Power beaming is clearly central to space-based solar power concepts. Here I will provide a quick overview of my understanding of power beaming, the various equations involved, typical example calculations.
If power beaming were efficient and cheap, I believe space-based solar power would be quite viable even for grid power. However it’s not, and that largely has to do with the distances involved AND the fact that you need to convert energy multiple times, with losses along the way. The distances involved aren’t a complete show-stopper, since you can solve that problem just by operating at a large enough scale. However, the conversion inefficiencies (and the need to dump waste heat, etc) is not going to go away simply by operating at greater scale (although it helps).
The first equation we need is the diffraction limit. Roughly speaking, the spot size of a transmitted beam (microwave or laser) is:
Spot size = distance-to-spot * wavelength/(aperture diameter).
This is close enough for an order-of-magnitude estimate. More detailed work to follow.
But if we have a satellite out in Geosynchronous orbit (36000km altitude) transmitting power at roughly 10GHz (3cm wavelength, the shortest wavelength that still penetrates readily through the atmosphere) with an ...