I did see a fellow once have like a tank with the center of the top cut out and a hole in the bottom with a magnifier and the inside was mirrored. Sun went in the top, bounced around for awhile then fell out the bottom. Would that be like a sun cone?
I don't know what he was trying to do or if it worked for anything, I just remember he made it for some reason and if I recall it got hot enough the grass under it was burnt!

That was like a big hot water tank or well presure tank I think and some type of mirrors to help reflect more sun into it than just what normally would shine through the hole in top. The center of the top was cut out to let sun in but the side of the top (like a ring) was still partly there to reflect the sun back down towards the bottom.
 That's about all I remember about it though.
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nothing to lose

The main disadvantage is that it must be tracked to the sun.
Of course you could make a smaller one, somewhat like a lampshade upsidedown and use aluminized mylar as a reflector.