Flux-surface variations of the electrostatic potential are typically neglected in standard neoclassical theory, but in 3D devices they can be large enough to affect the radial particle flux of ...impurities. The radially local drift-kinetic equation solver SFINCS (stellarator Fokker-Planck iterative neoclassical conservative solver) (Landreman et al 2014 Phys. Plasmas 21 042503) has been updated to account for these variations. In the present work we use SFINCS to perform a novel study of neoclassical particle transport in stellarators, where we simultaneously account for the flux-surface potential variations, several kinetic species including non-adiabatic electrons and non-trace impurities, and the full linearized Fokker-Planck-Landau collision operator for self- and inter-species collisions (with no expansion made in mass ratio). We also make a self-consistent calculation of the ambipolar radial electric field, to analyze how it is affected by the flux-surface variations and the presence of non-trace impurities. In a simulated Wendelstein 7-X plasma, we find that the impact of the flux-surface variations on the radial particle fluxes of all plasma species is small. In contrast, for an experimental impurity hole discharge in the Large Helical Device (LHD) the carbon flux can be strongly modified by the flux-surface potential variation and also the calculated ambipolar radial electric field can change. However, around mid radius the potential variations cause enhanced inward neoclassical carbon fluxes, rather than causing outward fluxes, thus suggesting that the role of flux-surface potential variations in neoclassical transport may not be the explanation for the impurity hole phenomenon observed in LHD plasmas.
A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently ...developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ion temperature gradient (ITG), trapped electron mode (TEM) and electron temperature gradient (ETG) modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermodiffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.
The accumulation of impurities in the core of magnetically confined plasmas, resulting from standard collisional transport mechanisms, is a known threat to their performance as fusion energy sources. ...Whilst the axisymmetric tokamak systems have been shown to benefit from the effect of temperature screening, that is an outward flux of impurities driven by the temperature gradient, impurity accumulation in stellarators was thought to be inevitable, driven robustly by the inward pointing electric field characteristic of hot fusion plasmas. We have shown in Helander et al. (Phys. Rev. Lett., vol. 118, 2017a, 155002) that such screening can in principle also appear in stellarators, in the experimentally relevant mixed collisionality regime, where a highly collisional impurity species is present in a low collisionality bulk plasma. Details of the analytic calculation are presented here, along with the effect of the impurity on the bulk ion flow, which will ultimately affect the bulk contribution to the bootstrap current.
A potential threat to the performance of magnetically confined fusion plasmas is the problem of impurity accumulation, which causes the concentration of highly charged impurity ions to rise ...uncontrollably in the center of the plasma and spoil the energy confinement by excessive radiation. It has long been thought that the collisional transport of impurities in stellarators always leads to such an accumulation (if the electric field points inwards, which is usually the case), whereas tokamaks, being axisymmetric, can benefit from "temperature screening," i.e., an outward flux of impurities driven by the temperature gradient. Here it is shown, using analytical techniques supported by results from a new numerical code, that such screening can arise in stellarator plasmas, too, and indeed does so in one of the most relevant operating regimes, where the impurities are highly collisional while the bulk plasma is at low collisionality.
In toroidal magnetic confinement devices, such as tokamaks and stellarators, neoclassical transport is usually an order of magnitude larger than its classical counterpart. However, when a ...high-collisionality species is present in a stellarator optimized for low Pfirsch–Schlüter current, its classical transport can be comparable to the neoclassical transport. In this letter, we compare neoclassical and classical fluxes and transport coefficients calculated for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we find that the classical transport of a collisional impurity is comparable to the neoclassical transport for all radii, while it is negligible in the LHD cases, except in the vicinity of radii where the neoclassical transport changes sign. In the LHD case, electrostatic potential variations on the flux surface significantly enhance the neoclassical impurity transport, while the classical transport is largely insensitive to this effect in the cases studied.
The presence of impurity species in magnetic confinement fusion devices leads to radiation losses and plasma dilution. Thus it is important to analyze impurity dynamics, and search for means to ...control them. In stellarator plasmas the neoclassical ambipolar radial electric field often points radially inwards (referred to as the ion root regime), causing impurities to accumulate in the core. This can limit the performance of nonaxisymmetric devices. In the present work we analyze neoclassical impurity transport in stellarator plasmas using a recently developed continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker- Planck Iterative Neoclassical Conservative Solver). The study is performed for a case close to the edge of W7-X using the standard configuration magnetic geometry. We investigate the sensitivity of impurity transport to impurity charge, main species density and temperature gradients, as well as ion temperature. At the studied radial location we find that the neoclassical impurity peaking factor can be very large, particularly for high-Z impurities. The ambipolar radial electric field is in the ion root regime, and impurity accumulation can thus be expected. The accumulation is strengthened by the large main species density and temperature gradients. Moreover we find that the size of the bootstrap current is affected by the value of the plasma effective charge, suggesting that employing a realistic ion composition can be important when calculating the bootstrap current.
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