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.

The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote byφ, can affect radial transport of highly charged impurities, and this has motivated its inclusion in some modern neoclassical codes. The number of neoclassical simulations in whichφ is calculated is still scarce, partly because they are usually demanding in terms of computational resources, especially at low collisionality. In this paper the size, the scaling with collisionality and with aspect ratio, and the structure ofφ on the magnetic surface are analytically derived in the 1/ν, √ ν and superbanana-plateau regimes of stellarators close to omnigeneity; i. e. stellarators that have been optimized for neoclassical transport. It is found that the largestφ that the neoclassical equations admit scales linearly with the inverse aspect ratio and with the size of the deviation from omnigeneity. Using a model for a perturbed omnigeneous configuration, the analytical results are verified and illustrated with calculations by the code KNOSOS. The techniques, results and numerical tools employed in this paper can be applied to neoclassical transport problems in tokamaks with broken axisymmetry. † Recently, both the prevalence of the radial electric field in the transport of impurities and the absence of impurity screening in three-dimensional magnetic fields have been brought into question for several collisionality regimes Helander et al. 2017).

The impurity dynamics in stellarators has become an issue of moderate concern due to the inherent tendency of the impurities to accumulate in the core when the neoclassical ambipolar radial electric field points radially inwards (ion root regime). This accumulation can lead to collapse of the plasma due to radiative losses, and thus limit high performance plasma discharges in non-axisymmetric devices. A quantitative description of the neoclassical impurity transport is complicated by the breakdown of the assumption of small E × B drift and trapping due to the electrostatic potential variation on a flux surfaceΦ compared to those due to the magnetic field gradient. The present work examines the impact of this potential variation on neoclassical impurity transport in the Large Helical Device (LHD) stellarator. It shows that the neoclassical impurity transport can be strongly affected byΦ. The central numerical tool used is the δf particle in cell (PIC) Monte Carlo code EUTERPE. TheΦ used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more generalΦ self-consistently with EUTERPE is also addressed and a preliminary calculation is presented.

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