Analyses of substantially different plasma current densities and safety factors reconstructed from magnetic diagnostics data

Abstract

The problem of plasma current density and safety factor reconstruction using magnetic field measurements is considered. In the traditional formulation, the problem is strongly ill-posed. In particular, substantially different current densities and safety factors can be equally well attributed to the same set of measurements. The paper presents an accurate mathematical formulation of the inverse problem and its variants. A numerical algorithm is given, which allows to find all substantially different solutions or to prove the absence of multiple solutions. Examples of very different current density and safety factor reconstructions for measurements with finite accuracy are presented. Cases of MAST, JET and ITER-like plasmas are considered. It is shown that including the Motional Stark Effect (MSE) measurements as constraints, provided the accuracy of MSE measurements is sufficient, allows identifying one solution. The approach of the paper can be used for a wide range of inverse problems in physics and help in selecting additional conditions, which can identify the most likely solution among several.

Evaluation of Epsilon-Net Calculated Equilibrium Reconstruction Error Bars in the European Integrated Modeling Platform

“…2), but were not used here in order to allow pure study of the pressure constraint (8) and the role of the directional derivatives constraint in (1). Joining all the constraints can reduce error bars.…”

“…A recently developed new technique, based on -nets and SDSS code [1][2][3] , allows addressing the fundamental challenges of the equilibrium reconstruction problem:…”

Improved equilibrium reconstructions by advanced statistical weighting of the internal magnetic measurements

“…In the case of advanced scenarios, this problem is particularly severe and it has been recently demonstrated that magnetic internal measurements are indispensable to identify the more appropriate solutions among many at first sight reasonable candidates. 4,5 The only two diagnostic techniques, extensively used to directly measure the internal magnetic fields in high temperature plasmas, are Polarimetry and the Motional Stark Effect (MSE). On the other hand, notwithstanding the importance of the internal measurements to determine the magnetic topology, no principled technique is available to select the most appropriate weights to be given to the various measurements used as inputs.…”

“…Since the equilibrium codes typically converge by applying a simple least square minimisation of the residuals, if the number of external measurements was increased by orders of magnitude (keeping the number of the internal measurements limited to about 10 typical of polarimetry), the importance of the internal measurements would tend asymptotically to zero, even if they are known to provide essential and unique information about the current profile in the plasma. 4,5 The fact that this problem is not only a theoretical hypothesis, but has clear practical implications, can be seen from the example shown in Figure 1. In this plot, the q profile of JET discharge 82700 is shown.…”

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