Corresponding author: Mitrishkin Yury V., D. Sc., Professor, Moscow State University, Faculty of Physics, Moscow, 119991, Russian Federation, yvm@mail.ru

Received on October 15, 2015
Accepted on November 16, 2015

The article is devoted to solving of the problem of identification of a complex dynamic plant with the distributed parameters — plasma in a tokamak magnetic field. This identification problem is solved not with the use of the advanced techniques of identification, such as subspace method or wavelets, but with application of the laws of physics and knowledge of the plasma as a controlled plant. Models of plasma are constructed from the magnetic measurements of the plasma by solving of the ill-posed problem in Hadamard's sense boundary value using the least squares method. Essentially, this is the problem of the plasma equilibrium distribution of the poloidal flux, toroidal current and of the plasma boundary reconstruction. Reconstruction (or static identification) is implemented on-line by means of the signals from the magnetic loops outside the plasma, as well as the signals from the Rogowski coils, which measure the plasma current and the currents creating the poloidal magnetic field. The plasma equilibrium is described by Grad-Shafranov equation with the unknown right-hand side (plasma current density). We approximate the plasma current density with the linear functions of the poloidal flux and iteratively solve the equation using Green's function method. Reconstructed equilibrium is used for computation of the effective inductance matrices of the system, which are applied for construction of the linear dynamic models of the tokamak plasma. The dynamic model equation is derived from the plasma force balance equation and the linearized Kirchhoff equations for plasma and tokamak coils. The constructed linear models may be used for synthesis of tokamak plasma position, current and shape control systems. The algorithms of plasma reconstruction and construction of the linear models were applied to the experimental data from spherical tokamak Globus-M (Ioffe Physical-Technical Institute of MS, St. Petersburg) in MATLAB and LabVIEW computing environments.

Keywords: identification, tokamak, plasma equilibrium reconstruction, distributed parameters, plasma shape, poloidal flux, toroidal current, linear dynamic models

Acknowledgements: The work was supported by the Russian Foundation for Basic Research, project no. 14-08-00380A.

For citation:
Korenev P. S., Mitrishkin Y. V., Patrov M. I. Reconstruction of Equilibrium Distribution of Tokamak Plasma Parameters by External Magnetic Measurements and Construction of Linear Plasma Models, Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 4, pp. 254—266.
DOI: 10.17587/mau/17.254-266

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