Honestly I'd leave it empty and cap the gap with pavers or similar. What it sounds like you are describing is how you build a smokeless fire pit and you'd want to avoid interrupting the airflow in that case.
Home Improvement
Home Improvement
This. Drill holes in the bottom of the outside ring and top of the inside ring. Though I'd recommend a much smaller gap if possible. If not possible, adding rock in such a way as to act as baffling would be good too. Metal louvers or ducting might work. The key is to get the air to heat up between the rings so when it exits the inner ring it burns quick and more completely.
do you want natural rock or is synthetic also ok? also do they need to be resistant to freezing water as well? its not clear if there will be any kind of roof above…
very conservative answer would be something like granite, diorite or similar dense rock.
if you have protection from water you can also use more porous rocks like sandstone.
Either is fine, I'm trying not to break the bank on it though. The pit will be outside, below a high canopy but not covered/roofed. I'm also not sure where I'd even find some of the more esoteric rocks. Would chipped marble work here?