Electrostatic potential variation on the flux surface and its impact on impurity transport

Abstract

The particle transport of impurities in magnetically confined plasmas under some conditions does not find, neither quantitatively nor qualitatively, a satisfactory theory-based explanation. This compromise the successful realization of thermo-nuclear fusion for energy production since its accumulation is known to be one of the causes that leads to the plasma breakdown. In standard reactor-relevant conditions this accumulation is in most stellarators intrinsic to the lack of toroidal symmetry, that leads to the neoclassical electric field to point radially inwards. This statement, that the standard theory allows to formulate, has been contradicted by some experiments that showed weaker or no accumulation under such conditions [1,2]. The charge state of the impurities makes its transport more sensitive to the electric fields. Thus, the short length scale turbulent electrostatic potential or its long wavelength variation on the flux surface Φ 1 -that the standard neoclassical approach usually neglects -might possibly shed some light on the experimental findings. In the present work the focus is put on the second of the two, and investigate its influence of the radial transport of C 6+ . We show that in LHD it is strongly modified by Φ 1 , both resulting in mitigated/enhanced accumulation at internal/external radial positions; for Wendelstein 7-X, on the contrary, Φ 1 is expected to be considerably smaller and the transport of C 6+ not affected up to an appreciable extent; and in TJ-II the potential shows a moderate impact despite of the large amplitude of Φ 1 for the parameters considered.

Inference of temperature and density profiles via forward modeling of an x-ray imaging crystal spectrometer within the Minerva Bayesian analysis framework

“…Additionally, a possible variation of the impurity density on the magnetic flux surface, as expected for highly charged ions [61][62][63] , or a possible misalignment of the spectrometer lines of sight can be taken into account. It should be mentioned that results from the first operational phases of W7-X does not show any significant up down asymmetries in the line intensities, different to previous observations made on ALCATOR-C Mod 64 , but in agreement to theoretical data 65 . An investigation of this effect for higher Z impurities such as iron or nickel is planned for the future.…”

On-surface potential and radial electric field variations in electron root stellarator plasmas

“…While in ref. [1] pitch angle scattering collisions without momentum conservation were applied, in the present work, a momentum-restoring field particle term similar to that implemented in other codes [32,33] is added. The detailed description for EUTERPE can be found in ref.…”

Large tangential electric fields in plasmas close to temperature screening

“…Even for peaked ion temperature profiles, in standard ion-root conditions [11] the radial electric field is bound to be as large as the ion temperature gradient, eE r ∼ T i , and Z I 1 ensures impurity accumulation. The large charge number Z I anticipates one of the additional physical mechanisms that is a candidate for explaining how impurities are flushed out from the plasma despite the negative radial electric field (that is, the exceptions mentioned above): the electrostatic potential is only approximately a constant on the flux surfaces of a stellarator [5,6,12] and, for low collisionalities of the bulk species, its variation on the flux surface, that we denote by ϕ 1 (in other words, the component of the electric field that is tangent to the flux surface), can in principle be a relevant drive for the radial transport of moderate-to-high Z I impurities. However, the simulations done so far [5,6] do not generally predict an outwards-directed impurity flux like the one observed, for example, in the impurity hole: the Z I eϕ 1 term brings the impurity flux closer to zero in some situations, but its effect is not large enough.…”