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Fusion power grows with density squared, so knowing what really sets this ceiling matters for reactors.","posed_since":"1988","precise":"Discharges disrupt or return to L-mode when line-averaged density approaches the Greenwald density $n_G = 1e14\\,\\mathrm{cm}^{-3} x (I_p / 1\\,\\mathrm{MA}) / (\\pi (a / 100\\,\\mathrm{cm})^2)$, with $I_p$ the plasma current and a the minor radius. Identify the mechanism (edge turbulence transition at critical collisionality or adiabaticity, radiative collapse and MARFE formation, tearing-island growth, plasma-wall self-organization) and derive whether the maximum density scales with heating power and wall conditions. An answer is a predictive criterion validated on several devices, including cases with $n/n_G$ above 1.","problem_ref":null,"references":"","settled_by":"A criterion that predicts the density limit, including its power and wall dependence, across at least three tokamaks.","status_note":"In 2025 DIII-D negative-triangularity plasmas reached Greenwald fractions near 2 with power-dependent limits (arXiv:2503.10854), and EAST reached $1.3\\ \\text{to}\\ 1.65\\,n_G$ with ECRH-assisted start-up (arXiv:2505.02710).","title":"Physical mechanism of the tokamak density 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