(Note: the following is one of various posts that were copied here from the Moonwards.com forum for the sake of preserving the early days of the project. It was originally posted there on Nov 6th, 2015)
Here's a deceptively simple model of Fresnel lenses focusing bands of sunlight on regolith fines that have been delivered and smoothed level by the crane. It's deceptive for several reasons. For instance, for me, it didn't feel simple deciding if the crane should level the fine-grain material or there should be dedicated robotic gizmos doing that, if the stuff should be tamped (i think no), whether the lenses should move on rails or suspended cables, et cetera. Also deceptive because you can't see the motorized gizmos that move the lenses around and aim them, even though they have a lot of detail. But enough whining.
Those lenses are roughly 7 m across. With about 1366 W/m^2 of solar energy to work with, and allowing that 10% will be reflected off the lenses, each one is thus focusing about 47 kW of energy onto the ground. Toasty. Maybe the thing would be to craft each one to focus to a different shape - one to a point, and the other three to bands of different widths. The positioning gizmos can raise and lower them to spread that 47 kW over the right area to get the depth and rate of melting for the application at hand.
What that boils down to (heh) i don't know. Because of the very jagged and irregular shapes of regolith particles, even at maximum compaction it is about half voids. It transmits heat very poorly. And heat would be coming in really fast. As top layers melt, they are going to sink into the regolith and leave a hole. That is why the fused regolith components shown in the illustration lie in troughs. The bottoms and sides of the shapes created could be quite irregular, shifting from pure fused material to a crust of bubbly stuff with an ever increasing proportion of voids. All shapes will be rounded - didn't get that in the model yet, i'll have to modify it later.
Still, it's so damn simple, just get used to it and make allowance for its properties, and you have a constant supply of building materials using nothing more than a few simple motors and very basic components. So what if they maybe aren't that sturdy for their size - use more of 'em, you can make them fast.
Sapphire lenses will last for decades. They and their positioning gizmos can be lifted off their rails at nightfall and taken by the crane into the dome under construction, where the residual heat from the day's lava production will protect all your gear from the deep freeze of night. Maybe throw a reflective sheet over everything, you're done. Nothing fancy here, that's super good when trying to build a base in space.