That said, the earth's atmosphere has a mass of about five billion billion tons. For reference, as a species, we produce about ten billion tons of concrete each year. This is just to give a sense to the scale of effort involved in replacing a planetary atmosphere.
Depending on the volume of surface ice (especially at the poles), might it be possible to produce atmosphere on a massive scale via orbital lenses or mirrors? With recent advances in solar sail technology, I can't imagine the implementation would be too far removed from current capabilities.
Think about how large of a lens you're talking about. Even if it were one hundred meters across and was able to collect 100% of the sun's energy passing through it, the amount of energy produced would be utterly insignificant compared to the problem we're discussing. And how would you get a one hundred meter lens to mars orbit? Even after that, you have to consider that we want an oxygen atmosphere, not one made of water vapors.
I don't know what you mean by "too far removed from current capabilities", but I doubt we'll even start working on the problem for two or three centuries.
No, it seems more likely to me that we'd use our growing knowledge of genetics and psychology to hack out the part of ourselves that needs to be outside, and opt for a purely enclosed existence on Mars.
The IKAROS sail (launched 2010) is 196 m^2, using aluminum as a reflector (about 90% efficiency). With regards to transferring a lens to orbit, that is a self-solving problem - a large lens or mirror can both be used as a solar sail, potentially even hauling additional mass to Mars orbit.
Mars receives 593 W/m^2 flux, so each IKAROS-sized reflector could produce about 100 KW of energy. Given the expected difficulty of large scale terraforming and colonization efforts, it seems the cost of, say, the equivalent of 10,000 IKAROS-sized mirrors (~1 GW, comparable to a large nuclear plant) would be relatively minor.
Whether that would be more cost effective than shipping an equivalently powerful reactor or other generator is questionable - it will presumably depend on our lifting capacities.
That's about ~250x the JWST. Given that we're talking about a society that has developed far enough to be sending people to Mars and terraforming the landscape, I don't think that 8 doublings would be an unreasonable multiplier of current capability. Still a flagship, many-decade mission though.
The James Webb mirror is a rigid, astonishingly precise focusing element. A solar energy mirror could instead be merely approximately parabolic, made of a foil instead of cryogenic, made of metalized kapton instead of gold-plated beryllium, would forego focusing elements, and so on.
However, the thought of a telescope-quality mirror 250x the size of the JWST is pretty amazing :)
With lenses you could also burn the soil to produce gases that add up to he atmosphere ... but we want breathable atmosphere. With lot's of oxygen and very little co2. And that is a bit harder ...
So you also couldn't just vaporize the ice, you need to split it up. Solar heat could be sufficient, but the water will then be missed everywhere else on mars where life wants to grow.
And Mars is dry.
So I would first use the water in enclosed habitats. And then after, if there is plenty of water left, one could start to think about smoking that up ..
But there might be other options, once you have lot's and lot's of autonomous machines and rockets available and allmost unlimited fuel (sun?). But without that? Not a chance ...
I wonder if it would be a reasonable colonization process to establish a non-breathable atmosphere, allowing postprocessing facilities to later separate oxygen from airborne water vapour.
The notable benefits from such an approach would be the ability to easily deliver asteroid-based water deposits (aim it at Mars, let reentry do the rest), as well as the significant simplification of ground based colonization technology - it's far easier to build resilient habitats for a non-breathable atmosphere than it is for a vacuum, and the risk of accidents and difficulty of venturing outside is much, much lessened (a face mask or filter and oxygen tank instead of a bulky spacesuit), not to mention the radiation protection afforded by a thick atmosphere.
Also many thermoforming efforts consider adding an artificial dynamo (using, say, superconducting rings) to protect both the atmosphere and life on the surface. The energy cost of maintaining an artificial dynamo would be less than the incremental maintenance cost of maintaining atmosphere and dealing with health risks from radiation.
