation facility capital cost comes to 130 trillion (1.3 10^14) dollars. Andrews (1993) calculated similar numbers, but notes that lower electrical generating costs could reduce the price. The cost is, of course, enormously sensitive to electrical price. Electrical costs are discussed in more detail in the appendix. Antimatter [Forward 1991] and particle-beam-pushed propulsion [Landis 1989, Andrews 1993] systems, as analyzed by Mileikowsky, are even higher in expense. Since the technology for these propulsion systems is less developed, in this paper I will constrain the analysis to only the case of laser-pushed lightsail propulsion. It is clear that the energy cost of even a small interstellar probe is likely to be huge. Hence, it is the purpose of this study to examine the interstellar flyby mission in more detail and to design a probe system which minimizes the required energy cost. Baseline Mission Description I will assume that the reader has a general familiarity with the literature on interstellar flight. A good introduction to the problems of interstellar flight can be found in Mallove and Matloff (1989). In this paper I will consider variations on the laser-propelled lightsail flyby probe first analyzed by Forward in 1984. The propulsion system consists of a large, stationary laser of extremely high power. In order to achieve the low divergence required, the laser is focussed by a lens. Forward assumes a lens of 1000 kilometer diameter. This large diameter lens is constructed as a Fresnel zone-plate, or "O'Meara para-lens"; that is, as a series of rings of ultra-thin transparent plastic sheet, alternating with vacuum. The transparent sheets are chosen to have a thickness exactly chosen such that the delay of the wavefront at each element is one half of the light wavelength. Since the lens structure is extremely flimsy, the structure, although a third the diameter of the moon, has a mass of only 560,000 metric tons. The large lens is required because of the fundamental divergence of a light beam emitted from a finite aperture due to diffraction. The minimum spot size which can be achieved, Dspot, at a distance d from the lens, is: Dspot = 2.44 d (lambda)/Dlens (1) where (lambda) is the wavelength of the light used. This equation defines the diameter of the first zero of the Airy diffraction pattern; 84% of the light is contained within this circle. Any units can be used for d, (lambda), and Dlens as long as the same units are used consistantly; it is convenient here to use meters. The laser power is focussed onto a spacecraft consisting of a thin reflective "sail" plus a small payload. By Einstein's relation, the amount of momentum in a light beam of energy E is: p = E/c (2) By reflecting the incident light, a momentum is transferred to the sail equal to twice the momentum of the incident photons (neglecting, in this approximation, the relativistic correction due to redshift, small the the speed considered). In conventional terms, this produces a force 6.7 newtons per gigawatt. While this is an extremely low force by the standards of the rocket-based systems used for conventional spaceflight systems, no reaction mass at all is expended. This makes the lightsail system extremely attractive for interstellar missions, which would otherwise require prohibitive mass-ratios to accomplish. The reflective sail is assumed to consist of an ultra-thin foil of aluminum, plus structural elements required to keep the sail roughly flat. Solar sails, which operate by reflection of sunlight, have been extensively considered in the literature. The sail analyzed by Forward differs from most proposed solar sail designs in that most solar sail designs typically assume that the reflective (aluminum) layer is a thin coating on a plastic (e.g., Kapton) sheet. Forward assumes that the plastic sheet can be elimiated, and that the aluminum alone is sufficient to serve as the structure. Forward also assumes that the aluminum layer is extremely thin, considerably thinner than that used by most solar sail proposals, in order to minimize the mass required. The probe analyzed by Forward reaches a top speed of 0.11 c, somewhat lower than the speed analyzed by Mileikowsky. Parameters for the baseline mission are shown in Table 1. While the reference also considers other mission concepts which decelerate to a stop at the destination, the simple fly-by probe analyzed does not. Travelling at 11% of the speed of light, the Forward probe requires 40 years before arrival at Alpha Centauri. Including three years for acceleration and four years for the information sent by the probe to return, results from the Forward flyby probe can be expected 47 years after the start of the mission. Table 1 Reference laser-pushed lightsail flyby mission Mission Velocity 0.11 c acceleration 0.36 m/sec^2 (thermally limited) distance at laser cutoff 0.17 LY (1.6 10^12 km) Laser Laser wavelength 1000 nm Lens diameter 1000 km Laser power 65 GW Laser pulse duration 3 years Total laser power 1.7 10^12 kW-hr Sail diameter 3.6 km area 10.2 km^2 material Al thickness 16 nm thermal emissivity e 0.06 temperature 600 K (2/3 of Tm) material density (D) 2.7 gr/cm3 reflectivity 82% Mass Total mass 1000 kg Areal density (total) 0.1 g/m^2 Sail 0.043 g/m^2 Structure 0.03 g/m^2 payload 0.027 g/m^2 Note that the electrical power of 650 GW required, assuming laser efficiency of 10%, is a hundred times less than the 65,000 GW assumed by Mileikowsky. This is partly due to the fact that the Forward probe speed is only one third as high, but primarily due to the fact the laser on time is 30 times longer than the time assumed by Mileikowsky. Nevertheless, the generating capacity required would cost 1.5 trillion dollars at today's power cost, and 37 billion dollars at the assumed evolutionary values for power generation cost discussed in the appendix. This paper analyzes approaches to reducing the total power required for an interstellar fly-by mission propelled by a laser-pushed lightsail without increasing the mission time. The constraints assumed no advances in physics beyond that currently known, and no technology advances beyond that now available (except for the lens and sail technology assumed in the baseline paper). Alternative Technologies The propulsion system described is achievable entirely within the currently known laws of physics, however, it requires significant advances in engineering. First, it requires development of large laser systems. Second, it requires the ability to fabricate gossamer structures of a thousant kilometers in diameter with the control to position the structure to within a few meters. Third, it requires the ability to fabricate a reflective film without a plastic substrate. The Forward mission scenario has been analyzed, and several difficulties pointed out, by Andrews and Zubrin (1988) and by Landis (1989). Of these technologies, the thousand-kilometer diameter para-lens is probably the most speculative, in particular considering the stringent positioning requirements. As noted by Landis (1989), the lens and the laser source are both required to be positioned to within an accuracy of 3 meters to maintain a beam wander of less than the sail radius at a distance of 0.17 LY. If the beam wander is slow, the probe can correct by detecting the beam and moving laterally to maintain correct positioning. However, to bring the technology closer to realization, it would be desirable to (1) reduce the required size of the lens, and (2) reduce the required focal distance. Landis (1989) also notes that optics considerations show that the laser aperture will be magnified at the optical image plane. However, as noted by Forward (1985/1989), as long as the laser maintains diffraction-limited coherence across the aperature, it is possible to focus the beam to a spot actually smaller than the magnified image of the laser aperture. This criticism thus reduces to a requirement for high coherence of the laser, and not a fundamental physical limitation on the technology. It is occasionally suggested that the requirement for the laser could be eliminated by directly focussing solar energy on the sail with a large lens. Unfortunately, this does not work. Focussing lenses cannot, in principle, produce power density at the sail higher than solar intensity unless the diameter of the focussing lens is larger than the apparent diameter of the sun. This is because the energy density per unit solid angle cannot be changed by a lens or any combination of lenses. Unless the lens diameter is comparable to the diameter of the sun, there is little advantage to using a lens at all. An alternative is to simply eliminate the lens system entirely, and to use a solar-sail propulsion. This has been analyzed in detail by Matloff (1984) and Mallove and Matloff (1989). Since the Forward probe mass is dominated by the sail and the structural system which supports it, merely reducing the payload requirement does not significantly reduce the probe mass. When the sail mass is reduced, the payload can be proportionately reduced. Thus, I adopt the scaling rule used by Forward: structure plus payload mass = 1.3 times sail mass. This assumption will be examined in more detail later. One alternative considered was to replace the solar sail by a photovoltaic array, and to use the power generated to run an electric propulsion system, such as an ion drive. This concept was analyzed by Landis (1994), and shown to produce, at best, only small improvements over the reference system. It will not be analyzed in detail here. Beam spread could be lowered by increasing the focussing lens diameter. This approach was not considered, since the O'Meara lens is one of the critical technological improvements required, and increasing the diameter could result in unacceptable additional cost. Only improvements which decreased lens diameter were considered. Three changes were analyzed: changes in wavelength used, changes in sail material, and changes in laser technology. Wavelength If a shorter wavelength is used, beam spread due to diffraction decreases, and hence the sail area can be decreased. A minimum wavelength is set by three factors: low sail reflectivity at ultraviolet wavelengths, low laser efficiency at short wavelength, and decreased lens transparency in ultraviolet. 500 nm is shown to be achievable. I will assume that, when the wavelength is reduced, both the para-lens and the spacecraft sail are reduced in equal proportions. This would thus allow the lens to be reduced to 707 km (from 1000) and the sail diameter to be reduced to 2.1 km (from 3.6). This results in a reduction of the sail mass by a factor of two (and a similar reduction of the lens mass.) Sail Material If the acceleration is increased, the required focus distance is reduced, and hence the sail area can also be decreased. For acceleration a and final velocity Vf, the distance at beam cut-off is (neglecting relativistic corrections): d = 0.5 vf^2/a (3) Higher acceleration allows the same velocity to be achieved over a lower distance. Hence, a smaller sail and thus lower power laser can be used to achieve the same maximum velocity. It also means that the amount of time used for the acceleration is lower. Acceleration is limited by the thermal capability of the sail, due to the fact that the sail material is not perfectly reflective, and the amount of light which is absorbed by the sail will result in heating. The thermally limited acceleration is (Forward 1984): a = 4 R/c [e (sigma) T^4]/(alpha)Dt (4) where R is the reflectivity, e is the emissivity, (sigma) is the Stefan-Bolzman constant, alpha the absorption, D the density, and t the thickness. Thus, if the reflectivity and the emissivity is constant, the figure of merit for a given material is the fourth power of the temperature divided by the density. All other considerations constant, the thermally-limited acceleration possible with a sail is proportional to the figure of merit. A considerable increase in the amount of power which could be applied to the sail, considered by Forward, can be made if the sail is constructed such that the reflectivity of the rear (laser-facing) side of the sail is high, while the thermal emissivity (e) of the front side of the sail is high. It is not clear, however, whether this is technically achievable without a proportional increase in mass. Thus, this solution is not assumed here. The emissivity of materials used for sails will be assumed to be constant at 0.06. The Forward mission scenario assumes that the maximum operating temperature of the sail is 2/3 of the melting temperature of the sail material. This assumption is a reasonable estimate, and will be used as a scaling law. Various sail materials were considered. Several apparently promising materials are eliminated by other considerations. Silver, despite a melting temperature higher than that of aluminum, apparently agglomerates at high temperature in thin-film form [Forward 1984]. Metallic tantalum and zirconium are greyish in color, indicating high optical absorption. Boron, with high melt temperature and low density, is a semiconductor rather than a metal; it is also greyish in color. Table 2 shows properties and the calculated figure of merit (compared to aluminum) for several candidate materials with better high-temperature performance than aluminum. Table 2: properties of metals for possible use in a lightsail Material D Tm T^4/D (gr/cm^3) (K) (norm. to Al) Aluminum (Al) 2.7 940 1 Platinum (Pt) 21.45 2045 2.8 Iridium (Ir) 22.4 2683 8. Titanium (Ti) 4.54 1950 11.0 Berylium (Be) 1.8 1550 11.1 Scandium (Sc) 2.99 1812 12.5 Niobium (Nb) 8.85 2741 22.7 Beryllium, with a melt temperature of 1550 K, is apparently an excellent candidate of the metallic films. The exceptional high temperature properties of beryllium sails for solar sail use was noted by Matloff (1984). Two metals with higher performance, due to a higher melt temperature, are scandium and niobium. Scandium is currently an extremely rare and costly material; perhaps it will be more available and less costly with further development, but at the moment, it is apparently too rare and expensive to consider. Niobium, on the other hand, is a highly reflective metal which is industrially available in large quantities, and is used in a number of applications, such as welding, stainless steel, and superconductors. Table 3 shows results calculated by using the best of these films, compared to the baseline aluminum sail. Acceleration is calculated from the figure of merit. For convenience, acceleration is calculated in gravities. The beam cut-off is assumed to occur at v=0.11 times the speed of light. From the calculation of distance, a calculation of the sail diameter can be made. Table 3: Thermally limited acceleration and distance travelled Material a (g) d (LY) Aluminum (Al) 0.036 0.17 (baseline case) Berylium (Be) 0.42 0.015 Niobium (Nb) 0.82 0.0075 Another class of possible sail materials is the dielectric thin film. Dielectric materials are transparent. By making a film exactly 1/4n times the wavelength of the light, the reflectivity can be quite high (Landis, 1989). The reflectivity at this quarter wave thickness is: R = [(n^2 - 1)/(n^2+1)]^2 (2) where n is the refractive index of the material. Forward (1986) considered multi-layer dielectric films, consisting of quarter-wavelength layers of dielectric materials alternating with quarter-wavelength spaces of vacuum. This approach can improve the reflectance to nearly unity, however, the ratio of reflectance to mass is maximized for single layers of quarter wavelength material, and so this is what was considered here. Table 4 shows three of the dielectric materials considered. Other materials are discussed in Landis (1989). For dielectrics, the thickness assumed is the quarter-wave (maximum reflectance) thickness for 500 nm light. The operating temperature Top is assumed to be 2/3 of Tmelt except for diamond, where it is 2/3 of the diamond-to-graphite transition temperature of 1800 K. Here the figure of merit (again figured relative to aluminum) is RT^4/tD, which accounts for the fact that the film is partly transparent, and also accounts for the fact that the thickness, specified as quarter wave, is not constant at 16 nm. Table 4: properties of dielectric sails Material D(gr/cc) n R(%) T(nm) Top(K) RT^4/tD Diamond (C) 3.51 2.41 50 42 1200 10.3 Silicon carbide 3.17 2.65 56 29 1333 17.4 Zirconia (ZrO2) 5.41 2.15 42 47 1810 34.7 Thin diamond (or "diamond-like carbon") films are currently being produced by a wide variety of methods. However, it is not yet possible to produce self-standing diamond films without a substrate. Likewise it is not clear that such films of silicon carbide films can be produced. Silicon carbide, while posessing a high figure of merit, is also typically not as transparent as desired. Zirconia films, with the highest figure of merit, are currently produced using electron-beam evaporation for optical coatings. A technology to remove the substrate still needs to be developed. While the figure of merit for the zirconia film is 50% higher than that for metallic niobium, the reduced reflectivity of 42% means that over half the light incident on the sail is lost. This means that, despite the possible shorter acceleration distance, a zirconia sail would require a higher laser power than a niobium sail. The use of a simple figure of merit, however, is only appropriate if the absorption (alpha) and the emissivity e are identical to that for aluminum. In fact, the dielectric films are likely to have both lower absorption and higher emissivity. This is a topic for future work, beyond the scope of the current study. Laser Efficiency Third, improvements in laser efficiency were considered. Raising the electrical to optical conversion efficiency hc directly lowers power cost. The highest conversion efficiency lasers manufactured today are semiconductor diode lasers. Semiconductor diode lasers available off the shelf have demonstrated efficiency of over 40%; 60% has been achieved int he laboratory devices (Friedman et al. 1994). Wavelengths in the blue have been achieved, for example with ZnSe laser diodes, and 500 nm operation should be achievable. The difficulty of using semiconductor diode lasers is that individual lasers diodes typically have a power of roughly 1 watt. Since it is necessary that the laser output be coherent across the entire array aperture, it will thus be necessary to phase-lock on the order of a billion individual emitting elements together. This can, in principle, be accomplished by running the lasers in a MOPA (Master Oscillator/Power Amplifier) configuration. However, the sheer magnitude of the problem makes it a daunting technical challenge. Another difficulty with semiconductor diode lasers is that thermal failures mean that long operating times require temperature control to keep the junction temperature at roughly room temperature or (preferably) lower. This means that active thermal radiators will be required. An alternate technology for high efficiency of laser power generation is the free-electron laser. High energy efficiency requires that the electron beam be recycled after the pass through the wiggler magnets. With recycling, it is claimed that the Novosibirsk FEL [Litvenko et al. 1994] can "easily" reach an e-beam to light conversion efficiency which "can exceed 30%." Efficiencies of 40% and higher are predicted as being achievable for wavelengths as low as 500 nm. Since there are two technologies (and probably others as well) for which electric to optical conversion efficiency of at least 40% is achievable, this is a reasonable extrapolation to assume for an advanced system. Directly solar-pumped lasers are also a possibility. Landis (1994) suggests that a directly solar-pumped semiconductor diode laser could be achieved using existing technology, with a conversion efficiency comparable to that of GaAs solar cells. This could further reduce the energy cost, if the laser cost is comparable to the cost of a similar-sized solar array. The difficulty of phase-locking large numbers of diode lasers is similarly difficult. Discussion Table 5 shows the results of the application of the suggested improvements in wavelength and material on the acceleration, the diameter of the lens and the sail, and finally on the total (sail, structure and payload combined) probe mass. Table 5 Thermally limited acceleration and distance travelled Sail Material lambda a Dlens Dsail Mass (nm) (g) (km) (km) (kg) Aluminum (Al) 1000 0.036 1000 3.6 1000. (baseline) Aluminum (Al) 500 0.036 707 2.5 500 Berylium (Be) 500 0.42 212 0.764 30 Niobium (Nb) 500 0.82 148 0.534 72 Note that, despite the higher acceleration, the niobium sail turns out to have a higher mass than the Be sail, due to the high density of niobium. This calculation has assumed, again, that the reduced size allowed by shorter wavelengths and higher acceleration are realized equally by lowering the sail diameter and lowering the lens diameter. The improvements over the baseline case are astonishing. Instead of requiring a 1000 km para-lens, the lens diameter is reduced to 212 km [for the Be sail]. The total lens mass is reduced from half a million tons to 23,000 tons. Likewise, required pointing tolerance is loosened by a factor of 5. The sail area is reduced from 3.6 km to only 760 meters. For this analysis, the payload has been considered to be a constant 27% of the probe mass. Incorporating all of the proposed changes into the reference mission allows the Forward probe mass to be decreased from 1000 kg (including 333 kg payload) to 30 kg (8 kg payload). Is it feasible to consider a payload as small at 8 kg? Table 6 shows the evolution of recent spacecraft designs. The improvement in mass from 100 kg to 19 kg is slightly more then the improvement in mass from Voyager to Pluto Flyby (25 years). A 19 kg payload may thus be feasible, if current trends in technological improvement, around the year 2030. For a fly-by mission, which will pass through the target solar system at high velocity, and not orbit at short distances to the (hypothetical) planets, the instruments of an interstellar probe will be more similar to the Hubble telescope than to a conventional planetary probe. It would require, for example, a large inflatable mirror of high optical quality. Alternatively, it may be possible that the lightsail mirror itself may be usable as the optical element for a telescope. This would probably require an adaptive secondary lens, since the lightweight structure is unlikely to be an optically surface of the required precision [for use as a lightsail alone, little tolerance is required on surface quality]. Communications will also be significantly more difficult. An interstellar probe will possibly use optical communications. This may be done with the same optical element used for the telescope mirror. Alternatively, the lightsail itself is a large metallized reflector; it could be designed to be used as a dish reflector for microwave or millimeter wave transmission. With the technology for such large solar-sail derived reflectors as microwave receivers, and the technology for large para-lenses as optical receivers, there should be no difficulty in receiving and amplifying even relatively small signals over interstellar distances. Thus, there seem to be no physics barriers to the technological advances required for such a spacecraft mass. Table 3 assumes that spacecraft mass decrease will be by evolutionary changes in technology. If revolutionary changes in technology occur (e.g., "Starwisp"; nanotechnology), no prediction is possible. Table 6: Spacecraft Mass Voyager (1977) 800 kg Clementine (1994) 200 kg Pluto Fast Flyby (proposed 2000+) 100 kg Interstellar (2020 +) : ??? Table 7 shows the effect of the improvements discussed on the required power levels. The most significant improvements come from the reduction of the wavelength from 1 micron to 500 nm and improvement of the laser electrical to optical conversion efficiency hc from 10% to 40%. These two factors drop the power from 650 GW to 81 GW, a factor of 8 improvement. The higher acceleration permitted by higher temperature and lower density sail material requires a proportionately higher laser power per unit area. The total power reduces proportionately to the square of the sail area, which decreases with distance and hence to the acceleration. If the lens area were held constant, and the sail area decreased with the acceleration, then the total required power would decrease proportionately to the improvement in acceleration. The design rule used, however, proportioned the advantages of the shorter distance equally to decreasing the sail and the lens diameter. The sail area thus decreases proportionately to the acceleration. This results in no change in the required power as the thermally limited acceleration improves. The density is the only factor in the power. By the use of a Be sail, the reduction in density of the material lowers the mass, allowing lower power. The Nb sail, on the other hand, because of the high density, actually requires a higher power level than the baseline. Table 7: Power Required Sail Material lambda P(laser) effic P(electr.) T Eelectric (nm) (GW) (%) (GW) (yrs) (GW-hr) Aluminum (Al) 1000 65 10 650 3 17.1 106 Aluminum (Al) 500 32 10 320 3 8.5 106 Aluminum (Al) 500 32 40 81 3 2.1 106 Berylium (Be) 500 22 10 220 0.27 0.52 106 Niobium (Nb) 500 107 10 1065 0.13 1.21 106 Berylium (Be) 500 22 40 54 0.27 0.13 106 With these changes, the required power is reduced from 650 GW to 54 GW. Even assuming no reduction in power costs from today's values, and assuming that direct solar-pumped lasers are not available, the power generation cost is reduced by two orders of magnitude. At the conservative cost of $2/watt, for example, the power generation cost is roughly 100 billion dollars, comparable to the cost of the Apollo program. At the advanced technology cost of $0.05 per watt, the cost is only 3 billion dollars, comparable to today's the cost of a large space mission such as Cassini. And, it must be emphasized, the power generation facility remains in place after the launch of the Forward probe is completed, and thus can be used either for additional prove launches, or to provide power for other applications. Global electrical usage in 1992 is 1200 GW. The baseline mission requires roughly half the world generating capacity. The redesigned mission requires about 4% of the world generating capacity. Since the rate of growth of world electrical capacity (between 1970 and 1992) is roughly 2.3 GW per year, the power generation capacity required is slightly less than that produced every two years. An alternate method to estimate electrical power costs is to look at the total amount of energy requried, Eelectric, the power times the time. Since the required amount of power is far less than the world generating capacity, it is interesting to calculate the cost assuming current prices for electrical power in the United States, which averaged 5.1! per kilowatt hour at industrial power levels in 1992. The final number, one hundred thirty thousand gigawatt-hours, would cost 6.63 billion dollars. This is very reasonable for the magnitude of the mission proposed! Conclusions Recent reviews of interstellar flight have underscored the immense cost of even a small interstellar probe. Mileikowsky (1994), for example, estimates the electrical power generating cost to send a 1000 kg interstellar flyby probe traveling at 0.3 times the speed of light as 130 trillion (1.3 10^14) dollars! Fortunately the problem turns out not to be so severe. In this paper the mission design for a laser-pushed lightsail probe has been redesigned with a "smaller, better, cheaper" philosophy. Using a shorter wavelength, more efficient lasers, and a higher temperature and lower density berylium sail, the lens and the lightsail sizes required can both be reduced by a factor of five, the acceleration increased by a factor of twelve, the probe mass reduced by a factor of 33, the power requirement reduced by a factor of twelve, and the total energy reduced by a factor of 130 compared to the baseline mission. At today's electrical generating costs, the energy cost to launch the interstellar probe is only 6.6 billion dollars. This is quite reasonable for the magnitude of the mission proposed. Additional improvements possible by using a dielectric material instead of a metal for the sail have not yet been quantified. An interstellar probe is feasible with technology known today. Appendix: Power Cost Mileikowsky (1994) notes that a one thousand kilogram probe traveling at 0.3 c has a kinetic energy of 1,180 billion kilowatt hours. Analyzing the laser-pushed lightsail propulsion proposed by Forward (1984), and assuming an electrical-to-light conversion efficiency of 30%, and a light-to-probe kinetic energy conversion efficiency of 6-7%, 65,000 GW must be supplied for 900 hours. At a capital cost of $2/W, the electrical generation facility capital cost comes to 130 trillion (1.3 10^14) dollars. At current U.S. electricity costs of 3!/kW-hr, the cost of the power used is 1.77 trillion (1.77 10^12) dollars. The capital cost of $2/watt is close to typical of the electrical power industry systems in operation in the United States today, typically coal, natural gas, and oil-fueled generators. Nuclear generating capacity is currently slightly more expensive. The operating costs of 3!/kW-hr is slightly lower than the 1990 value for average fuel, operating, and maintenance cost. The total cost to the industrial consumer, calculated in 1990, including both cost of capital and operating cost, is 5.1! per kilowatt-hour, averaged across the United State, varying somewhat from location, slightly lower in the Northwest, where there is a large amount of hydroelectric power, and somewhat higher in the northeast. Space power systems, of course, are now considerably more expensive, typically closer to $1000 per watt. The power generating system for such a laser system would likely be photovoltaic. Terrestrial photovoltaic manufacturing technology is capable of producing solar arrays in quantity at a cost of roughly $2/peak watt, where a "peak watt" is defined as the production of one watt of energy under full illumination of 1 kW/m^2 (i.e., noon on a cloud-free day). However, space solar arrays are subject to considerably more difficult requirements, such as tolerance to ultraviolet, particulate radiation, and thermal cycling, and require lighter weight technologies than terrestrial systems. Nevertheless, it is reasonable to assume that space technology, at a sufficiently large (multi-gigawatt) scale, would be able to approach (and possibly improve on) the terrestrial cost. Thus, the $2/watt value assumed is reasonable for systems typical of todays technology. Such a system likely would likely produce energy without a significant operating cost, and hence the 3!/kW-hr operating cost assumed by Mileikowsky is probably not appropriate. However, since this represents only one percent of the energy cost, the difference is negligible. Using terrestrial photovoltaic technology, however, lower costs may be possible, since a large space-based system may operate closer to the sun than the Earth's orbit, and hence at higher solar intensity. Unfortunately, output power does not increase linearly with incident intensity, since the conversion efficiency of photovoltaic cells decreases at increased operating temperatures. Nevertheless, it is not unreasonable to assume that, with innovative design of passive thermal radiation systems, it may be possible to produce ten times higher power levels out of photovoltaic systems by operating them at higher intensity without huge increases in cost. This would reduce the capital cost by an order of magnitude, from $2 to $0.2 per watt. In 1977, the United States Department of Energy made a goal for the Photovoltaic research program of $0.50 per watt, in then-current year dollars. This cost was believed to be achievable, and even lower prices of $0.10 to $0.30 possible [Maycock 1978]. While these goals are somewhat higher expressed in current dollars, it is still evident that the technology of low-cost solar arrays has not been developed to the maximum extent possible, and it is likely that future solar array prices may be considerably lower than current values. The production of hundreds of gigawatts of power generation capability would certainly result in highly efficient economies of scale! A factor of 4 reduction in price with advances in technology and low-cost production methods seems to be a reasonable, and possibly conservative, assumption. This would bring the capital cost for space-generated electricity down to $0.05 per watt. The net effect of these two modifications to the baseline power cost is to reduce the power generation cost from the $130 trillion estimate of Mileikowsky to roughly 3 trillion (3 10^12) dollars. This is still an unreasonable price for any mission to be feasible in the currently existing world sociopolitical environment. As pointed out by Andrews (1993), the power system, once built, remains in operation after the probe is launched. Hence, the capital cost can be amortized over many flights, to lower the per-flight cost; alternatively, the power system can be used for other purposes, to recoup the capital costs. One solution is to reduce the cost of power by several orders of magnitude, for example, by creating a space infrastructure incorporating self-reproducing factories to produce solar cells. Andrews, for example, considers a reduction of three to four orders of magnitude lower than existing costs. In principle, this approach could reduce the power generation price to the cost of making the initial self-reproducing factory. This technology is as yet, however, still speculative. These analyses have not included the costs of power conditioning and distribution, which have been assumed to be negligible. An detailed engineering analysis of a flight system would have to include such items. An additional consideration is the laser cost. Lasers manufactured today typically cost upwards of $1000 per watt. Clearly, lower cost technology for lasers is necessary before lightsail propulsion can be considered a viable technology. References Andrews, Dana G., and Zubrin, Robert (1988), "Magnetic Sails and Interstellar Travel," paper IAF-88-553, 39th Congress of the International Astronautical Federation, Bangalore, India. Andrews, Dana G. (1993), "Cost Considerations for Interstellar Missions," paper IAA-93-706; also presented at Conference on Practical Robotic Interstellar Flight, New York University, August 29-Sept. 1, 1994. Forward, Robert L. (1984), "Roundtrip Interstellar Travel Using Laser-Pushed Lightsails," J. Spacecraft and Rockets, Vol. 21, Mar-Apr., pp. 187-195. Forward, Robert L. (1985), "Starwisp: an Ultra-light Interstellar Probe," J. Spacecraft and Rockets, Vol. 21, May-June, pp. 345-350. Forward, Robert L. (1985/1989), private communications to G. Landis (letters). Forward, Robert L. (1986), "Laser Weapon Target Practice with Gee-whiz Targets," presented at Laser Propulsion Workshop, Lawrence Livermore National Laboratories, 7-8 July. Forward, Robert L. (1991), "21st Century Space Propulsion," Journal of Practial Applications in Space, Winter, Vol. 2, No. 2, 1-35. Friedman, Herbert, et al. (1994), "Scaling of Solid-state Lasers for Satellite Power Beaming Applications," SPIE Optics, Electro-optics & Laser Conference, Los Angeles CA, Jan. 24-28; Laser Power Beaming, SPIE Proceedings Volume 2121, 49-57. Landis, Geoffrey A. (1989), "Optics and Materials Considerations for a Laser-Propelled Lightsail," paper IAA-89-664, 40th Congress of the International Astronautical Federation, Oct. 7-12 1989, Malaga, Spain. Landis, Geoffrey A. (1991), "Laser-Powered Interstellar Probe," APS Bulletin, Vol. 36 No. 5, 1687-1688. Landis, Geoffrey A. (1994), ""Prospects for Solar Pumped Semiconductor Lasers," SPIE Optics, Electro-optics & Laser Conference, Los Angeles CA, Jan. 24-28; Laser Power Beaming, SPIE Proceedings Volume 2121, 58-65. Landis, Geoffrey A. (1994A) "Laser-Powered Interstellar Probe," presented at Planetary Society Conference on Practical Robotic Interstellar Flight, NY University, Aug. 29-Sept. 1. Litvinenko, Vladimir N. et al., "Component Technologies for a Recirculating Linac Free-electron Laser," SPIE Optics, Electro-optics & Laser Conference, Los Angeles CA, Jan. 24-28; Laser Power Beaming, SPIE Proceedings Volume 2121, 21-37. Mallove, Eugene and Matloff, Gregory (1989), Chapters 5-6, The Starflight Handbook, John Wiley and Sons, NY, 71-105. Matloff, Gregory L. (1984), "Interstellar Solar Sailing: Consideration of Real and Projected Sail Materials,: J. Brit Interplanetary Soc., Vol. 37, Mar., 135-141. Maycock, Paul D. (1978), "The Development of Photovoltaics as a Power Source of Large-Scale Terrestrial Application," Proc. 13th IEEE Photovoltaic Specialists Conference, IEEE, NY, 5-8. Mileikowsky, Curt (1994), "Cost Considerations Regarding Interstellar Transport of Scientific Probes with Coasting Speeds of About 0.3c," paper IAA-94-655, 45th Congress of the International Astronautical Federation, Oct. 9-14, 1994, Jerusalem, Israel. An earlier version of this paper was presented as Mileikowsky (1994A). Mileikowsky, Curt (1994A), "How and When Could We Be Ready to Send a 1000 kg Probe With a Coasting Speed of 0.3c to a Star?" Conference on Practical Robotic Interstellar Flight, New York University, August 29-Sept. 1, 1994. ____________________________________________ Geoffrey A. Landis, Ohio Aerospace Institute at NASA Lewis Research Center physicist and part-time science fiction writer