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In this work, we present the first experimental evidence of the presence of zonal flow (ZF) structures in the optimized stellarator Wendelstein 7-X. Using an assortment of diagnostics, flux surface-uniform, electrostatic flow oscillations have been measured, showing a radial scale in the range of tens of ion gyroradii. Such measurements show remarkable agreement with the ZF predicted by local and global non-linear gyrokinetic simulations. These results represent the first direct measurement of ZF in a large stellarator, suitable for the validation of models in reactor relevant conditions., Comment: Submitted to Physical Review Letters

CIEMAT-QI4 is a quasi-isodynamic stellarator configuration that simultaneously features very good fast-ion confinement in a broad range of $\beta$ values, low neoclassical transport and bootstrap current, and ideal magnetohydrodynamic stability up to $\beta=5\%$. In this paper it is shown that CIEMAT-QI4 also exhibits reduced turbulent transport. This is demonstrated through nonlinear electrostatic simulations with the gyrokinetic code stella, including kinetic ions and electrons. The relation between reduced turbulent transport and the fact that CIEMAT-QI4 very approximately satisfies the so-called maximum-J property is discussed., Comment: 12 pages, 9 figures

The first experimental campaigns of Wendelstein 7-X (W7-X) have shown that turbulence plays a decisive role in the performance of neoclassically optimized stellarators. This stresses the importance of understanding microturbulence from the theoretical and experimental points of view. To this end, this paper addresses a comprehensive characterization of the turbulent fluctuations by means of nonlinear gyrokinetic simulations performed with the code stella in two W7-X scenarios. In the first part of the paper, the amplitude of the density fluctuations is calculated and compared with measurements obtained by Doppler reflectometry (DR) in the OP1 experimental campaigns. It is found that the trend of the fluctuations along the radius is explained by the access of the DR system to different regions of the turbulence wavenumber spectrum. In the second part of the article, frequency spectra of the density fluctuations and the zonal component of the turbulent flow are numerically characterized for comparisons against future experimental analyses. Both quantities feature broad frequency spectra with dominant frequencies of O(1)-O(10) kHz., Comment: 27 pages, 16 figures

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al. 2022) with no electron temperature gradient]. The flux-tube version of the $\delta$f code stella (Barnes et al. 2019) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g. through current drive) has a stabilising effect on the turbulence and thus reduces the nonlinear energy transport.

A systematic study of the impact of impurities on the turbulent heat fluxes is presented for the stellarator Wendelstein 7-X (W7-X) and, for comparison, the Large Helical Device and ITER. By means of nonlinear multispecies gyrokinetic simulations, it is shown that impurities, depending on the sign of their density gradient, can significantly enhance or reduce turbulent ion heat losses. For the relevant scenario of turbulence reduction, an optimal impurity concentration that minimizes the ion heat diffusivity emerges as a universal feature. This result demonstrates the potential of impurities for controlling turbulence and accessing enhanced confinement regimes in fusion plasmas and, in particular, in W7-X., Comment: 8 pages, 8 figures

In reactor-relevant plasmas, neoclassical transport drives an outward particle flux in the core of large stellarators and predicts strongly hollow density profiles. However, this theoretical prediction is contradicted by experiments. In particular, in Wendelstein 7-X, the first large optimized stellarator, flat or weakly peaked density profiles are generally measured, indicating that neoclassical theory is not sufficient and that an inward contribution to the particle flux is missing in the core. In this Research Letter, it is shown that the turbulent contribution to the particle flux can explain the difference between experimental measurements and neoclassical predictions. The results of this Research Letter also prove that theoretical and numerical tools are approaching the level of maturity needed for the prediction of equilibrium density profiles in stellarator plasmas, which is a fundamental requirement for the design of operation scenarios of present devices and future reactors., Comment: 8 pages, 6 figures, updated the title and incorporated the appendix into the main letter

A recent characterization of core turbulence carried out with a Doppler reflectometer in the optimized stellarator Wendelstein 7-X (W7-X) found that discharges achieving high ion temperatures at the core featured an ITG-like suppression of density fluctuations driven by a reduction of the gradient ratio $\eta_i = L_n/L_{T_i}$ [D. Carralero et al., Nucl. Fusion, 2021]. In order to confirm the role of ITG turbulence in this process, we set out to establish experimentally the relation between core density fluctuations, turbulent heat flux and global confinement. With this aim, we consider the scenarios found in the previous work and carry out power balance analysis for a number of representative ones, including some featuring high ion temperature. As well, we evaluate the global energy confinement time and discuss it in the context of the ISS04 inter-stellarator scaling. We find that, when turbulence is suppressed as a result of a reduction of $\eta_i$, there is a reduction of ion turbulent transport, and global performance is improved as a result. This is consistent with ITG turbulence limiting the ion temperature at the core of W7-X. In contrast, when turbulence is reduced following a decrease in collisionality, no changes are observed in transport or confinement. This could be explained by ITG modes being combined with TEM turbulence when the later is destabilized at low collisionalities., Comment: Submitted to PPCF, 47th EPS special issue

The ongoing development of electromagnets based on High Temperature Superconductors has led to the conceptual exploration of high-magnetic-field fusion reactors of the tokamak type, operating at on-axis fields above 10 T. In this work we explore the consequences of the potential future availability of high-field three-dimensional electromagnets on the physics design point of a stellarator reactor. We find that, when an increase in the magnetic field strength $B$ is used to maximally reduce the device linear size $R\sim B^{-4/3}$ (with otherwise fixed magnetic geometry), the physics design point is largely independent of the chosen field strength/device size. A similar degree of optimization is to be imposed on the magnetohydrodynamic, transport and fast ion confinement properties of the magnetic configuration of that family of reactor design points. Additionally, we show that the family shares an invariant operation map of fusion power output as a function of the auxiliary power and relative density variation. The effects of magnetic field over-engineering and the $R(B)$ scaling of design points with constant neutron wall loading are also inspected. In this study we use geometric parameters characteristic of the helias reactor, but most results apply to other stellarator configurations

The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, documented and verified set of gyrokinetic simulations in W7-X geometry against which new codes or upgrades of existing codes can be tested and benchmarked. This paper attemps to provide such a set of simulations in the form of a comprehensive benchmark between the recently developed code stella and the well-established code GENE. The benchmark consists of electrostatic gyrokinetic simulations in W7-X magnetic geometry and includes different flux tubes, linear ion-temperature-gradient (ITG) and trapped-electron-mode (TEM)} stability analyses, computation of linear zonal flow responses and calculation of ITG-driven heat fluxes.

A large diffusive turbulent contribution to the radial impurity transport in Wendelstein 7-X (W7-X) plasmas has been experimentally inferred during the first campaigns and numerically confirmed by means of gyrokinetic simulations with the code stella. In general, the absence of strong impurity accumulation during the initial W7-X campaigns is attributed to this diffusive term. In the present work the diffusive contribution is also calculated in other stellarator plasmas. In particular, the diffusion (D) and convection (V) coefficients of carbon and iron impurities produced by ion-temperature-gradient (ITG) turbulence are obtained for W7-X, LHD, TJ-II and NCSX. The results show that, although the size of D and V can differ across the four devices, inward convection is found for all of them. For W7-X, TJ-II and NCSX the two coefficients are comparable and the turbulent peaking factor is surprisingly similar. In LHD, appreciably weaker diffusive and convective impurity transport and significantly larger turbulent peaking factor are predicted. All this suggests that ITG turbulence, although not strongly, would lead to negative impurity density gradients in stellarators. Then, considering mixed ITG/Trapped Electron Mode (TEM) turbulence for the specific case of W7-X, it has been quantitatively assessed to what degree pellet fueled reduced turbulence scenarios feature reduced turbulent transport of impurities as well. The results for trace iron impurities show that, although their turbulent transport is not entirely suppressed, a significant reduction of V and a stronger decrease of D are found. Although the diffusion is still above neoclassical levels, the neoclassical convection would gain under such conditions a greater specific weight on the dynamics of impurities in comparison with standard ECRH scenarios., Comment: 16 pages, 8 figures

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube, full-flux-surface, and radially global domains. Two problems are studied: the linear relaxation of zonal flows and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The zonal flow relaxation properties obtained in different flux tubes are found to differ with each other and with the radially global result, except for sufficiently long flux tubes, in general. The flux tube length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different flux tubes provide different results, but the discrepancy between them diminishes with increasing flux tube length. Full-flux-surface and flux tube simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the flux tube and the full-flux-surface domains. Radially global simulations provide results close to the full-flux-surface ones. The radial scale of unstable ITG modes is studied in global and flux tube simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found., Comment: submitted to Nuclear Fusion

First results from the optimized helias Wendelstein 7-X stellarator (W7-X) have shown that core transport is no longer mostly neoclassical, as is the case in previous kinds of stellarators. Instead, turbulent transport poses a serious limitation to the global performance of the machine. Several studies have found this particularly relevant for ion transport, with core ion temperatures becoming clamped at relatively low values of $T_{i} \simeq 1.7$ keV, except in the few scenarios in which turbulence can be suppressed. In order to understand turbulent mechanisms at play, it is important to have a clear understanding of the parametric dependencies of turbulent fluctuations, and the relation between them and turbulent transport. In this work we use Doppler reflectometry measurements carried out during a number of relevant operational scenarios to provide a systematic characterization of ion-scale ($k_\perp\rho_i\simeq 1$) density fluctuations in the core of W7-X. Then, we study the relation between fluctuation amplitude and plasma profiles and show how distinct regimes can be defined for the former, depending on normalized gradients $a/L_{ne}$ and $a/L_{Ti}$. Furthermore, we discuss the importance of other potentially relevant parameters such as $T_e/T_i$, $E_r$ or collisionality. Comparing the different regimes, we find that turbulence amplitude depends generally on the gradient ratio $\eta_i=L_{ne}/L_{Ti}$, as would be expected for ITG modes, with the exception of a range of discharges, for which turbulence suppression may be better explained by an ITG to TEM transition triggered by a drop in collisionality. Finally, we show a number of scenarios under which $T_{i,core} > 1.7$ keV is achieved and how core fluctuations are suppressed in all of them, thus providing experimental evidence of microturbulence being the main responsible for the limited ion confinement in W7-X., Comment: Manuscript submitted to Nuclear Fusion in May 2021

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: ITG, TEM and 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 thermo-diffusion 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., Comment: 19 pages, 10 figures, 2 tables

In this work, the first nonlinear particle-in-cell simulations carried out in a stellarator with the global gyrokinetic code EUTERPE using realistic plasma parameters are reported. Several studies are conducted with the aim of enabling reliable nonlinear simulations in stellarators with this code. First, EUTERPE is benchmarked against ORB5 in both linear and nonlinear settings in a tokamak configuration. Next, the use of noise control and stabilization tools, a Krook-type collision operator, markers weight smoothing and heating sources is investigated. It is studied in detail how these tools influence the linear growth rate of instabilities in both tokamak and stellarator geometries and their influence on the linear zonal flow evolution in a stellarator. Then, it is studied how these tools allow improving the quality of the results in a set of nonlinear simulations of electrostatic turbulence in a stellarator configuration. Finally, these tools are applied to a W7-X magnetic configuration using experimental plasma parameters., Comment: 24 pages, 19 figures

KNOSOS (KiNetic Orbit-averaging SOlver for Stellarators) is a freely available, open-source code (\href{https://github.com/joseluisvelasco/KNOSOS}{https://github.com/joseluisvelasco/KNOSOS}) that calculates neoclassical transport in low-collisionality plasmas of three-dimensional magnetic confinement devices by solving the radially local drift-kinetic and quasineutrality equations. The main feature of KNOSOS is that it relies on orbit-averaging to solve the drift-kinetic equation very fast. KNOSOS treats rigorously the effect of the component of the magnetic drift that is tangent to magnetic surfaces, and of the component of the electrostatic potential that varies on the flux surface, {\varphi}_1. Furthermore, the equation solved is linear in {\varphi}_1, which permits an efficient solution of the quasineutrality equation. As long as the radially local approach is valid, KNOSOS can be applied to the calculation of neoclassical transport in stellarators (helias, heliotrons, heliacs, etc.) and tokamaks with broken axisymmetry. In this paper, we show several calculations for the stellarators W7-X, LHD, NCSX and TJ-II that provide benchmark with standard local codes and demonstrate the advantages of this approach.

Main ions influence impurity dynamics through a variety of mechanisms; in particular, via impurity-ion collisions. To lowest order in an expansion in the main ion mass over the impurity mass, the impurity-ion collision operator only depends on the component of the main ion distribution that is odd in the parallel velocity. These lowest order terms give the parallel friction of the impurities with the main ions, which is typically assumed to be the main cause of collisional impurity transport. Next-order terms in the mass ratio expansion of the impurity-ion collision operator, proportional to the component of the main ion distribution that is even in the parallel velocity, are usually neglected. However, in stellarators, the even component of the main ion distribution can be very large. In this article, such next-order terms in the mass ratio expansion of the impurity-ion collision operator are retained, and analytical expressions for the neoclassical radial flux of trace impurities are calculated in the Pfirsch-Schl\"uter, plateau and $1/\nu$ regimes. The new terms provide a drive for impurity transport that is physically very different from parallel friction: they are associated to anisotropy in the pressure of the main ions, which translates into impurity pressure anisotropy. It is argued that main ion pressure anisotropy must be taken into account for a correct description of impurity transport in certain realistic stellarator plasmas. Examples are given by numerically evaluating the analytical expressions for the impurity flux., Comment: 40 pages, 4 figures. Published version

The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote by $\tilde\varphi$, 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 which $\tilde\varphi$ 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 of $\tilde\varphi$ on the magnetic surface are analytically derived in the $1/\nu$, $\sqrt{\nu}$ and superbanana-plateau regimes of stellarators close to omnigeneity; i. e. stellarators that have been optimized for neoclassical transport. It is found that the largest $\tilde\varphi$ 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., Comment: 30 pages, 12 figures, 1 table. Published version

In the present work we report recent radial electric field measurements carried out with the Doppler reflectometry system in the TJ-II stellarator. The study focuses on the fact that, under some conditions, the radial electric field measured at different points over the same flux surface shows significantly different values. A numerical analysis is carried out considering the contribution arising from the radial dependence of $\Phi_1$ as a possible correction term to the total radial electric field. Here $\Phi_1$ is the neoclassical electrostatic potential variation over the surface. The comparison shows good agreement in some aspects, like the conditions under which this correction is large (electron-root conditions) or negligible (ion-root conditions). But it disagrees in others like the sign of the correction. The results are discussed together with the underlying reasons of this partial disagreement. In addition, motivated by the recent installation of the dual Doppler reflectometry system in Wendelstein 7-X (W7-X), $\Phi_1$ estimations for W7-X are revisited considering Core-Electron-Root-Plasma (CERC) plasmas from its first experimental campaign. The simulations show larger values of $\Phi_1$ under electron-root conditions than under ion root ones. The contribution from the kinetic electron response is shown to become important at some radii. All this results in a potential variation size noticeably larger than estimated in our previous work in W7-X \cite{Regana_nf_57_056004_2017} for other plasma parameters and another configuration., Comment: 23 pages, 10 figures

The control of impurity accumulation is one of the main challenges for future stellarator fusion reactors. The standard argument to explain this accumulation relies on the, in principle, large inward pinch in the neoclassical impurity flux caused by the typically negative radial electric field in stellarators. This simplified interpretation was proven to be flawed by Helander et al. [Phys. Rev. Lett. 118, 155002 (2017)], who showed that in a relevant regime (low-collisionality main ions and collisional impurities) the radial electric field does not drive impurity transport. In that reference, the effect of the component of the electric field that is tangent to the magnetic surface was not included. In this Letter, an analytical calculation of the neoclassical radial impurity flux incorporating such effect is given, showing that it can be very strong for highly charged impurities and that, once it is taken into account, the dependence of the impurity flux on the radial electric field reappears. Realistic examples are provided in which the inclusion of the tangential electric field leads to impurity expulsion., Comment: 10 pages, 1 figure. Published version

Low-collisionality stellarator plasmas usually display a large negative radial electric field that has been expected to cause accumulation of impurities due to their high charge number. In this paper, two combined effects that can potentially modify this scenario are discussed. First, it is shown that, in low collisionality plasmas, the kinetic contribution of the electrons to the radial electric field can make it negative but small, bringing the plasma close to impurity temperature screening (i.e., to a situation in which the ion temperature gradient is the main drive of impurity transport and causes outward flux); in plasmas of very low collisionality, such as those of the Large Helical Device displaying impurity hole, screening may actually occur. Second, the component of the electric field that is tangent to the flux surface (in other words, the variation of the electrostatic potential on the flux surface), although smaller than the radial component, has recently been suggested to be an additional relevant drive for radial impurity transport. Here, it is explained that, especially when the radial electric field is small, the tangential magnetic drift has to be kept in order to correctly compute the tangential electric field, that can be larger than previously expected. This can have a strong impact on impurity transport, as we illustrate by means of simulations using the newly-developed code KNOSOS (KiNetic Orbit-averaging-SOlver for Stellarators).

We review in a tutorial fashion some of the causes of impurity density variations along field lines and radial impurity transport in the moment approach framework. An explicit and compact form of the parallel inertia force valid for arbitrary toroidal geometry and magnetic coordinates is derived and shown to be non-negligible for typical TJ-II plasma conditions. In the second part of the article, we apply the fluid model including main ion-impurity friction and inertia to observations of asymmetric emissivity patterns in neutral beam heated plasmas of the TJ-II stellarator. The model is able to explain qualitatively several features of the radiation asymmetry, both in stationary and transient conditions, based on the calculated in-surface variations of the impurity density.

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 \cite{Ida_pop_16_056111_2009, Yoshinuma_nf_49_062002_2009}. 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 wave-length variation on the flux surface $\Phi_{1}$ -- 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 $\Phi_{1}$, both resulting in mitigated/enhanced accumulation at internal/external radial positions; for Wendelstein 7-X, on the contrary, $\Phi_{1}$ 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 $\Phi_1$ for the parameters considered.

First observations of electrostatic potential variations within the flux surfaces of a toroidal magnetic confinement device are presented. Measurements are taken in the TJ-II stellarator with two distant Langmuir probe arrays. The edge floating potentials display differences of several tens of Volts in electron-root wave-heated plasmas. The differences are reduced for higher densities and lower electron temperatures after the ion-root electric field forms at the plasma edge. Neoclassical Monte Carlo simulations estimate the correct order of magnitude for the overall variation in potential and predict the trend observed with the radial electric field. However, for the specific location of the probes, the simulations give differences smaller than those observed experimentally.

Fully-ionised carbon impurity flow is studied in ion-root, neutral beam heated plasmas by means of Charge Exchange Recombination Spectroscopy (CXRS) in the TJ-II stellarator. Perpendicular flows are found to be in reasonable agreement with neoclassical calculations of the radial electric field. The parallel flow of the impurity is obtained at two locations of the same flux surface after subtraction of the calculated Pfirsch-Schl\"uter parallel velocity. For the medium density plasmas studied, $\bar{n}_{\rm e}\in(1.2-2.4)\times 10^{19}$ m$^{-3}$, the measured impurity flow is found to be inconsistent with a total incompressible flow, i.e. $\nabla\cdot{\bf u}_z\ne0$, thus contradicting the usual assumption of a constant density on each flux surface. The experimentally observed velocity deviations are compared with the parallel return flow calculated from a modelled impurity density redistribution driven by ion-impurity friction. Although the calculated return flow substantially modifies the incompressible velocity pattern, the modifications do not explain the in-surface variations of impurity parallel mass flow at the precise locations of the CXRS measurements. Small inhomogeneities of the electrostatic potential in a surface are also shown to affect the impurity redistribution but do not provide a better understanding of the measurements., Comment: 22 pages, 11 figures

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 $\mathbf{E}\times \mathbf{B}$ drift and trapping due to the electrostatic potential variation on a flux surface $\tilde{\Phi}$ 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 by $\tilde{\Phi}$. The central numerical tool used is the $\delta f$ particle in cell (PIC) Monte Carlo code EUTERPE. The $\tilde{\Phi}$ used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more general $\tilde{\Phi}$ self-consistently with EUTERPE is also addressed and a preliminary calculation is presented., Comment: 11 pages, 15 figures, presented at Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas, 2012. Accepted for publication to Plasma Phys. and Control. Fusion

Taking advantage of the electron Bernstein waves heating (EBWH) system of the TJ-II stellarator, an electron Bernstein emission (EBE) diagnostic was installed. Its purpose is to investigate the B-X-O radiation properties in the zone where optimum theoretical EBW coupling is predicted. An internal movable mirror shared by both systems allows us to collect the EBE radiation along the same line of sight that is used for EBW heating. The theoretical EBE has been calculated for different orientations of the internal mirror using the TRUBA code as ray tracer. A comparison with experimental data obtained in NBI discharges is carried out. The results provide a valuable information regarding the experimental O-X mode conversion window expected in the EBW heating experiments. Furthermore, the characterization of the radiation polarization shows evidence of the underlying B-X-O conversion process., Comment: 21 pages, 14 figures