Physical meaning of one-machine and multimachine tokamak scalings

Specific features of energy confinement scalings constructed using different experimental databases for tokamak plasmas are considered. In the multimachine database, some pairs of engineering variables are collinear; e.g., the current I and the input power P both increase with increasing minor radius a. As a result, scalings derived from this database are reliable only for discharges in which such ratios as I/a ² or P/a ² are close to their values averaged over the database. The collinearity of variables allows one to exclude the normalized Debye radius d* from the scaling expressed in a nondimensional form. In one-machine databases, the dimensionless variables are functionally dependent, which allow one to cast a scaling without d*. In a database combined from two devices, the collinearity may be absent, so the Debye radius cannot generally be excluded from the scaling. It is shown that the experiments performed in support of the absence of d* in the two-machine scaling are unconvincing. Transformation expressions are given that allow one to compare experiments for the determination of scaling in any set of independent variables.