Empirical formulas that predict how long a plasma retains its thermal energy, distilled from decades of tokamak experiments worldwide.
Energy confinement time, τE, is the single number that captures how quickly a magnetically confined plasma loses heat. Because first-principles transport theory still cannot reliably predict τE from plasma micro-instabilities alone, the fusion community relies on empirical scaling laws fitted to large multi-machine databases.1
A scaling law expresses τE as a power-law product of engineering and physics variables—plasma current Ip, toroidal field BT, line-averaged density n̄e, heating power P, major radius R, elongation κ, isotope mass A, and others. The most widely cited is the ITER Physics Basis (IPB98(y,2)) scaling for H-mode plasmas:2
The ITER confinement database (ITERDB) aggregates thousands of stationary, sawtoothing H-mode discharges from JET, DIII-D, ASDEX Upgrade, JT-60U, and other devices. Entries are filtered for stationarity, ELMy conditions, and reliable power-balance measurements. Log-linear regression then yields the exponents.1
Different confinement regimes require separate scalings. L-mode plasmas follow the ITER89-P law; stellarators use the ISS04 scaling; and spherical tokamaks are developing their own expressions because their extreme aspect ratios fall outside the conventional database.3
Every next-step device—ITER, SPARC, DEMO—sizes its magnets, heating systems, and plasma current around a scaling-law prediction. The H-factor (H = τE,measured / τE,scaling) is the standard figure of merit: H ≈ 1 means the device matches the empirical expectation; H > 1 signals better-than-expected confinement. ITER targets H98(y,2) ≈ 1.0 for its Q = 10 baseline scenario.2
Despite their limitations, confinement scaling laws remain the principal bridge between present experiments and future reactors, encoding the collective empirical knowledge of the global fusion program.