operational space is the bounded region of parameter space in which a 📝fusion device can actually run — the set of density, temperature, current, field and shape combinations that violates none of its physics or engineering limits at once.
Each boundary comes from a different discipline, and each is hard. The 📝Greenwald limit caps density. The 📝safety factor (q) at the edge must stay above roughly two, which caps 📝plasma current against 📝kink instability. A 📝plasma beta limit caps pressure. Below the L-H power threshold no 📝H-mode exists at all; above a 📝divertor heat-flux limit the exhaust surface does not survive the discharge. Installed field, heating power and 📝pulse length bound the rest. Taken singly these are curves; taken together they enclose a region, often a small one, and the design point sits inside it with margin on every side — because several of the walls are not gently sloped. Crossing the density limit or the current limit ends in 📝disruption.
Which coordinates the space is drawn in decides what it reveals. Volume-averaged density against temperature gives the 📝POPCON; inverse edge safety factor against Greenwald fraction gives the Hugill diagram. Both are core-averaged frames, which is the wrong place to stand for the boundaries that govern exhaust, since those are set at the 📝plasma edge.
📝Thomas Eich and co-authors recast the problem in edge coordinates in "The separatrix operational space of next-step fusion experiments: From ASDEX Upgrade data to SPARC scenarios" (Nuclear Materials and Energy, 2025, DOI 10.1016/j.nme.2025.101896). The SepOS framework plots electron density against 📝electron temperature at the 📝separatrix, ordered by a turbulence control parameter, and its boundaries separate 📝L-mode, H-mode and density-limit disruption. Fitted against 6688 individual measurements from the 📝ASDEX Upgrade tokamak, it reproduces how the H-mode boundary moves with plasma current and magnetic field strength; normalised to the L-H minimum, the boundaries of different machines nearly coincide, which is what allows a result on one device to be translated to another. Used predictively, the framework identifies a candidate operating point for 📝SPARC free of type-I 📝edge localized mode (ELM)s, in the quasi-continuous-exhaust regime, at a separatrix electron density of 4 × 10²⁰ per cubic metre and a separatrix electron temperature of 156 electronvolts. The database is ASDEX Upgrade's and is measured; the SPARC point is a projection.