Is it possible to extract information on the plasma pressure profile from magnetic measurements in stellarators?

Abstract

The free boundary stellarator equilibria are studied in the framework of averaged equations. The structure of external magnetic fields created by currents flowing inside the plasma column is analysed. In all cases considered the dipole component of the magnetic field (in agreement with previous investigations) can only be used to determine the volume averaged value of the parameter @ if the net toroidal current is known. For zero net current operation it is shown that the quadrupole component of the external magnetic field can be used for an estimate of the plasma pressure distribution, for example, in the framework of a one parametric set of profiles. The dependence of the external magnetic field on the current distribution for the given pressure profile is also investigated, and it is shown that there is a possibility of distinguishing at least strongly different current distributions (such as the peaked and offcentred current profiles considered here) either for a large shear system at high @ or for a device with averaged vertical elongation of the vacuum magnetic surfaces.

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.…”

“…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.…”

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

“…We use here nearly the standard procedure, described in detail in Ref. [8]. For 3-D vacuum magnetic fields it is convenient to use the following representation:…”