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This paper on solar power satellite concepts makes brief reference to the ground receiver receiving an elliptical beam due to the angle it is at to the transmitter (2nd paragraph). The angle isn't that steep, some 35 degrees, and it would always receive from the same direction, so the dipole antennas could be spaced ideally.

In looking at power beaming in a similar fashion for the Moon*, the solar power satellites would move relative to the ground station, and so it would have to be able to efficiently receive power from a range of angles when the satellite was in range, and the angle would continuously change. Over what range of angles can a large grid of dipole antennas covering the ground be efficient this way?


* I'd appreciate not getting into whether space solar power is a good idea. This is for a work of hard science fiction, I'm just trying to draft the system correctly.

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  • \$\begingroup\$ I appreciate somebody getting his data correct. Not like the SF I read which said: "We are all done. Let's make a 360 and go back home." \$\endgroup\$ – Oldfart Apr 30 '18 at 17:58
  • \$\begingroup\$ This quora.com/… says there are Lagrange point in the Earth-moon system where a satellite would stay stationary against the moon. Would that help? \$\endgroup\$ – Oldfart Apr 30 '18 at 18:17
  • \$\begingroup\$ @oldfart The Lagrange points are (relatively) stationary with respect to the whole Moon. But as the Moon rotates, a base on its surface would have a constantly changing angle to that point. \$\endgroup\$ – kim holder Apr 30 '18 at 18:23
  • \$\begingroup\$ Are you talking about our moon? It does not rotate. The same side is always pointed at the earth. So it would be stable against an Earth-moon Lagrange point. \$\endgroup\$ – Oldfart Apr 30 '18 at 18:27
  • \$\begingroup\$ Right... That was slow of me. Well, the solar arrays currently are on space stations that use their power when it isn't being beamed to the ground. However the whole thing could be reconfigured so they all get power from the Lagrange point arrays... I have to think about it... \$\endgroup\$ – kim holder Apr 30 '18 at 18:31
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So, we characterize antennas using antenna pattern diagrams.

For example, the dipole has the following directivity pattern:

RadPatt-lin.png
CC BY-SA 3.0, Link

If you imagine that dipole to extent vertically in the center of this image, you can see that the maximum amount of energy transmitted (or captured, if used in receive direction) is perpendicular to the dipole's length.

Now, you'd really want that main lobe to point in the direction of your source – otherwise, energy will just be lost. While you could certainly go and rotate your dipoles, you could also do what's been pretty standard in many high-power radar applications:

Beam steering.

Since I find this easier to understand when talking about transmitting antennas, I'll explain it as if we're sending power from base station to satellite – since everything (antenna, propagation) involved here works reciprocally, it directly applies to receiving power just as well.

You might have heard of the Huygens-Fresnel Principle. The idea is that if you've got a wave front, then you can model every point on that wave front as a source of "elemental" waves, extending in a perfectly circular fashion. Only the superposition of all these means that the wave front propagates in a straight line; in essence, they constructively interfere in that direction, and cancel out perpendicularly to that direction.

Now, let's revert that idea. If all we have to do to create a wavefront going in a specific direction is to generate elemental waves that are offset in time in such a manner that the ones closer to the direction we want to steer in are just enough set off in time that the beam "slants" toward them. This wikipedia image visualizes a phased array pretty nicely:

Phased array animation with arrow 10frames 371x400px 100ms.gif
By Chetvorno - Own work, CC0, Link

All you need to have is adjustable phase delay elements for each dipole antenna (these are the \$\phi\$ boxes in the animation; \$\phi\$ is the commonly used letter for phase) and you can steer your angle \$\Theta\$ within wide boundaries, pretty much up to the point where the main beam is no longer perpendicular to your antenna array (which it would be if all the \$\phi\$ would be identical), but along the length of it.

As said, what works in transmit works in receive direction, too.

The question here really is how hard and expensive it'll be to build high-power, low-loss (because that's all heat that you'd need to get away - a problem in space), accurate phase shift units.

In the end, a large, mechanically adjustable, mesh dish antenna might be easier to realize, especially on the moon, where there's no storms against which that would need to be save against, as well as lower gravity. On the other hand, building an arbitrarily large array of dipoles can reduce the opening angle (and hence the efficiency in one specific direction) very very much (basically, the beam width as angle is antiproportional to the size of the array), and doesn't contain a single point of failure – so this might be a more scaleable solution!

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  • \$\begingroup\$ This is a lot of help. What about the way the beam from the transmitter has a larger, elliptical cross-section as it comes from a larger angle to the antenna? The flat field of antennas on the ground would also need a larger number of individual elements, right? \$\endgroup\$ – kim holder Apr 30 '18 at 19:42
  • \$\begingroup\$ Well, yes, you'd try to capture all of the beam, and that basically would require the RF-illuminated swath to be covered. I only skimmed the paper, but don't forget that if the satellite antenna array is kilometers in size, then the beam coming from that will be very, very narrow. \$\endgroup\$ – Marcus Müller Apr 30 '18 at 20:57

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