Space Based Solar Power Radio Interference

Work in progress, may be many errors

Look up satellites by position and frequency

The Analemma

A lightweight space power satellite under light pressure cannot remain in a geostationary spot without large expenditures of delta V. If it had a very small sail ratio (area over mass), it is still subject to lunar and solar tidal effects, which require an average of 50 m/s of delta V per year to counteract, or orbit errors will accumulate over many years, following a cycle proportional to the 18.6 year nodal precession of the moon's orbit. SSPS in GEO will require at least this level of control to meet ITU requirements of staying within 0.1° of an assigned 1° slot. Newer, higher frequency satellites may be twice as closely spaced, and require even better angular control. There's 250 billion dollars worth of ground and space assets devoted to the current setup, and this will approach trillions over the next two decades. The ITU will not tolerate interference with these systems.

But power satellites have enormous areas, many square kilometers, and unless they weigh millions of tons they will have much larger sail ratios than a typical communication satellite. This means they will get blown around the sky by light pressure. Without enormous delta V per year, the only way to keep them in a predictable orbit is to let it drift in a controlled way. Similar to a server sky array, an array can be in an elliptical orbit, with perigee towards the sun. Assume 15e6 m² area and 40e6 kg, sail ratio 0.375 for a big SSPS array. GEO circular orbit velocity (sidereal) is 3075 m/s. The eccentricity is e = 3 * 4.56e-6 * 0.375 * 3.156e7 / 4 π 3075 = 4.2e-3 . A geosyncronous (but not geostationary) satellite with that eccentricity will appear to swing back and forth by 2 e radians from center, a total width of 0.0168 radians or about 1 degree. Since modern comsats are supposed to hold position within a small fraction of a degree, our satellite must occupy two (expensive) GEO slots. A lighter SSPS with twice the sail ratio will swing back and forth twice as much.

One way to cut down the slot usage is to add some inclination along with the eccentricity, so the satellite sweeps a figure 8 against the sky. This figure is called the "Analemma" and might take many shapes depending on the angle of perigee relative to the ascending node of the orbit. A power satellite beaming power to a particular spot on earth must shift its beam by phasing; the position of the grating lobes will shift, too.

A rectenna composed of halfwave dipoles with diode arrangements creating DC power will be very nonlinear, and create harmonics. The arrays won't be 100% absorptive; there will be some reflection from the rectenna at the opposite of the incidence angle, there will be Airy disk outliers, and there will be grating lobes. For the harmonics, there will be far more grating lobes, since the element spacing will be far larger than half a wavelength for frequencies 3*F and 5*F. Assuming the rectenna has elements spaced at λ/2 at F, then they will appear to be spaced at 3*λ/2 at 3*F and 5*λ/2 at 5*F.

If the incident signal is coming in at 45° then the signals will arrive at neighboring elements with a phase difference of 0.7071 π radians. This will make 9 beams of third harmonic reflection in a 3x3 grid at -56°, -9°, and +30.5&deg from east/west from zenith. As the SSPS swings one degree east/west, these 9 reflections will swing about 3 degrees east/west, and by 3 times whatever north/south angle the analemma traverses, in effect painting the analemma with 3 times larger in each angular direction, 9 times in the sky. This also makes 25 analemmas of 5th harmonic reflection centered at -56°, -25°, -2°, +22°, and +50° from zenith, swinging about 5 degrees east/west across the sky. So, for just those two harmonics (and there may be many), 34 large analemmas are drawn in the sky.

These harmonic reflections may intercept the path of a comsat, and saturate its highly sensitive input amplifiers; the International Telecommunications Union will probably require the SSPS to shut down to prevent interference if this happens. Since comsats fill geosynchronous orbit at 1 degree spacings, and that their uplink antenna dishes probably have less than 40 dB of angular selectivity, we can assume that we should not reflect any significant harmonic signal power anywhere on that belt.

Imagining all those 35 analemmas (1st, 3rd, and 5th harmonic) sweeping up and down, back and forth, painting the sky. How many times per orbit will they cross the equatorial plane, requiring power shutdown? I haven't done the calculation, but I would guess a lot. This MUST be studied.

Space Power Satellite Bands

Broadband satellite systems typically employ the 27.5-30.0 GHz SHF frequency range for uplink transmissions (earth-to-space) and the 17.7-20.2 GHz range for downlink transmissions (space-to-earth)

Distance from GEO to 45N, 38000 km, 1.8e16 m². 1W EIRP (0 dBW) produces 5.5e-17 W/m² or 5.5e-18 mW/cm² at antenna dish.

2GW powersat produces 30mW/cm², 300W/m² an EIRP of 187 dbW on beam. Sidelobe power is 0.01mW/cm² or 0.1 W/m², an EIRP of 153 dBW, and the "floor" is 100nW/cm², 1μW/m², an EIRP of 103 dBW.

I don't know how much we must filter this spike of energy to keep it from degrading a signal. Chances are, a pure tone won't land directly in the signal band, but nonlinearities in LNA and mixer could shift the frequency into the baseband. Let's be very optimistic and assume that we can tolerate a signal or harmonic of the same power as the comsat signal.

Terrestrial Microwave Links

There are far more terrestrial microwave links than GEO satellites, tens of thousands of point-to-point line segments painted over the globe. India has thousands of such links connecting its rural cell towers to the fiber optic networks following the rail lines, providing cell phone service to almost a billion customers. Imagine each of the microwave receivers with a "reception cone" a few degrees wide, pointed at the transmitter it is coupled to, but extending from there into space. Tens of thousands of cones, tangential to the earth, but pointed in tens of thousands of directions from the spherical earth.

GEO communication satellites typically confine their output to an area along the same longitude, typically between 70° north and south, usually less. The EIRP at low ground elevations is much less than 20 dBW, so the satellites will put very little power into the reception cone of these microwave links, probably less than 1e-17 mW/cm². A Gbps microwave link with efficient coding and a 2 meter dish might operate with 1e-9 mW/cm² illumination of the receiver.

A GW SSPS satellite is a different story. The sidelobe power might be as high as 1e-4 mW/cm² in the first harmonic within a degree of the main beam, perhaps 2e-6 mW/cm² (WAG) within 9 degrees of the main beam, and potentially much more from harmonic sidelobes. That will swamp any microwave link reception cone that happens to be pointed at part of the SSPS analemma. The ITU will protect the existing microwave links and never permit this.

LEO/MEO SSPS

These power satellites can have smaller transmit and receive antennas because of the closer distance. However, they will be much closer to communication antennas as well, and their "analemmas" are the entire sky of the regions they orbit over. Besides the fact that 70% of the time they will orbit over the sea and be useless as power generators, and that many of them will be needed to power a particular place on earth, they will create so much frequent interference that they will probably need to be shut down many times per minute to avoid interference.

Gigawatts versus Canada?

Anik F2 was launched in 2004 to provide services to Canada and the United States, including 2 way satellite internet. It is positioned at 111.1° W, the longitude of La Paz Mexico, Tucson Arizona, and Fort McMurray Alberta. The satellite has 50 90W Ka transponders (EIRP ranging from 44 to 62 dbW), 40 127W Ku transponders (38 to 50 dBW), and 24 30W C (33 to 41 dBW) transponders ( emission, reception ) , consumes 16 kW EOL, and weighs 5900 kg. It is built on a Boeing 702HP satellite bus. A brief 2011 malfunction interrupted communications, grounded flights, and closed banks in northern Canada. Comsats are an integral part of the world economy.

Oregon is in the Anik F2 Ka 12 spot beam, about 800 km across at at 60dBW EIRP and 38227km, elevation 35 degrees. According to the ViaSat Products Manual (Release Date: October 2013 page 14) the receive signal occupies 27 MHz bandwidth. Area of sphere at 38227km = 4π(38227000^2) = 1.8363e16 m². The power level in the spot beam is 1E6W / 1.8363e16 m² = 5.45e-11 W/m² = 5.45e-15W/cm². Power per Hz is 5.45e-15/27e6 -> 2e-22 W/Hz-cm² .

A Potential Fix

Microwave systems operate at frequencies above 100 GHz - admittedly inefficiently, but that will improve with time. These frequencies do not penetrate the atmosphere very well. At 183 GHz, water in the troposphere attenuates incoming microwaves by more than 150 dB at zenith, 300 dB at 30° elevation. Water vapor freezes out below the tropopause; there is very little in the stratosphere, and the attenuation from space is small.

A much smaller transmitter at GEO can aim at a much smaller rectenna on an aerostat platform in the stratosphere. Stratosolar is looking at placing arrays of solar cells up there; rectennas for 183 GHz would be smaller.

The most difficult issue would be maintaining sufficient control over the phasing of the orbiting emitter. Keeping the Strehl ratio for the transmitter array under 10% requires 0.05 wavelength control of phasing, and measuring the position of the emitters within 0.1 mm over a 300 meter diameter emission surface - which will be lightweight, subject to changing tidal and thermal stresses, perhaps even vibrated by coolant pumps. This will not be impossible, but it will be a challenge. 5.8 GHz antennas have this challenge as well, in the same proportion, but at a larger scale. Note that Strehl losses will spread into sidelobe power, creating interference.