I think these problems are easily solved. Put it inside the orbit of the earth instead, so you need far less material, and have the panels fold their wings when they would transit the sun from the viewpoint of any planet. Silicon won't work at higher temperatures, but plenty of other semiconductors are available, including many that are good insulators at Earth room temperature. The paper erroneously assumes that semiconductor bandgaps don't vary with temperature, but in fact they vary dramatically, permitting efficient photovoltaic energy conversion with exotic materials even at much higher temperatures than ours.
Maybe? I thought about it for a while, but my grasp of orbital dynamics is not good enough to be sure if that's possible or not. But I think it probably is not.
Think of it this way: Build a model where earth is part of the swarm. This alone would work over the short term, but if the other members of the swarm don't have the same gravity as Earth, then earth will knock them out of orbit (and the other members may affect Earth's orbit.
To avoid the affects of Earth's gravity, chose a tighter orbit with half the period, then from Earth's point of view, the orbital path makes two loops than ends up right back where it started. This way, it's really easy to choose a path where those two loops don't cross between earth and the sun, and this can be done for the whole swarm. This also works for other fractions, with differing numbers of loops before the repeat, much like a Spirograph.
Right, I'm just not sure how that interacts with the ellipticity of Earth's orbit and how stable those orbits are.
Suppose we go for 4 times Earth's orbital period, so about 1/8 of its orbital radius, where solar radiation is 64 times stronger than the 1.36kW/m² that we get above the atmosphere here, 87kW/m², corresponding to a blackbody temperature about 1100 K, at which point we might want to use semiconductors that are excellent insulators at Earth temperatures. (This would put a large dim yellow ball around the white sun we see in the sky, but for the moment let's assume that's OK.) This radius is about 19 gigameters, only 27 times the sun's own radius, and far inside Mercury's orbit. The area of the sphere is 4.4 × 10²¹ m², so if it's 10 microns thick (probably close to a minimum for an effective solar panel, since even metals get transparent this thin) it's 4.4 × 10¹⁶ m³, and so probably about 10¹⁷ tonnes, 10²⁰ kg. Mercury is 3000 times more massive, and our own Moon is 700 times more massive, so I wonder if the orbiting power satellites would perturb each other's orbits in a difficult-to-control way.
I think these problems are easily solved. Put it inside the orbit of the earth instead, so you need far less material, and have the panels fold their wings when they would transit the sun from the viewpoint of any planet. Silicon won't work at higher temperatures, but plenty of other semiconductors are available, including many that are good insulators at Earth room temperature. The paper erroneously assumes that semiconductor bandgaps don't vary with temperature, but in fact they vary dramatically, permitting efficient photovoltaic energy conversion with exotic materials even at much higher temperatures than ours.