A Hierarchy of Empirical Models of Plasma Profiles and Transport
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Two families of statistical models 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, ψ̅, and the engineering variables, u = (I_p,B_t,n̅,q_95)^†. The log-additive temperature model assumes that [T(ψ̅, u)] = f_0 (ψ̅) + f_I (ψ̅)[I_p] + f_B (ψ̅) [B_t] + f_n (ψ̅) [ n̅] + f_q[q_95]. The unknown f_i (ψ̅) are estimated using smoothing splines. A 43 profile Ohmic data set from the Joint European Torus 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 [ χ (ψ̅, u)] = g_0 (ψ̅) + g_I (ψ̅) [I_p] + g_B (ψ̅) [B_t ] + g_n (ψ̅) [ n̅ ]. 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 g_i (ψ̅). 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.
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