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Imagine a large cavern on the moon, around the theoretical size limit determined by Purdue university - about 1.5 kilometers high, and 5 kilometers across on the floor. This cavern is a kilometer or so underground, and is covered by several billion years of volcanic basalts. Let's say it's an empty magma chamber, with a vent filled with loose materials from when the magma receded. Then it was covered with many layers of lava when the mare were formed.

Now, a few hundred million years ago something causes an overturn in the mantle, and a large amount of gas-rich magma rises under the dome such that water vapor and other gases from the magma makes its way into the vent. Assume the cavern is otherwise gas-tight, but started out as a vacuum. The amount of water vapor from below is very large.

This chamber is at equilibrium temperature with the upper crust, or about -20C.

Here's my WAG: Consider the water vapor alone. As I see it, it would enter the chamber, and then begin to crystallize as frost on the various surfaces. It would continually sublimate and re-freeze until the vapor pressure inside the chamber hit about 103 Pascals, the vapor pressure of ice at -20C. Then the vapor would simply begin to accumulate as ice. Eventually, I assume an ice cap would form at the bottom of the chamber until the pressure of the ice over the vent prevented any more leakage. Or alternatively, the pressure could begin to build until it's at equilibrium with the pressure of the source.

I assume I'm missing lots of details, as I know very little about geology and chemistry. For example, would the ice accumulate evenly everywhere? Or would it collect at the bottom? At -20C water molecules leave a surface at over 500 m/s, and could climb hundreds of kilometers on the moon, so I assume that height isn't a factor inside the cave.

The sublimation would cool the surfaces, but they would be reheated by the surrounding rock until back at a -20 equilibrium, I imagine. I assume that would be the source of energy driving whatever is going on in this cavern.

So I'm guessing that after the vapor pressure rose enough you would get hundreds of millions of years of constant sublimation/refreezing, and possibly enough water molecules to adsorb into the surface of the rocks or into the pores and freeze to act as a further barrier to leakage of vapor through the rock? Or would the constant freezing and sublimation actually start to break down the rock walls of the cavern?

Am I missing any critical details in figuring this out? I understand it's very hard to justify a 'gas tight' cavern on the Moon, but I'm making that a requirement just to understand what would happen if such a thing was possible. Ideas for how it might happen would be for another question. And it looks like it's possible at least rarely as there is evidence of fairly recent explosive outgassing on the moon.

Would the interior of this thing look like the inside of a freezer, with rime frost everywhere? Or would the quantity of water be small enough at equilibrium that you'd just see specular highlights? Or would the water ultimately collect at the bottom, leaving a chamber with a sheet of ice at the bottom and mostly dry rock elsewhere?

If we assume that other gases were present, would it change anything? Eventually the chamber would also have argon from potassium decay in the rocks, and maybe other gases from below.

Basically, any answers that help nail down the behavior of water and ice over time in such a cavern is what I'm looking for, since I'm not sure I know enough to know what I don't know. If it helps, I would accept a simplified scenario exploring what would happen if we chilled a huge dome to -20 and then inserted enough water to create an equilibrium vapor pressure, then sealed it up for a a long time. What would happen inside?

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