> how would a world be with Two Rings of Fire or more?

The "Ring of Fire" is just a colloquial term for an ocean basin mostly surrounded by subduction zones and associated volcanic arcs and has no real formal definition. While the current plate configuration has one semi-continuous ocean basin that is partially rimmed by subduction zones (i.e., the "Ring of Fire"), you could expect a later stage of a supercontinent cycle to have two ocean basins with some amount of subduction going on around their edges (though there are definitely some open questions here). I.e., at the moment, there is dominantly subduction happening around the Pacific, which is effectively the remnant of Panthalassa, i.e., the former exterior ocean surrounding Pangea, but assuming the next supercontinent forms via "introversion" (i.e., closure of the "interior" ocean basin, namely the Atlantic, to form the next supercontinent, see Murphy & Nance, 2013 for additional information on extro- vs introversion in this context), then we would expect some period in the future where subduction (and volcanism) may still be occurring around some portion of the Pacific perimeter, but has also initiated around portions of the Atlantic. Ultimately though, there's generally the expectation of having one semi-continuous ring of subduction zones (i.e., the "subduction girdle") that reflects a particular style of large-scale mantle flow (i.e., "degree 2 mantle flow") that has two broad zones of upwelling (centered above antipodal LLSVPs) and then a circular girdle of downwelling, i.e., subduction, between them (e.g., Mitchell et al., 2021). Thus ultimately, assuming mantle convection, tectonics, and the supercontinent cycle works vaguely like it does on Earth, we primarily expect there to be one "Ring of Fire" that would be coincident with this subduction girdle feature.

> How would it interact with the various species Carbon or nay?

I don't know what you're asking here.

> And what happens if a planet has no Rings of Fire?

If we interpret this to mean that a planet has no active subduction zones and thus no active volcanic arcs, given that subduction is the primary driver of plate motion (e.g., see our FAQ on this subject), we would have to interpret this to mean that said planet did not have active plate tectonics, or at least did not have mobile lid tectonics in the same style as Earth. If we relax our definition of "Ring of Fire" (and since it has no real formal definition, that's fine) to just mean that there are subduction zones, but not a configuration where one ocean basin is largely being consumed from all sides, again, this is potentially a viable part of the supercontinent cycle. I.e., there could be a period during future introversion where subduction has ceased around large swaths of the Pacific and at the same time, large-scale subduction of the Atlantic has not yet started around enough of the rim to be meet our arbitrary definition of the "Ring of Fire". The feasibility of such a state really depends on how many subduction zones and how continuous they need to be to satisfy the condition of being, or not being, a "Ring of Fire". Ultimately, as described in the Mitchell et al. paper from above, the extent to which the "subduction girdle" and associated 2 degree mantle flow is a persistent feature or something that switches between that and 1 degree mantle flow (one zone of upwelling and one somewhat more concentrated zone of downwelling, i.e., subduction zones), with or without some potential intermediate behaviors, as part of the supercontinent cycle remains an open question, but would be relevant for understanding whether we expect for the "subduction girdle" to ever truly shut down.

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