triangularity (δ) measures how far the top and bottom of a tokamak 📝plasma cross-section are displaced horizontally from its widest point — the shaping parameter that turns an ellipse into a D, or, with the sign reversed, into a backwards D.
Formally it is the horizontal offset of the cross-section's highest point from the geometric centre, normalised to the minor radius and usually averaged over the top and bottom. Positive triangularity pulls those corners inward, toward the machine's central column, producing the D-shape familiar from 📝ITER and from every conventional diverted 📝Tokamak; negative triangularity pushes them outward, giving the mirror-image cross-section. With 📝elongation it forms the leading pair of shape parameters, and the division of labour between them is clean: elongation mainly buys 📝plasma current, triangularity mainly buys edge stability.
Positive triangularity raises the 📝pedestal. The shaped edge improves stability against 📝ballooning modes, so the edge pressure gradient can be pushed steeper before the peeling-ballooning boundary is crossed, lifting the pedestal top and — through core profile stiffness — the whole temperature profile beneath it. It also eases access to 📝H-mode and shapes the 📝X-point region that steers exhaust into the 📝divertor. The cost is arriving with the benefit: the same tall pedestal that raises performance is the thing that erupts as an 📝edge localized mode (ELM).
Negative triangularity is the live alternative, and the reason the parameter carries a sign at all. Plasmas with the corners pushed outward suppress core turbulence, and in experiments on the 📝TCV and 📝DIII-D tokamaks they reach good confinement in 📝L-mode with no pedestal — and therefore no type-I ELMs. What they surrender is the pedestal's own contribution to performance and, in a reactor, considerable plasma volume, because the shape fits a torus poorly. A 2026 preprint by Yüksek and Golfinopoulos (arXiv:2603.01208) surveys whether 📝SPARC, designed throughout for positive triangularity, could produce negative-triangularity equilibria at reduced field, and finds double-null shapes at a triangularity of −0.35 and an elongation of 1.68 achievable at 8 📝tesla and 2.1 megaamps — at the cost of 43 percent of the plasma volume, since the vessel is built to the positive-triangularity boundary. That is a scoping calculation on a machine that has not yet run.