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

Abstract

Restrictions on magnetic diagnostics are discussed. Being related to the integral nature of the measurable quantities, these follow from the fundamental laws of electromagnetism. A series of examples demonstrating the strength of these restrictions is analysed. The general rule is emphasized that information obtained from external magnetic measurements is insufficient for reliable evaluation of plasma current and pressure profiles in tokamaks and in stellarators. The underlying reason is that outside the plasma the self-field of the equilibrium plasma currents is determined by the boundary conditions on the plasma surface alone.

Identification of edge-localized moments of the current density profile in a tokamak equilibrium from external magnetic measurements

“…This amounts to 20 free shape parameters, well in excess of the number of identifiable moments of the current distribution but with the advantage of being free of the bias that commonly affects parameterizations with a low number of free parameters: Overly restricted models can result in artificially well determined pressure and current density profiles using only magnetic data, as was correctly pointed out in [11]. The choice of 10 knot locations has the dual purpose of (a) ensuring that, apart from the effects of regularization, the model is free of significant bias and (b) allowing the same model to be used when the equilibrium solution is additionally constrained by kinetic profile data or other internal diagnostic data where many knots may be required to satisfactorily model the data.…”

“…Here we present analysis and results from reconstructions of a database of randomly generated ASDEX Upgrade equilibria as well as from experimental data which show that additional moments of j φ , strongly localized in the edge region of the plasma, are identifiable from magnetics when the plasma is bounded by a separatrix with one or more X-points. Before proceeding, however, it is first necessary to address a previous claim [11] that magnetics are unable to identify any details of the current distribution, based on the result that the magnetic field at a point r outside the plasma generated by volume currents flowing in the plasma:…”

“…The equivalent surface current density i = n × B/µ 0 = (B zθ − B θẑ )/µ 0 has an axial component i z = −B θ /µ 0 . Except for the degenerate case of circular flux surfaces where B θ is independent of θ, i z varies with θ on a surface of constant ψ and hence violates the conditions for force balance, thereby invalidating the reasoning leading to the main conclusion in [11].…”

Numerical Simulation of Electromagnetic Diagnostics System of the Tokamak T-15

“…В рамках модели тороидальной геометрии таких теорем нет. Более того, приводятся примеры инте-грально неразличимых конфигураций [6,18], что подтверждает сложность задачи. Для конкретной уста-новки прежде всего важно определить предел точности магнитных измерений (), при превышении ко- торого невозможно различить два профиля, отличающихся на заданную величину  [19,20].…”

Diagnostics for steady state plasmas

“…This is due to the nature of the equilibrium reconstruction, where the modifications by the plasma can be considered as a perturbation on the flux surface geometry. The reconstruction of the equilibrium including the current profile by the external magnetic measurements is an ill-posed problem [295,308,309]. Thus, the quality of any equilibrium reconstruction is very sensitive to inaccuracies as introduced by noise, stray fields and systematic errors due to signal integration imperfections (section 12.…”