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During a typical pyroclastic eruption, gas and pyroclasts exit a volcanic vent at speeds of tens to hundreds of meters per second. At the vent the mixture is negatively buoyant, and rises as a plinian column only if it ingests and heats sufficient air to attain positive buoyancy. As erosion increases vent radius r during an eruption, eruptive mass flux increases with r2, but the mass of air entrained increases only with r1. Hence the column ingests progressively less air relative to its mass and eventually, at some threshold mass flux m, collapses. The threshold mass flux m depends strongly on the air entrainment coefficient ɛ, ie the velocity of inrushing air normalized to the upward jet velocity. The value of ɛ is not well characterized in the near-vent region, and likely varies with vent geometry, overpressure, and jet density among other factors. Theoretical scaling relations suggest that a two-fold variation in ɛ (eg 0.05-0.10 …