2D interpolation and extrapolation of discrete magnetic measurements with toroidal harmonics for equilibrium reconstruction in a tokamak

Abstract

We present a method based on the use of toroidal harmonics and on a modelization of the poloidal field coils and divertor coils for the 2D interpolation and extrapolation of discrete magnetic measurements in a tokamak. The method is generic and can be used to provide Cauchy boundary conditions needed as input by a fixed domain equilibrium reconstruction code like Equinox [1]. It can also be used to extrapolate the magnetic measurements in order to compute the plasma boundary itself. The proposed method and algorithm are detailed in the paper and results from numerous numerical experiments are presented. The method is foreseen to be used in the real time plasma control loop on the WEST tokamak [2].

Robust sparse linear regression for tokamak plasma boundary estimation using variational Bayes

“…The spatial distribution of the magnetic flux ψ(r, z) can be decomposed into an infinite series of basis functions f i (see [3] for details). Using the assumption of symmetry of the threedimensional plasma column in the toroidal direction, for each point in the vicinity of the plasma with coordinates (r, z) in the poloidal plane the flux distribution can be decomposed into an infinite series:…”

“…However, full reconstruction of the equilibrium magnetic field (which includes the plasma shape) is a complex task due to non-linear behavior of the plasma. In [3], it was shown that the plasma boundary can be modeled by a linear combination of a specific kind of basis functions. Since the basis functions are known, the estimation problem can be formulated as a simple linear regression with a potentially infinite number of regressors.…”

Tokamak Plasma Boundary Reconstruction Using Toroidal Harmonics and an Optimal Control Method

“…The number of harmonics to be used need not be large to obtain precise fit to the measurements. 9 Typically the order of the harmonics is chosen to be 4, 5 or 6. Figure 2 shows a WEST example case of boundary reconstruction with the code using toroidal harmonics only (called VacTH).…”

“…This is done by least square fitting a truncated series of toroidal harmonic functions to the magnetic measurements. In principle this first step can be sufficient to determine the plasma boundary [2][3][4][5][6][7][8][9] (also see the review article 10 ). Indeed the toroidal harmonics expansion is valid anywhere in the vacuum surrounding the plasma.…”

Validation of equilibrium tools on the COMPASS tokamak

“…In this study, FREEBIE is used in the so-called inverse mode, which predicts PF coils currents from a give plasma boundary and profiles. The third code employed in this study is VacTH [4], which provides a fast reconstruction of the plasma boundary from magnetic measurements using a toroidal harmonics basis.…”