In the article Breakthrough Starshot tricks out massive telescope for planet hunting there is casual mention of a "phased array of lasers in the 100GW range" that will propel a gram scale spacecraft to 0.2 c in a matter of minutes. That gave me pause, but usually when you read about huge powers of laser beams they are pulsed at nanoseconds or picoseconds, and the actual average power is modest.
But it works out. Just doing approximate math, the momentum of the spacecraft (non relativistic approximation) will be:
$$p_{sat} = m_{sat}v_{sat} = 0.2mc = \text{0.2} \times \text{0.001} \times \text{3E+08} = \text{6E+04 kg m/s.}$$
For photons, the energy is related to the momentum as simply:
$$E = pc$$
so you don't have to specify any particular wavelength. If the sail were a perfect mirror at normal incidence, reflecting light gives you double the momentum kick, since you're actually reversing the momentum of the photon, but let's assume 50% efficiency. Thus
$$E_{tot} = p_{sat}c = \text{6E+04} \times \text{3E+08 kg m}{}^2 / \text{s}^2$$
or 1.8E+13 Joules, or, yes, 100 Gigawatts for the time it takes to cook a three minute egg.
For three full minutes, this laser array will be using power at roughly the same rate that the US uses at peak demand. I think the idea is that you can't do it slowly, or the satellite will get too far away too soon.
There can't be a single laser with this much power, it would be a very large phased array of smaller lasers. That means they would have to be phase-coherent at optical frequencies to synthesize a beam spot on the moving satellite narrow enough to get most of the power on to it's sail.
Is there any quantitative discussion how this power might be stored and then delivered, and how atmospheric seeing might be compensated coherently across the entire distributed array simultaneously?
