Data-Driven Scaling Laws
Empirical relationships fit across devices that predict confinement and performance from engineering parameters.
What a scaling law is
A confinement scaling law is an empirical formula predicting a global quantity, most famously the energy confinement time, as a power-law product of engineering parameters like current, field, size, power, and density. Fit across many devices, such laws have guided the design and expected performance of larger machines.
How they are built
A multi-device database of discharges is assembled, and a regression (classically log-linear, giving power-law exponents) is fit. Modern work adds machine learning to capture nonlinearity and regime dependence that a single power law misses.
- Inputs: current, toroidal field, major and minor radius, density, heating power
- Output: confinement time or another figure of merit
- Method: log-linear regression, or nonlinear ML with care for extrapolation
The extrapolation danger
Scaling laws are used precisely where they are least trustworthy: to predict machines larger than any in the database. A power law fit within a range says little about behavior beyond it, and ML models extrapolate even worse than power laws, often confidently. This is the central caution.
Good practice
Report the range of the data behind the fit, quantify uncertainty in the exponents, and be explicit about how far a prediction extrapolates. Cross-validate across devices, not just within one. Treat a scaling-law prediction for a new regime as a hypothesis to be tested, not a settled number.
Design use
Scaling relations inform early sizing of any concept, including spherical tokamaks. They are one input among physics-based models, and for a design such as the Kronos breeder they are used with explicit acknowledgment that the design regime may lie outside the fitted database.