elongation (κ) is the ratio of a tokamak 📝plasma cross-section's height to its width — the number saying how far the plasma has been stretched from a circle into a vertically extended D.
Formally it is the plasma's semi-height divided by its minor radius, so a circular cross-section has an elongation of 1, a conventionally shaped tokamak runs between roughly 1.5 and 2, and a 📝spherical tokamak can exceed 2.5. Definitions differ in the detail, and careful papers say which they use: the elongation quoted at the 📝separatrix is larger than the areal elongation derived from the cross-sectional area. The distinction worth holding is against 📝aspect ratio, which compares the two radii of the torus and fixes the machine's silhouette seen from above; elongation instead describes the shape of the poloidal cross-section, and the two vary independently. Together with 📝triangularity, elongation forms the leading pair in the standard parametrisation of plasma shape.
Elongation is bought for 📝plasma current. A taller cross-section encloses more area at the same minor radius, so at fixed 📝toroidal field and fixed 📝safety factor (q) the plasma carries substantially more current — and because both 📝confinement scaling laws and the 📝Greenwald limit improve with current, stretching the plasma raises attainable performance without strengthening a single magnet. It also raises plasma volume at fixed major radius, which feeds 📝fusion power directly.
The price is that a vertically elongated plasma is vertically unstable. Producing the shape requires a shaping field whose curvature pushes the plasma further from the midplane once it has drifted off it, so a small vertical displacement grows exponentially, and faster the more elongated the plasma is. Elongation is therefore limited by controllability rather than by any pressure limit: the machine needs a conducting wall close enough to slow the motion passively, plus fast feedback on 📝poloidal field coils driven by 📝magnetics diagnostics, and losing that loop is a 📝vertical displacement event. 📝SPARC is designed for an areal elongation near 1.75, with a vessel wall thick enough for 📝disruption forces that also holds the predicted vertical growth rate at or below roughly 100 per second (Nelson et al., arXiv:2401.09613).