Equilibrium magnetic fields and currents in a nonaxisymmetric torus: external magnetic fields in stellarators

Abstract

The three dimensional (3-D) and axisymmetric (2-D) magnetic fields produced by currents flowing in plasmas that are confined in stellarators with a nearly planar geometrical axis are investigated. Using the Green's function method to solve the 3-D linear equation derived previously, a simple procedure is presented here to determine the structure of plasma induced external magnetic fields in stellarators. A detailed numerical analysis of the values of the external 3-D magnetic fields and their dependences on the plasma profiles is performed. Analytical formulas are derived that could be useful for estimations. The possibility of using the measurements of these fields for the experimental identification of the magnetohydrodynamic (MHD) equilibria is considered. Also discussed are some interesting aspects of the influence of the magnetic hump on the value of the Pfirsch-Schliiter currents (that appear in recent Heliotron-E experiments) and the influence of different features of the vacuum magnetic field on the dipole component of plasma induced field is classified. The results of calculations related to the modern experiments are presented, and the case that may be typical for future experiments is also considered.

Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems

“…In fact, this possibility was not proved either in Refs [6][7][8] nor in the theory in general. But the style of articles [6][7][8] is, nevertheless, over-optimistic with respect to the solvability of the problem.…”

“…In fact, this possibility was not proved either in Refs [6][7][8] nor in the theory in general. But the style of articles [6][7][8] is, nevertheless, over-optimistic with respect to the solvability of the problem. It is enough to recall that "the magnetic probe system needed for the determination of both the plasma pressure profile and the current distribution" [8] is given as the goal of the study and analysed in minute detail.…”

“…In theoretical articles the reasons for this (which we are going to discuss) were mentioned allusively or incompletely, whereas the complex models, bulky calculations and abundance of accompanying details always served to shift the accent of the work to other subjects. So until now particular consequences have been discussed [7,8,18,19] instead of a justification of the reasons for these, and the belief has been maintained that for stellarators the problem of current and pressure profile reconstruction from external magnetic measurements might nevertheless be resolved if the simulation model and the accuracy of the measurements were to be improved or the number of magnetic probes increased and their arrangement optimized [6-8, 13, 15]. This belief is based on unconvincing results that are interpreted without proper caution and ignoring the warnings from the tokamak theory [9][10][11][12].…”

“…The formulation of this problem is simple: Is it possible to determine the plasma current distribution and/or the plasma pressure profile from external magnetic measurements? The very statement of the question [1][2][3][4][5] shows the hope for a positive answer that until recently has determined the style of some publications [6][7][8], although the 'conservative' majority gave up this hope a long time ago [9][10][11][12].…”

“…However, the unjustified optimism about the aforementioned reconstruction of the profiles has not disappeared completely. Although little supported by published results [3][4][5], optimism about this was taken up by stellarator researchers [13][14][15][16][17], among whom attempts to gather evidence in favour of a positive answer still continue [6][7][8]. Earlier such attempts were made with a strong belief in a positive outcome, later with reinsuring reserves (leaving, however, freedom even for mutually exclusive conclusions), but always along the same lines, prescribing different profiles first and then demonstrating that they correspond to different amplitudes of measurable magnetic quantities.…”