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And why not just generate it up there, and beam it down here?

Yeah, yeah, somebody in the 70's studied that and it was impractical. But fast forward 50 years of technology and it's entirely practical now. Never mind that space-tech-guy who says it's dumb to put solar in space because you lose three times converting from light to electricity to light (to beam it down) to electricity (on the ground at the receiver). That can be very efficient now, much more efficient than the 50% average losses we get on the ground to to the periodical terrestrial eclipse we call 'nighttime'.

The "just" is doing a lot of work...

Converting from photons to something else that can be beamed and then converting it again seems more complicated than "just" a mirror that points to already existing equipment on earth

Opposite is true. Light isn't the best thing for getting to the ground, not by far. Witness clouds.

You want microwaves. Creating and focusing them is well understood, as is receiving them.

It won't 'kill us all' as is so glibly thrown around. It has some hazard, but so does clear-cutting for solar farms or coal mines. Put the receiver in a large unobstructed space.