A solar sail would have to be highly reflective, and able to withstand the same temperatures as the quartz fresnel lens, but it might work. That would make the Earth always visible.
The efficiency of transmission is limited by the optics. Even perfect lenses create diffraction fringes that degrade the quality of an image projected over a distance. There would be similar diffraction losses for power transmission. The relationship for transmission efficiency with diffraction-limited, otherwise perfect optics (including radio antennas) is:
At * Ar = lambda^2 * d^2 * ln(1/(1-n))
where,
At = area of transmitter
Ar = area of receiver
lambda = wavelength
d = distance of transmission
n = spot size collection effiiciency
Microwaves get horrible performance, their long wavelengths requiring huge collectors even for distances equivalent to geosynchronous orbit. Sunlight however, is composed of much shorter wavelengths, about 50% of which is between 400-700 nanometers. To get best results would require integrating across the spectrum. But for the sake of example, at 700 nm, a 505-meter Fresnel lens focussing a beam of sunlight, would only require a 523-meter diameter collector at a distance of 149.6 million kilometers (1 AU), to collect 98% of the energy transmitted (aberration losses neglected)!
Much larger collectors have been proposed, so I think it is reasonable to effectively achieve 100 percent collection efficiency, meaning the full 1-terawatt of power would be successfully beamed all the way to Earth. A second lens placed in front of the Fresnel lens could adjust the focal length, just like a telescope focussing a blurry image, so that the focus is at a convenient location near Earth. The collector could be a solar concentrator for converting heat into electricity. The quartz Fresnel lens can withstand temperatures of at least 1700 deg.Kelvin, but since the aluminum mirrors would melt at just 933 deg.Kelvin, diffusion optics would likely be needed to reduce the power density at the collector.
With the Fresnel lens, and the focussing lens, beam transmission of 81 percent efficiency can be achieved. Of that, about 20 percent can be converted to electricity, for a total of about 16 percent efficiency. So a single Fresnel lens 505 meters in diameter might provide about 162 gigawatts of electrical power in orbit. For my ARMXER Orbital Skyhook Infrastructure it would need about four large Fresnel lenses orbiting the Sun to move one percent of the world's population annually. The energy can be moved around very efficiently with ordinary optics, using beam splitters to send it this way and that - losing only 10 percent of it's power with each transfer.
Microwave beaming stations might be too big. I'm thinking ordinary sunlight might be best.
Space/Science » in reply to Forced orbit around the Sun...
re: Good Idea!
