My back-of-an-envelope calculation suggests that if you're collecting 3.4GW, and converting it at 85% efficiency, that's 510MW of heat that these satellites need to dump back into space.

That amount of waste heat generated in such processes is substantial ! What about harnessing it rather than dumping ? A bit of a challenge with the lack of air or water. Could thermoelectric generators be the solution? The recent coverage by SKY News suggests that this technology (Solar Farm) could be operational by the year 2030.

I'd not be surprised if it (transmission efficiency) ended up  worse than that - I'm not aware of a DC to RF method for the frequencies proposed that manages more than 70% when one includes the RF distribution losses. Even if the satellite is 500miles away, and the beam on earth is 5 miles in diameter, you are looking at something like a 3 degree beam - an antenna that has a beam-width of 3 degrees has a gain of ~35dB  (4000 or so ) in the main beam direction relative to isotropic,  A higher orbit gets proportionally narrower beam angle, and harder.

That degree of pattern control in turn implies a radiating aperture larger than a few hundreds of wavelengths across, filled with up to tens of thousands of in -phase radiating elements. This implies some dBs of  feeder losses, which at full power with central generation of the RF would be glowing, so  perhaps more easily coherent central low power Rf generation distribution with losses at proportionally low levels - after all who cares if we lose half the power in feeder loss, if it is a fraction of a watt at that point?

The low evel RF is then stepped up by an RF power amp to the 100-1000 watt level behind each antenna element or small group of elements, generating the RF  as near as practicable to the antenna sub-element feed-point. This also allows the gain and phase of the signal from each region of the transmit array to be individually adjusted to give control over beam focus and squint.

That is do-able, and spreading the  amplifiers out eases the cooling problems a bit, but creates one heck of a control problem. And all those PAs still need DC power and cooling to somewhere.

Mike.

Worth a try, But Newton law of action equal reaction will still apply.  How are you going to anchor the apparatus to stop it flying backwards?

How are you going to anchor the apparatus to stop it flying backwards?

Really!

The gradual change in orbital period and orbit height from the reaction from the radiation pressure will be the least of the worries, as the orbits will need to be tracked to keep the beam more or less focused on the ground station anyway. 

Realise we are talking about 3 newtons (300grams force) per gigawatt intercepted /radiated ( well approximating c= 1/3 *10^9 rather than the more common 3 *10^8 or if you prefer a more accurate answer consider it 3,33N per GW )

The effect on the earth's orbit and day length will be quite a lot less than that already occurring due to the moon pulling the sea about to form tides, and a small fraction of that energy being dissipated  eroding coasts and so on - yes the moon is coming in, but really slowly, not like 'London Calling' , no need to worry.

Cheers.

Mike

PS afterthoughts

Of course there are 3 lots of pressure to consider - the sunlight intercepted, the RF generated and if we radiate heat off the back of our satellite in an attempt at cooling the RF stages, it will to some extent undo this. I suspect that with some cunning we can get the various  forces to cancel to a degree over a time equal to the lowest common multiple of the earths orbit (~ 24Hrs) and the period of the satellite orbit.

How are you going to anchor the apparatus to stop it flying backwards?

Really!

The gradual change in orbital period and orbit height from the reaction from the radiation pressure will be the least of the worries, as the orbits will need to be tracked to keep the beam more or less focused on the ground station anyway. 

Realise we are talking about 3 newtons (300grams force) per gigawatt intercepted /radiated ( well approximating c= 1/3 *10^9 rather than the more common 3 *10^8 or if you prefer a more accurate answer consider it 3,33N per GW )

The effect on the earth's orbit and day length will be quite a lot less than that already occurring due to the moon pulling the sea about to form tides, and a small fraction of that energy being dissipated  eroding coasts and so on - yes the moon is coming in, but really slowly, not like 'London Calling' , no need to worry.

Cheers.

Mike

PS afterthoughts

Of course there are 3 lots of pressure to consider - the sunlight intercepted, the RF generated and if we radiate heat off the back of our satellite in an attempt at cooling the RF stages, it will to some extent undo this. I suspect that with some cunning we can get the various  forces to cancel to a degree over a time equal to the lowest common multiple of the earths orbit (~ 24Hrs) and the period of the satellite orbit.