Co-orbiting calibration of the SSPS Wavefront
One of the unexamined assumptions of the canonical space solar power satellite design is that the vast array of emitters across the transmission antenna can be calibrated from a "pilot beam" from Earth. Unfortunately, this requires an additional source of perfect timing information, and that the emitters are able to receive and transmit simultaneously, or close to it.
The Phasing Problem: Interference, not merely Inefficiency
The fundamental problem is that the transmission antenna will not be perfectly rigid and flat; it will curve and have ripples and mechanical vibrations, because it is oriented in a nonlinear gravity and centrifugal field ("tidal" effects) and is made from lightweight materials with nonuniform mass distribution and nonuniform stiffness. This will cause efficiency losses, and an unacceptable amount of scattered intereference power.
Over a kilometer-sized antenna, with a 12 centimeter wavelength, a 20 part-per-million average flatness error is 2 centimeter, which is a phase error of 16% and a Strehl ratio of 12%; that is, 12% of the power will be randomly scattered. This is not a showstopping amount of loss, but 12% of a 50 Terawatt constellation of space solar power satellites is 6 Terawatts. If that is scattered into an average 1 steradian wide beam in the general direction of Earth, with an average path length of 40,000 km, and divided by 4, the globe-to-disk ratio, that is about 1 milliwatt per square meter of noise illumination across the planet.
1 mW/m² is not biologically lethal, but the interference will wipe out all microwave communications on Earth. Radios are designed for ambient noise environments of picowatts per square meter, not milliwatts.
WIFI, bluetooth, zigbee all use the ISM bands, and will be directly destroyed. Higher frequency microwave communications (like satellite downlinks and uplinks) and radar would also be blinded, because they depend on a broadband low-noise amplifier (LNA) to amplify signals above the noise floor, before the first filter, mixer, and detector in the microwave receiver. Because these sensitive amplifiers are not perfectly linear, they "mix" high power interferers with low power signal, creating intermodulation, creating noisy images of the desired signal and other signals that subsequent filters cannot remove. Filters cannot be put in front of the low noise amplifier - filters create resistive noise, which is why the LNAs are there first. This is a well known problem for radio system design.
SSPS advocates who attempt to create this problem, and expect others to magically learn how to solve it, are few and easily ignored. As they have been, for good reasons, for half a century. The path forward requires knowledge, accomodation, and cleverness, not ignorant arrogance. We are few, they are many, and they are right.
Phase Compensation - Minimizing Strehl Error
The usual handwaving assumption is that a pilot beam, sent from Earth, will be used to calibrate the phasing of the emitters. If the pilot beam wavefront arrives at the emitter element late, then the power transmit beam is sent early to compensate.
Late and early compared to what?
Perhaps each of these emitters has a perfect source of timing, a temperature compensated oscillator with zero drift and phase error, or a cable connected to one. But how do we determine what the phase of the oscillator should be? Where is the emitter in relation to the outgoing wavefront? All the different emitters will be different distances from Earth, the transmit antenna will not be perfectly perpendicular to the outgoing beam. It will move in tidal forces, perhaps turn intentionally, and so a measurement that is valid at 0 seconds will not be valid at 0.1 seconds. The speed-of-light round trip delay over a 40,000 kilometer path is 0.27 seconds, and a 1 kilometer transmit antenna rotating at one degree per minute is moving 15 centimeters per second at the edge, 4 centimeters in one round-trip time.
The antenna may also be rippling and vibrating with much larger amplitudes. I have not seen estimates of this in the SSPS literature; but starting and stopping movement in a thin, distributed, nonuniform structure without external damping suggests it will vibrate, on a very large and persistent scale, like the flags planted on the Moon.
Ultimately, the biggest problem is that the compensation is a phase subtraction. We are subtracting the pilot beam time from a reference time, inverting, and adding the difference to the outbound signal. At microwave oscillation rates. How accurately must we do this?
Assume we must reduce Strehl error to a nanowatt per square meter. That is still vastly larger than receive signal power for microwave systems, but perhaps we can replace all of them with more robust systems designed to reject SSPS noise. Note to accounting: include replacing billions of $100 to $10,000 systems, and the entire comsat and radar fleet, in the SBSP budget. We break it, we fix it.
So, how accurate must the phase compensation be? 1 centimeter created 1 mW/m² of interference, and the behavior of Strehl noise is roughly square law. To get to 1 mW/m², the phase error (in space) must reduce to 1e-2/sqrt(1e6) m or 1e-5 meters, 10 μm. At the speed of light, 10 μm is 30 femtoseconds average timing error, 1 part in ten trillion of a 0.27 second path length. Perhaps our design is more clever than that, and the appropriate ratio relates to the 2.5 GHz, 400 picosecond transmit frequency. That is an error of 75 parts per million, including the whole chain of reference creation and generation, including aging, thermal expansion, and component accuracy. Seems unlikely.
There's an elephant in the room, and it is pooping on an old, broken idea.
Pilot Beam from the Back, Verification in from the Front
The noisy difference becomes a perturbation on a reference signal if the pilot beam is supplied from the opposite side of the SSPS. We still need to perform accurate phase calculations at each emitter, but more of the the errors cancel, not add. If we place the reference source nearby (say 10 kilometers spacewards of the power satellite), then a large delay is subtracted from our position estimate; distance measurement errors are reduced by a factor of 4000, acceleration measurement errors by a factor of 6e7 .
Indeed, we can estimate from multiple backside pilot beams, and construct a realtime three dimensional model of the transmit surface (or more precisely, the reference receiver plane on the back), and use that to calibrate our realtime mechanical simulations of the surface. The low power calibration surface on the back will be isolated from the high power transmit surface on the front.
In addition, we can measure the wavefront coming out the front side of the SSPS with multiple nearby test receivers in the beam, perhaps 10 kilometers Earthward. Rather than wait 270 milliseconds for ground confirmation that we are calibrated, we only have to wait 70 microseconds. That is a much tighter control loop. There will still be ground confirmation arriving 270 milliseconds later (probably from MANY terrestrial test receivers) which we can use to calibrate the nearby test receivers.
We no longer rely on a distance-attenuated pilot beam from Earth, or a difficult phase conjugation. Instead, we compute and calibrate phase corrections locally, in microseconds, and build an accurate model of our SSPS that we use to null out remaining errors. This will require a lot of local computation, but we have the power for that, and computers have improved a billion fold since the early space solar power designs.
But how do we make our calibrators hover in front and back?
We don't. We put hundreds of them in "co-orbits" around the central SSPS.