Solar Power Satellites

A. Guidelines and Assumptionsp. 10

• Operational date 2000; two 5 GW systems a year, 300 GW total for costing purposes.
• Every rectenna sized for 5 GW. Geosynchronous orbit. Operating frequency 2.45 GHz.
• Microwave power density no more than 23 mW/cm² at the rectenna centre and 1 mW/cm² at its edge.
• All materials from Earth. A 30-year life, with no salvage value or disposal cost.
• Zero launch failures. Technology available by 1990.
• No cost margins; 1977 dollars; a 25 percent weight-growth factor reflected in costs.

B. System Overviewpp. 10–16

The system is sized for 5 GW of DC power into a conventional grid. It has one antenna, at one end, transmitting to one rectenna. The array is planar and built from graphite composite. Its size is dictated primarily by the efficiency chain (p. 11): with about 7 percent overall efficiency, 5 GW at the busbar needs about 70 GW of intercepted sunlight.

From the report · Fig. 4, p. 12

The GaAlAs option has five troughs: 26.52 km² of cell blanket, 53.04 km² of reflector and a planform of 55.13 km². The silicon option uses no concentration: 52.34 km² of blanket on a 54.08 km² planform. Either way the satellite flies with the antenna's main rotation axis perpendicular to the orbit plane (p. 11). The planforms are simply length times width: 10.4 × 5.2 = 54.08 km² and 10.5 × 5.25 = 55.13 km².

The quoted efficiency is a worst case. It includes the summer-solstice factor (0.9675), the seasonal variation (0.91) and end-of-life cell efficiency after annealing. For GaAlAs, the reflectors are 0.83 reflective at end of life, but only half the intercepted light reaches the cells by reflection, so the equivalent factor is $(1+0.83)/2=0.915$ (p. 11). Each element's factor multiplies:

From the report · Fig. 5, p. 13

The rectenna has 78.5 km² of active panel area, exactly a circle 10 km across ($\pi \times 5^2$). Construction crews are 555 for silicon (480 in GEO, 75 in LEO) and 715 for GaAlAs (680 in GEO, 35 in LEO) (pp. 11, 14).

C. Solar Cells and Blanketspp. 14–17

Both cell types are carried as reference options. Each makes a different bet on how to survive 30 years of radiation (pp. 14, 17):

From the report · Fig. 8, p. 18

From the report · Fig. 9, p. 18

At the stated densities the GaAlAs blanket comes to about $0.252\times 26.52$ km² ≈ 6.7 million kg and the reflectors to $0.018\times 53.04$ km² ≈ 0.955 million kg, the figures that appear in the mass statement (Table 1). Appendix A notes that with concentration the gallium system has a cost advantage, while without it silicon would be competitive; because of this close competition both stay as candidates (p. A-13).

D. Solar Array and Structurepp. 17–19

Blankets go up in rolled or folded modules and are wired in series and parallel to reach 40 to 45 kV. GaAlAs reflector panels are pleated like an accordion, rolled for launch, and hung from the structure on catenary cables. The primary structure for both the array and the antenna is an open truss of graphite-fibre-reinforced thermoplastic, with beams designed for automatic fabrication in space (p. 19).

E–G. Power Distribution, Rotary Joint and Attitude Controlpp. 19–25

These three short sections are merged here. The array is split into switchable power sectors, so any sector can be isolated for annealing or repair. Voltage is held by switching groups of cell strings on and off. On the antenna, DC–DC converters and switchgear feed the klystrons, and about 12 MWh of batteries carry the antenna through eclipses and shutdowns (pp. 19, 22).

Power crosses to the antenna through slip rings and brushes in a rotary joint. A 350 m mechanical turntable turns the antenna yoke once a day. The antenna hangs in the yoke on a compliant joint and is aimed by control moment gyros on its own structure (p. 22).

Attitude control for the GaAlAs satellite uses 64 argon ion thrusters, about 36 of them operating at once, in four locations; this allows for annual maintenance, 5,000-hour grid life and a five-year mean time between failures. Each thruster gives 13 N at a specific impulse of 13,000 s, draws 1,275 kW, has a 1 m aperture and weighs 120 kg. The system averages 34 MW (pp. 22–25, Fig. 13). The satellite flies with its long axis perpendicular to the orbit plane.

H. Microwave Power Transmission Systempp. 25–46

DC-to-RF converters feed a 1 km phased array with a 10-decibel Gaussian taper: the power density falls by a factor of ten from centre to edge. The antenna is built from 7,220 subarrays, each about 10 m square, with slotted aluminium waveguides on the front and the power tubes on the back. Every subarray has its own receiver and phasing electronics, which lock onto a pilot beam sent up from the rectenna. The subarrays add into one coherent beam focused on the rectenna centre. About 88 percent of its energy falls within 5 km of boresight, and the beam is 1.2 arc-minutes wide (p. 25).

From the report · Fig. 14, p. 26

Antenna characteristicspp. 29–30

The primary structure is an octagonal open truss 130 m deep and over 1,000 m across. A deployable cubic truss 9.93 m deep holds the subarrays. Of the illumination functions studied, with phase and amplitude errors and failed elements included, the 10-dB Gaussian taper performed best overall within the density limits at both ends (p. 29).

The taper is built in ten steps: 36 tubes per subarray at the centre, falling to 4 at the edge, for 101,552 tubes of 70 kW each. A 50 kW alternative would need about 140,000, from 50 per subarray at the centre down to 6 (p. 30).

From the report · Fig. 16, p. 31

Step	Outer radius, m	Subarrays	Elements / subarray	Tubes	kW/m²
1	93.9	276	36	9,936	22.14
2	177.3	632	30	18,960	18.45
3	229.5	644	24	15,458	14.76
4	271.2	628	20	12,560	12.30
5	323.3	784	16	12,544	9.84
6	365.1	900	12	10,800	7.38
7	396.3	664	9	5,976	5.54
8	417.2	612	8	4,896	4.92
9	458.9	1052	6	6,312	3.69
10	500.6	1028	4	4,112	2.46
Total		7,220		101,552

Radii from Fig. 17, elements per subarray and power density from Fig. 16, subarray and tube counts from Fig. 17.

The beam at the rectennapp. 30–37

Antenna errors give a wider, weaker main beam and higher sidelobes. Only part of the main lobe is collected; the sidelobes spread over a huge area at densities too low to be worth collecting (p. 30). The peaks are 23 mW/cm² at boresight, 1 mW/cm² at the rectenna edge and 0.08 mW/cm² in the first sidelobe, two orders of magnitude below the U.S. standard of 10 mW/cm² (p. 30).

For a circular aperture of uniform rings at range $R$, the far-field density on the ground at distance $\rho$ from boresight is

$$S(\rho )=\frac{1}{{\lambda }^2{R}^2}{\left|\sum _{i=1}^{10}2\pi \sqrt{q_i}{\left[\frac{r{J}_1(ur)}{u}\right]}_{r_{i-1}}^{r_i}\right|}^2,u=\frac{2\pi \rho }{\lambda R}$$

$q_i$ and $r_i$ are each step's density and outer radius (Figs. 16–17), $\lambda =12.24$ cm at 2.45 GHz, $R=35,800$ km (App. A, p. A-2), and $J_1$ is the Bessel function. At the centre this reduces to $S(0)={\eta }_{ap}{P}_t{A}_t/({\lambda }^2{R}^2)$, where ${\eta }_{ap}=0.90$ is the taper's aperture efficiency, worked out from the Fig. 16 densities.

From the report · Fig. 18, p. 33

• Ground power density
• Report's printed values (Fig. 15)
• Inside the rectenna (dashed: edge)
• U.S. exposure standard 10, USSR guideline 0.01 mW/cm²
• Beam defocused (no pilot signal) 0.003 mW/cm²

10-dB taperUniform

With error budgetPerfect array

Rectenna radius

5.00 km

The reference rectenna is 10 km across, measured square to the beam.

Centre

23.2mW/cm²

At edge

0.82mW/cm²

Captured

90.1%

1st sidelobe

0.083@ 8.0 km

If phase control fails completely, for example if the pilot transmitter shuts off, the subarrays lose phase and the beam spreads out. The peak falls to 0.003 mW/cm², which the report calls a fail-safe feature, below the USSR guideline. Sensors near the rectenna would also detect large changes and shut the antenna down (p. 30).

$$S_{\text{defocused}}\approx \frac{P_t{A}_{\text{sub}}}{{\lambda }^2{R}^2}$$

Why the fail-safe works: with random phases the subarrays add in power rather than in field, so the whole 6.7 GW is spread as if by a single 108 m² subarray ($A_{\text{sub}}$) instead of the full 1 km aperture.

Far sidelobes from one satellite are three to four orders of magnitude below 0.01 mW/cm². Even 200 satellites would stay one to two orders below it. The downlink sits in the 2,400–2,500 MHz industrial, medical and scientific band, which some eastern European countries do not recognise (p. 34).

Grating lobes repeat every 440 km on the ground. They come from the regular subarray spacing and depend on mechanical misalignment; uniquely, they stay put while their strength varies, because of the retrodirective phasing. Keeping them under 0.01 mW/cm² requires antenna tilt under 1 arc-minute and random subarray tilts under 3 (pp. 34–37). Their spacing is $\lambda R/d$ for subarray pitch $d=10.4$ m; at a slant range of about 37,400 km, typical of a mid-latitude rectenna, that is 440 km.

Close to the antenna the beam has not formed yet. On the axis, density peaks at about 32 kW/m² some 1,600 km out (p. 37, Fig. 23).

Rectenna characteristicspp. 37–43

The rectenna is a field of half-wave dipoles, each feeding a Schottky-barrier diode through a two-stage low-pass filter that suppresses harmonics and matches impedance. To save money it is built as rows of serrated panels square to the incoming beam rather than a continuous surface. Each panel has a steel-mesh ground plane of 75–80 percent optical transparency on steel framing and concrete footings, with aluminium collector wiring (p. 37). The total active panel area is 78.5 km² (p. 41).

Of the incident power, about 98 percent is collected by the dipoles and 2 percent reflected, upward and toward the southern horizon. About 1 percent leaks through the mesh, and about 7 percent becomes heat in the elements and diodes. Diode harmonics are −25, −40 and −70 dB for the second, third and fourth (pp. 41–43).

From the report · Fig. 24, p. 42

The beam arrives at a slant, so its circular cross-section lands as an ellipse. A 10 × 13 km rectenna (Fig. 7) implies a stretch of 1.3, which corresponds to a site near 35° latitude below a satellite on the same meridian (from the geometry of geostationary orbit). The 78.5 km² is the area measured square to the beam.

I. Mass Statementpp. 47–48

Mass falls into three parts: solar array, antenna, and the interface between them (rotary joint, slip rings, yoke). The antenna is the same for both options and is dominated by the transmitter subarrays with their klystrons and waveguides. Concentration halves the GaAlAs blanket area and with it most of the mass difference (p. 47).

J. Space Transportationpp. 47–58

The fleet is dedicated to the program and designed for minimum total cost, with energy use, environmental impact and critical materials kept low. Cargo goes up on the HLLV and people on the PLV. Between low orbit and geosynchronous orbit, cargo rides the COTV and people the POTV (pp. 47, 49).

From the report · Fig. 27, p. 50

K. Natural Resourcespp. 58–64

Table 4 lists the materials, in tonnes, for the satellite, rectenna and every vehicle, split into what is specific to the silicon program, what is shared, and what is specific to GaAlAs. Table 5 totals them for the first satellite, which carries the construction bases and the COTV fleet, and for each later year of two satellites. The GaAlAs program's construction bases appear only as total-mass estimates, still under study (pp. 58, 64).

L. Operationspp. 64–76

Each satellite needs mass production on a new scale: about $10^{11}$ solar cells, $10^5$ klystrons and $10^{10}$ dipoles. Launches burn about $10^6$ t of hydrocarbon propellant a year, and options from coal processing to rectenna-powered electrolysis were under study. Packaging matters: densities range from 12 kg/m³ for antenna subarray elements to about 2,500 kg/m³ for conductors, so loads are mixed to fill each launch (pp. 64–66).

From the report · Fig. 33, p. 65

Startup. Before any satellite is built there are two years of preparation. For silicon: six months to build the LEO base, three for the first COTV, three more for the second and third, and a year for the rest of the fleet; the first COTVs carry up the GEO base, which takes nine months. For GaAlAs the GEO base is built in LEO first, builds the COTVs there, and is then towed up by two of them (p. 69).

Steady state. All the material for one satellite reaches LEO in six months, rides COTVs for six months to GEO, and is assembled during a six-month arrival window. The sequence for any pair takes 18 months, but once it is running two satellites come off the line each year (p. 69).

In commercial service, output varies with season, time of day and orbit, and eclipses cause shutdowns, so ground plants must be able to throttle to follow demand. With about $10^5$ klystrons failing at random and blanket sections occasionally replaced after meteoroid damage, each satellite needs 5 to 20 people in GEO, probably based at the construction base (p. 73). Program headquarters, launch control, the LEO and GEO bases, and a control unit at each rectenna make up the management concept (p. 76).

M. Costsp. 76

This section is two sentences long. Costs had been estimated, but they were held for the DOE Comparative Assessment Study and are not given here (p. 76).

Key assumptions

• Program ground rules (p. 10): two 5 GW satellites a year for 30 years starting in 2000, zero launch failures, technology available by 1990, no cost margins, and no salvage or disposal cost. The fleet, crew and materials figures are built on these.
• The ionospheric limit. A peak of 23 mW/cm² at the beam centre sets the antenna size, the rectenna size and the power per satellite. The report describes it as a theoretical threshold awaiting experiment (p. 29).
• The transmitter heat limit of 22 kW/m² (21 kW/m² in Appendix A) reflects how much klystron waste heat the antenna can reject.
• Worst-case rating. The 5 GW is set at summer solstice with end-of-life cells (p. 11). Eclipses of up to about 75 minutes around local midnight, for some six weeks each spring and autumn, are outside the rating (p. A-10).
• Antenna tolerances of 10° rms phase, ±1 dB amplitude and 2 percent failed tubes (Fig. 15) underlie the beam pattern, the 88 percent beam capture and the 63 percent link efficiency.
• Earth materials and geostationary assembly throughout, with lunar materials and other orbits left for later study (p. 9).

Where further work would help

The two microwave limits. Because transmitter density scales as $P/D^2$ and beam-centre density as $P{D}^2$, the largest output per satellite scales as $\sqrt{q^{\ast }{S}^{\ast }}$ and the antenna diameter as $(S^{\ast }/q^{\ast }{)}^{1/4}$ (see the sizing figure). Measurements of how the ionosphere responds near 23 mW/cm², which the report notes were under way both theoretically and experimentally (p. 29), and of achievable antenna heat rejection would show how far the 5 GW, 1 km, 10 km combination can move.

Building and holding the array's tolerances. The beam shape, sidelobes and grating lobes depend on the phase, amplitude, failure and alignment budgets of Fig. 15 and on the open choice between phase conjugation at each subarray or at each tube (p. 43). Hardware tests of subarrays and of the pilot-beam phasing system, which head the report's list of critical questions (p. 80), would show how well the design holds over a 1 km structure.

Thirty years in orbit. The end-of-life efficiencies assume annealing recovers radiation damage: self-annealing at 125 °C for GaAlAs, laser annealing for silicon. Long-duration tests of blanket materials under radiation, UV and plasma at 40–50 kV, of 30-year slip rings, and of composite stability in GEO and LEO (pp. 80–81) would show whether these factors carry over the full design life.

Scale-up on the ground and in space. Each satellite needs about $10^{11}$ cells, $10^5$ klystrons and $10^{10}$ dipoles (p. 64), and the construction scenario depends on space fabrication, electric orbit transfer and a fully reusable heavy lifter that did not yet exist. Rectenna construction methods had not yet been worked out (p. 73). Demonstrations at intermediate scale would show how the timeline and fleet sizes extrapolate to two satellites a year.

Costs and siting. Cost estimates were held for DOE's comparative assessment (p. 76), and rectenna land use and latitude are left to later studies. Both are needed before the reference system can be compared with other power sources.