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The core concept is a bastardized fusion of utility fogs, and the magical barriers of witches from the anime Puella Magi Madoka Magica.

Utility fogs are swarms of 100 micrometer robots, foglets, that have several arms, which they can extend and retract and "grab" the arms of other foglets.

Witches and their barriers are usually depicted as their own realm, with "familiars" roaming the place. Though neither witches nor familiars are immune to conventional weaponry, some can still tank a lot.

Barrier Magic gets it's name from the "barrier" of utility fog, that separates the magic user from the outside world, similar to what we see in Madoka, though it can't warp space and doesn't necessarily look like an LSD trip. A barrier can easily get very huge, and utility fogs are supposed to be able to manifest just about any building, so that's a similarity.

Magic always happens in barriers, but it's possible for a magic user to detach slivers of their own barrier and remotely control it. These slivers are called familiars.

Fogs "move" by forming layers that slide on each other. Basically, the top layer moves from foglet to foglet, pulling itself to the next. Once the top layer moved far enough from the edge of the bottom layer, the bottom catches up.

Barriers get most of their energy in the form of radiation. While narrowcast is less-than-ideal in most circumstances, barriers can get very large, so they're both easier to hit and are fine with a decreased energy density, a match Made In Heaven.

Now, there are magic users, mahoutsukai as I call them 'cause once you get Dorohedoro, you can't get out. Mahoutsukai are supposed to be so destructive, they can raze an entire city when going all-out.

That's okay, because they're all gone now, but it still leaves the question of how can utility fogs achieve such destruction without the barrier utterly annihilating itself in the process?

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  • $\begingroup$ 100 micrometers is only 1/10th of a millimeter. These machines are intended to be big enough to be visible to the naked eye? $\endgroup$ – James McLellan Feb 19 at 13:28
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Presumably the fog has some way to replenish itself (or used to, at least). Foglets will be lost to time, mishaps and just plain old wear and tear, so they need remaking. That could be by a fog factory or by each other (or somewhere in between).

Given that this is true: why care about destroying the fog? The amount of energy your fog can call on is (necessarily) immense, as must it’s energy transfer and storage capacity be. If you want to go all-out-blow-up-a-City with it then just do that. Have all your foglets in an area power up to max charge, then blow ‘em. If your foglets density is high enough the ones that self destructed will be rapidly replaced with nearby units and the overall foglet numbers will slowly be replaced by your foglet replacement capability.

This can act as ‘mana’ (can’t blow up foglets unless there’s enough of them) or ‘charge time’ (can’t blow up foglets until I’ve gathered enough of them). If you only blow up foglets on the leading edge of a barrier then the barrier will present as a wall of flame. How long you can keep it burning is limited only by the density of nearby foglets.

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It doesn't seem this question is answered sufficiently, so here is my take:

There are several ways that utility fogs could wreak the kind of havoc you describe. For the sake of this answer I will focus on the uses of the fog, and ignore the issues that could arise with things like control, destruction of foglets, and energy requirements to name a few.

Ps, I haven't seen the anime you're referring to, so I'm going purely off your description of utility fogs, and the one I found on Wikipedia.

Grater
Foglets will by definition be very small. And as a result be relatively sharp. When divided into small strips in a raster like pattern, one could turn a utility fog effectively into a grater. Use enough force to push this to a building, with a little vibrating action for good measure, and you'll be left with a pile of rubble when you're done. High end users could use this to sweep through a city from one end to another, or form a barrier around the city slowly going in, leaving destruction in its wake.

Stabbing
Similar to above, with a bit more control you could form these strips into tentacle-like shapes instead. Ramming razor sharp points into anything and everything you wish. The scale will be effectively smaller, but not as much energy would be needed to force through objects. One could split their barrier into a few separate tentacle monsters, and use them simultaneously.

Crushing
If sharpness isn't your thing, and you prefer a uniform barrier throughout, then you could use a crushing barrier instead. This would work by filling a room, building, or street with a dense fog, then have them push outwards against each other and the walls. With enough outward energy, this could have the same effect as a bulldozer. Or a slow bomb. You could also use this in reverse, by surrounding a whole town with the barrier, and crushing inwards.

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