I assume this question is sparked by the ending of a recent episode of the >!Rings of Power!< (tagging as a spoiler since this is a new show, any subsequent details that refer to the events in said show will also be spoiler tagged). In general, the interaction of water with a magma body can definitely produce a major eruption. There are two broad types of eruptions that can result, either phreatic or phreatomagmatic, where (following the definitions from Brown & Lawless, 2001), both are eruptions primarily caused by flashing of water after encountering magma, and the distinction between the two is basically whether any lava is erupted, phreatic eruptions just expel solid products of overburden/country rock, whereas phreatomagmatic include eruptions of liquid magma/lava. >!Based on at least the quick glimpse we see of the eruption at the end of Episode 6, it's a little hard to know how to classify it, but I would lean toward a phreatomagmatic. There is clearly a pyroclastic flow and what are probably lava bombs, though to be really sure, would like to see some more clear evidence of fresh lava erupting, probably will get some clarity in the next episode!<.

Typically, in real scenarios, the water that is encountered by magma is groundwater, usually in the process of magma ascent interacting with ground water, but can there can also be phreatic or phreatomagmatic eruptions from interactions with sea water, sub-glacial water, or lakes, and there have been cases of caldera lakes basically being injected by eruptions and thus triggering phreatic/phreatomagmatic eruptions (e.g., Houghton et al., 2015, Rouwet & Morrissey, 2015). In terms of a hypothetical diversion of a river into an active volcano, whether this would trigger a phreatic or phreatomagmatic eruption depends on the details. We can consider Valentine et al., 2014, which is basically highlighting that whether you get a phreatic or phreatomagmatic eruption when magma interacts with water depends on the volume of both water and magma (and the ratio between the two) as this will set the explosive force and then the depth of where the interaction is occurring, as the for there to be an eruption, there needs to sufficient explosive force to overcome the strength of the overburden.

While phreatic and phreatomagmatic eruptions are definitely a thing (and tend to be some of the most destructive and violet type of eruptions), the feasibility of diverting a river into the active magma chamber of a volcanio is more problematic. In general, it's actually kind of hard to open up a sustained hole into a magma chamber, because it tends to seal itself. For example, when the magma chamber of the Krafla volcano was accidentally drilled into (e.g., Elders et al., 2011), the base of the hole was quickly filled with quenched magma (i.e., rock), effectively plugging the hole. Thus, arguably, artificially reaching a magma chamber to add water to it to induce an eruption would be a bit of a challenge, >!especially in the specific instance here, i.e., digging what amounts to a canal and then breaching the side of a volcano with hand tools!<. Finally, with reference to the specific representation of the "magma chamber" in the particular show in question, >!the depiction of a literal chamber full of molten rock and air is not particularly realistic.!< Broadly, magma chambers are best pictured as spaces filled with mixtures of liquid rock and significant amounts of crystals (i.e., a "crystal mush"). We would not generally expect significant air filled spaces in these chambers, especially magma chambers at depth. Lava tubes, which tend to be much more shallow, can have periods where they have both molten rock and air (i.e., they are not totally filled with molten rock), but this would broadly not be the case for magma chambers.

TL;DR If there was a feasible way to introduce a large amount of river flow into an active magma chamber, depending on the depth of the magma chamber, this could be a very effective way to produce a violent eruption, specifically either a phreatic or phreatomagmatic eruption. The less feasible part relates to how this diversion could actually reach the magma chamber as holes dug/drilled into magma chambers would probably tend to be sealed by erupting lava before the diversion could be completed. There might be some narrow set of conditions that could allow for this to happen, but >!probably not in the way depicted in the Rings of Power!<.

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