### Application of the balanced identification method to the reconstruction of the parameters of fast nonlocal heat transfer in a plasma of magnetic thermonuclear fusion

#### Abstract

The method of balanced identification, which consists in finding the optimal (in the sense of minimizing the mean square error of cross-validation) correlation between the complexity of the model and the quantity and quality (error) of experimental data, was used to correctly pose the problem of reconstructing the parameters of fast nonlocal heat transfer (FNHT) in plasma in installations for magnetic thermonuclear fusion. These phenomena manifest themselves in the instantaneous (on the time scale of heat diffusion described by the heat conduction equation) response of the spatial profile of the electron temperature to its local perturbation. The balanced identification method was used to identify the parameters of FNHT models and to verify the models themselves. These models are based on nonlocal heat transfer by electromagnetic (EM) waves with a large mean free path, described by integral (superdiffusion) equations, with respect to space variables, that are not reducible to diffusion-type differential equations. In particular, it was shown that FNHT by the EM waves in a plasma requires too high a reflectivity of the walls of the vacuum chamber to describe the experimental data on tokamaks and stellarator. Here we give a brief overview of the previous results and present the latest results of the FNHT model, which assumes strong internal reflection of waves in plasma and is compatible with the model of “wild cables” for the transfer of TEM waves along magnetically-coupled skeletal nanostructures. It is shown that for superdiffusive physical models of FNHT the balanced identification method is an effective tool for their verification. The calculations are carried out using the optimization modeling services deployed in the Everest distributed computing environment (http://everest.distcomp.org/).

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