A hierarchy of empirical models of plasma profiles and transport

Abstract

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,ψ, and the engineering variables, u = (I p , B t ,n, q 95 ) † . The log-additive temperature model assumes that ln [T (ψ, u). The unknown f i (ψ) 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] 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(ψ, u)] = g 0 (ψ) + g I (ψ) ln[I p ] +g B (ψ) ln[B t ] +g n (ψ) ln[n]. 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 (ψ). 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.

Profile shape parameterization of JET electron temperature and density profiles

“…As discussed in Ref. [3], neither the profile measurements nor the accuracy of the measurements are symmetric with respect to ρ. The outboard side measurements are more accurate than the inboard side.…”

“…The flux radius is normalised such that the toroidal flux through a given radius, ρ, is equal to ρ 2 times the total flux. In our previous articles [2,3] , we used the normalised poloidal flux radius,ψ, instead of the normalised toroidal flux radius. For the line average, we use n ≡ 1 0 n(ρ)dρ instead of the more common definition of n ≡ n(R)dR/ dR. For each profile, we calculate the line average electron density from the LIght Detection And Ranging (LIDAR) diagnostic measurements instead of using the interferometry measurement.…”

“…The Ohmic database is described in Ref. 3. Table 1 summarises the variation of the control variables.…”

“…Our previous Ohmic temperature fit is described in detail in Ref. 3. To a reasonable degree of accuracy, the JET Ohmic electron temperature profile can be fit with the "profile resilient" form:…”

“…Scaling law-like expressions are needed to estimate the performance of the next generation of experimental fusion machines. While much effort has been spent on generating scaling laws for performance parameters, only the Ohmic temperature profile shapes have been parameterised in terms of the engineering variables [1,2,3] . In this article, we report the results of the parameterisation of the Joint European Torus [4] (JET) electron temperature profiles and density shapes for different confinement regimes.…”