confinement scaling laws are empirical formulas, fitted to results from many tokamaks, that predict how long a plasma holds its heat as a function of machine size, magnetic field, 📝plasma current, and heating power.
The laws exist because turbulent transport long defied first-principles prediction. Rather than wait for theory, the field pooled measurements from dozens of machines into international databases and fitted power laws to them. The best known is the ITER H98(y,2) scaling, published in the ITER Physics Basis in 1999, which predicts the energy confinement time of an 📝H-mode 📝plasma to within about 15 percent across machines spanning orders of magnitude in size. Its structure carries the field's core lessons: confinement improves with machine size, magnetic field, and plasma current, and degrades as heating power rises.
A scaling law is a regression, not a theory — its danger is extrapolation beyond the database that built it, and its counterpart is first-principles simulation. Confinement projections for new machines now lean on both: the empirical scalings that sized ITER and every next-generation 📝Tokamak, cross-checked by 📝gyrokinetics, which computes the turbulent transport the scalings only parameterize.