Greenwald limit is the empirical ceiling on the density of a tokamak plasma — proportional to 📝plasma current divided by cross-sectional area — above which discharges tend to disrupt.
The limit is named for physicist Martin Greenwald of the 📝MIT Plasma Science and Fusion Center, who in 1988 distilled density-limit data from multiple machines, including MIT's high-field Alcator tokamaks, into a strikingly simple formula: the limiting density in units of 10²⁰ particles per cubic meter equals the plasma current in megaamperes divided by the cross-sectional area in square meters. No fundamental constant appears in it, and no first-principles theory fully explains it — the leading picture involves radiative cooling and collapse of the 📝plasma edge — yet it has organized 📝Tokamak operation for nearly four decades.
The limit is a boundary of practice rather than a law of nature: discharges with density peaked at the center, fueled by pellet injection, have exceeded it without disrupting. Its design consequence is large, because 📝fusion power rises with the square of density: a machine that packs high plasma current into a small cross-section raises its own density ceiling, one of the core arguments for compact, high-field tokamaks.