A Hierarchy of Empirical Models of Plasma Profiles and Transport

Two families of statistical models of increasing statistical complexity are presented which generalize global confinement expressions to plasma profiles and local transport coefficients. The temperature or diffusivity is parameterized as a function of the normalized flux radius, ψ̄, and the engineering variables, u = (Ip, Bt, n̄, q95) †. The log-additive temperature model assumes that ln[T (ψ̄,u)] = f0(ψ̄) + fI(ψ̄) ln[Ip] +fB(ψ̄) ln[Bt] +fn(ψ̄) ln[n̄]+fq ln[q95]. The unknown fi(ψ̄) are estimated using smoothing splines. The Rice selection criterion is used to determine which terms in the log-linear model to include. A 43 profile Ohmic data set from the Joint European Torus [P. H. Rebut, et al., Nuclear Fusion 25 1011, (1985)] is analyzed and its shape dependencies are described. The best fit has an average error of 152 eV which is 10.5 % percent of the typical line average temperature. The average error is less than the estimated measurement error bars. The second class of models is log-additive diffusivity models where ln[χ(ψ̄,u)] = g0(ψ̄) + gI(ψ̄) ln[Ip] +gB(ψ̄) ln[Bt] +gn(ψ̄) ln[n̄]. These log-additive diffusivity models are useful when the diffusivity is varied smoothly with the plasma parameters. A penalized nonlinear regression technique is recommended to estimate the gi(ψ̄). The physics implications of the two classes of models, additive log-temperature models and additive log-diffusivity models, are different. The additive log-diffusivity models adjust the temperature profile shape as the radial distribution of sinks and sources. In contrast, the additive log-temperature model predicts that the temperature profile depends only on the global parameters and not on the radial heat deposition. PACS NUMBERS: 02, 52.55Fa, 52.55Pi, 52.65+z