Magnetic Flux Surfaces Research Articles

Multi-diagnostic analysis of plasma filaments in the island divertor

Filaments or blobs are well known structures in turbulence in magnetic fusion devices, they are considered to be the major cross-transport channel in the scrape off layer. They originate at the last closed magnetic flux surface and propagate out on the low field side of toroidal devices due to polarization in the curved magnetic field. The Wendelstein 7-X stellarator has a complex three-dimensional magnetic field structure and additionally the plasma is bounded by a chain of magnetic islands, forming an island divertor. After the first observation of filaments in Wendelstein 7-X with video cameras a multi-diagnostic study is presented in this paper to reveal their 3D structure and dynamics. Filaments are seen to be born at the edge and, at least in some cases, seen to extend to up to 4 toroidal turns. After moving radially out a few cm they enter the edge island. Here they disappear from the equatorial plane and about 200 microseconds later reappear on the outboard side of the island. A long-wavelength (∼20–30 cm) quasi coherent mode is observed in both regions where filaments appear. The similarities and differences between the filaments seen in W7-X and other devices are discussed. Possible explanations for this strange radial propagation are considered, together with the likely role of filaments in the edge and island density profile.

Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices

We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The technique combines time-stepping in canonical coordinates with quadrature in non-canonical coordinates and is applicable in systems where a global transformation to canonical coordinates is known explicitly but its inverse is not. A fully implicit class of symplectic Runge-Kutta schemes has recently been introduced and applied to guiding-center motion by Zhang et al. (2014) [9]. Here a generalization of this approach with emphasis on semi-implicit partitioned schemes is described together with methods to enhance performance, in particular avoiding evaluation of non-canonical variables at full time steps. For application in toroidal plasma confinement configurations with nested magnetic flux surfaces a global canonicalization of coordinates for the guiding-center Lagrangian by a spatial transform is presented that allows for pre-computation of the required map in a parallel algorithm in the case of time-independent magnetic field geometry. Guiding-center orbits are studied in stationary magnetic equilibrium fields of an axisymmetric tokamak and a realistic three-dimensional stellarator configuration. Superior long-term properties of symplectic methods are demonstrated in comparison to a conventional adaptive Runge-Kutta scheme. Finally statistics of fast fusion alpha particle losses over their slowing-down time are computed in the stellarator field on a representative sample, reaching a speed-up of the symplectic Euler scheme by more than a factor three compared to usual Runge-Kutta schemes while keeping the same statistical accuracy and linear scaling with the number of computing threads.

A study of planar toroidal–poloidal beveling of monoblocks on the ITER divertor outer vertical target

The design of the monoblocks constituting the ITER divertor vertical targets comprises a simple toroidal (i.e. toroidally-facing) bevel of 0.5 mm in order to magnetically shadow poloidal (i.e. poloidally-running) leading edges, arising from radial misalignments between toroidally neighbouring blocks, from parallel heat loads between and during edge-localised modes (ELMs). Previous studies suggest that excessive heating of long toroidal edges could also occur, possibly leading to melting during ELMs. Furthermore, despite the toroidal bevel, tiny regions of the poloidal leading edges known as ‘optical hot spots’, accessible along magnetic field lines through toroidal gaps, remain exposed to parallel heat flux from ELMs. The intense heat flux onto those optical hot spots could be large enough to trigger tungsten boiling. A possible solution at the outer vertical target is to implement a planar toroidal–poloidal bevel that would hide all poloidal and toroidal edges and eliminate the optical hot spot. It will be demonstrated that a reasonable ‘shallow’ toroidal–poloidal bevel solution solves all these problems with minimal trade-offs, under the condition that monoblocks on neighbouring plasma-facing units be well aligned poloidally in order to prevent the appearance of exposed leading edges, meaning, in the worst case, a stepwise downward shift of each toroidally upstream plasma-facing unit by −2 ± 2 mm with respect to their downstream neighbours. A more deeply beveled solution has also been studied that is immune to poloidal misalignments, but which comprises important trade-offs in terms of higher heat load to the main wetted surface, and excessive ELM heat loads onto the magnetically shadowed side of the toroidal gaps. Unfortunately, due the inclination of magnetic flux surfaces, the planar toroidal–poloidal beveling solution does not work at the inner vertical target, meaning that its application at the outer target alone leaves the inner toroidal gaps unprotected. This, together with the technologically challenging requirement for a high degree of poloidal alignment of toroidally neighbouring plasma-facing units, has led to a decision not to apply the poloidal–toroidal bevel solution on the ITER vertical targets.

Diamond Window Technology for Electron Cyclotron Heating and Current Drive: State of the Art

Nuclear fusion power plants require electron cyclotron (EC) heating and current drive (H&CD) systems for plasma heating and stabilization. High-power microwave beams between 1 and 2 MW generated by gyrotrons propagate in a dedicated waveguide transmission system to reach the plasma at specific locations. Key components in this transmission system are the chemical vapor deposition diamond windows on both the torus and gyrotron sides of the reactor as they allow transmission of high-power beams while acting as confinement and/or vacuum boundaries. Diamond windows consist of a polycrystalline diamond disk integrated in a metallic housing. In the conventional configuration, there is one disk perpendicular to the beam propagation direction. A steering mechanism is then used to deploy the fixed frequency beam at different locations in the plasma. This is, for instance, the configuration used in the ITER EC H&CD system. Movable parts close to the plasma will be problematic for the lifetime of launchers in future fusion reactors like the DEMOnstration nuclear fusion reactor (DEMO) because of the higher heat loads and neutron fluxes. Therefore, one of the alternative concepts is to deploy the beams directly at the desired resonant magnetic flux surface by frequency tuning gyrotrons. In this case, diamond windows able to work in a given frequency range, like the diamond Brewster-angle window, are required. It is an elegant and compact broadband window solution with the disk inclined at the Brewster angle with respect to the beam direction. This paper shows the development and the current state of different diamond window concepts including the design, the numerical analyses, and application of standard construction nuclear codes and of a specific qualification program.

Electron Demagnetization in a Magnetically Expanding Plasma.

Electron demagnetization in a magnetically expanding plasma, a fundamental process for plasma flow and detachment in magnetic nozzles, is experimentally investigated using a rf plasma source and magnetic nozzle (MN). Measurements of the plasma potential spatial profile reveal an ion-confining potential surface, indicative of the edge of a magnetized plasma, that extends along the outermost magnetic flux surface. The downstream extent of the potential surface scales inversely with a characteristic electron Larmor radius, which agrees with an existing theory [E. Ahedo and M. Merino, Phys. Plasmas 19, 083501 (2012)PHPAEN1070-664X10.1063/1.4739791] for electron demagnetization via finite electron Larmor radius (FELR) effects. These results represent the first experimental evidence of FELR demagnetization, and provide an empirical metric for the significance of FELR effects based on the degree of separation between electron and magnetic flux surfaces. With this metric, a critical magnetic field strength is found that ensures electrons remain magnetized through the MN turning point, thus avoiding the rapid plume divergence associated with premature demagnetization.

Performance assessment of long-legged tightly-baffled divertor geometries in the ARC reactor concept

Extremely intense power exhaust channels are projected for tokamak-based fusion power reactors; a means to handle them remains to be demonstrated. Advanced divertor configurations have been proposed as potential solutions. Recent modelling of tightly baffled, long-legged divertor geometries for the divertor test tokamak concept, ADX, has shown that these concepts may access passively stable, fully detached regimes over a broad range of parameters. The question remains as to how such divertors may perform in a reactor setting. To explore this, numerical simulations are performed with UEDGE for the long-legged divertor geometry proposed for the ARC pilot plant conceptual design—a device with projected heat flux power width () of 0.4 mm and power exhaust of 93 MW—first for a simplified Super-X divertor configuration (SXD) and then for the actual X-point target divertor (XPTD) being proposed. It is found that the SXD, combined with 0.5% fixed-fraction neon impurity concentration, can produce passively stable, detached divertor regimes for power exhausts in the range of 80–108 MW—fully accommodating ARC’s power exhaust. The XPTD configuration is found to reduce the strike-point temperature by a factor of ∼10 compared to the SXD for small separations (∼1.4) between main and divertor X-point magnetic flux surfaces. Even greater potential reductions are identified for reducing separations to ∼1 or less. The power handling response is found to be insensitive to the level of cross-field convective or diffusive transport assumed in the divertor leg. By raising the separatrix density by a factor of 1.5, stable fully detached divertor solutions are obtained that fully accommodate the ARC exhaust power without impurity seeding. To our knowledge, this is the first time an impurity-free divertor power handling scenario has been obtained in edge modelling for a tokamak fusion power reactor with of 0.4 mm.

Asymmetry of parallel flow on the Large Helical Device

An asymmetric parallel return flow, which modifies the parallel component of the flow, is expected to meet the zero divergence of the flow on a flux surface based on the common neoclassical theory for torus plasma. The full flow structure is measured by charge exchange spectroscopy on the Large Helical Device. Inboard/outboard asymmetry of the parallel flow is observed according to the full flow profile measurement. Flow asymmetry is considered to be induced by the Pfirsch–Schlüter flow closely associated with the radial electric field. A linear relationship between the integrated flow asymmetry and the electric potential difference is obtained in different magnetic fields and configurations. A model based upon the incompressibility of the flow is applied to acquire a geometric factor hB, which only connects to the magnetic configuration from the experiment. The asymmetric component of the parallel flow measured is compared with the asymmetric component of parallel flow calculated in the incompressibility conditions of flow on the magnetic flux surface. The measured asymmetric flow is consistent with the calculation in plasma with a small toroidal torque input in the inward shifted configuration. However, the measured asymmetric flow is significantly smaller than that calculated for plasma with a large toroidal torque or in the outward shifted configuration. One possible explanation for this variation could be radial transport due to anomalous perpendicular viscosity as well as strongly poloidally asymmetric radial flow.

Magnetic flux coordinates for analytic high-beta tokamak equilibria with flow

Magnetic flux coordinates are constructed from an analytic solution (Ito and Nakajima 2009 Plasma Phys. Control. Fusion 51 035007) for the reduced magnetohydrodynamics (MHD) equilibrium equations for high-beta tokamaks in the presence of poloidal and toroidal flows comparable to the poloidal sound velocity. The analytic solution indicates non-circular magnetic flux surfaces and transition between sub- and super-sonic poloidal flows. The magnetic flux coordinates for such non-circular magnetic flux surfaces are obtained for stability analysis. The flux coordinates are numerically obtained from the high order polynomial equations for the relation with the geometrical coordinates. As applications, pressure profiles in the poloidal direction on each flux surface, which become non-constant due to flow, and the flux average of the pressure are obtained. The transitions of the pressure profiles and the flux average of the pressure between sub- and super-sonic poloidal flows are discussed in relation with the radial force balance. The flux coordinates are also obtained analytically by expanding the coordinate relations with respect to the inverse aspect ratio.

Mapping of the HIDRA stellarator magnetic flux surfaces

The Hybrid Illinois Device for Research and Applications (HIDRA) is a classical stellarator designed for conducting plasma material interaction experiments and developing novel Plasma Facing Components (PFCs). Notably, the testing of two open-channel liquid lithium PFCs is imminent. Determining the shape of the plasma and its magnetic structure inside HIDRA is essential to carry out these tests. For this, electron traces were captured to build up the images of the HIDRA magnetic flux surfaces for several magnetic configurations, following the same procedure previously employed on the WEGA stellarator coupling an electron gun with a fluorescent detector. The FIELDLINES code has then been used to generate computational surfaces matching the experimental results. The obtained surfaces were found to be subject to a similar n = 1 error field as the one observed on WEGA, suggesting that the origin of this error field is inherent to the HIDRA vacuum vessel. Also, the effect of adding a vertical field was investigated, demonstrating the ability to radially shift the magnetic axis and move to a regime free of low-order rational resonances. This additional control over the HIDRA plasma and magnetic structure allows more freedom in setting up the PFC tests in the limiter and divertor regions.

Experimental and synthetic measurements of polarized synchrotron emission from runaway electrons in Alcator C-Mod

This paper presents the first experimental analysis of polarized synchrotron emission from relativistic runaway electrons (REs) in a tokamak plasma. Importantly, we show that the polarization information of synchrotron radiation can be used to diagnose spatially-localized RE pitch angle distributions. Synchrotron-producing REs were generated during low density, Ohmic, diverted plasma discharges in the Alcator C-Mod tokamak. The ten-channel motional Stark effect diagnostic was used to measure spatial profiles of the polarization angle and the fraction of detected light that was linearly-polarized. Spatial transitions in of —from horizontal to vertical polarization and vice versa—are observed in experimental data and are well-explained by the gyro-motion of REs and high directionality of synchrotron radiation. Polarized synchrotron emission is modeled with the synthetic diagnostic Soft; its output Green’s (or detector response) functions reveal a critical RE pitch angle at which flips by 90° and is minimal. Using Soft, we determine the dominant RE pitch angle which reproduces measured and values. The spatiotemporal evolutions of and are explored in detail for one C-Mod discharge. For channels viewing REs near the magnetic axis and flux surfaces q = 1 and 4/3, disagreements between synthetic and experimental signals suggest that the sawtooth instability may be influencing RE dynamics. Furthermore, other sources of pitch angle scattering, not considered in this analysis, could help explain discrepancies between simulation and experiment.

Vacuum solution for Solov’ev’s equilibrium configuration in tokamaks

In this work, we construct a tokamak plasma equilibrium generated by a combination of currents flowing within the plasma and in distant external magnetic field coils. The plasma toroidal current density takes the simple form inside the plasma (where r and z are cylindrical coordinates, and a, b, and R are constants), and is zero in the surrounding vacuum. The Grad–Shafranov equation possesses a well-known exact analytic solution within the plasma due to Solov’ev. We use a Green’s function method to compute the poloidal magnetic flux generated by plasma currents, together with a parameterized homogeneous solution to the Grad–Shafranov equation (that is well-behaved at small r and z), to construct the vacuum solution. The vacuum solution is matched to the analytic solution on the last closed magnetic flux surface (LCFS) to determine the parameters in the homogeneous solution. This procedure is performed for both up–down-symmetric double-null and up–down-asymmetric single-null equilibria. We find that any magnetic X-points on the LCFS are distorted due to the fact that one quadrant is filled by a current-carrying plasma, whereas the other three are filled by a vacuum in which no current flows. In particular, the vacuum quadrant opposite the plasma-filled quadrant expands at the expense of the other three quadrants.

Linking the two-field dynamics of plasma edge turbulence with the one-field balanced model through systematic unstable forcing at low resistivity

After the original contributions of Hasegawa and Wakatani (HW), basic two-field models such as the modified and balanced Hasegawa-Wakatani (BHW) models improve the understanding of plasma edge turbulence. The recent two-field flux-BHW model provides an improved treatment for the balanced electron dynamics on magnetic flux surfaces. The Hasegawa-Mima (HM) model offers another simplified one-field characterization of the zonal flow–drift wave interaction mechanism. A major restriction in the original HM model is the lack of intrinsic instability which is essential to maintain drift wave turbulence and plasma transport. We overcome this limitation by linking this model with the two-field HW equations with drift instability while keeping the simplicity in the one-field balanced formulation. A systematically derived unstable forcing is introduced to the modified HM model mimicking the role of the inherent instability near the low resistivity limit, where the unstable branch of the HW solution gradually becomes aligned with the HM potential vorticity. Detailed numerical experiments are performed to test the skill in the one-field model with unstable forcing. It is shown with qualitative and quantitative agreement that the one-field modified HM model is able to replicate the typical drift wave and zonal flow interacting procedure under a more analytically tractable framework. The insight gained from the simple model analysis can also offer guidelines for the development of model reduction methods for more complicated systems.

Wave modes excited by photosphericp-modes and mode conversion in a multi-loop system

Context. Waves are ubiquitous in the solar corona and there are indications that they are excited by photosphericp-modes. However, it is unclear howp-modes in coronal loops are converted to sausage modes and transverse (kink) modes, which are observed in the corona.Aims. We aim to investigate how those wave modes are excited in the lower corona by photospheric acoustic waves.Methods. We built 3D magnetohydrostatic loop systems with multiple inclinations spanning from the photosphere to the lower corona. We then simulated these atmospheres with the MANCHA code, in which we perturb the equilibrium with ap-mode driver at the bottom of the domain. By splitting the velocity perturbation into components longitudinal, normal, and azimuthal to the magnetic flux surfaces we can study wave behavior.Results. In vertical flux tubes, we find that deformed fast sausage surface waves and slow sausage body waves are excited. In inclined flux tubes fast kink surface waves, slow sausage body waves, and either a fast sausage surface wave or a plane wave are excited. In addition, we calculate a wave conversion factor (0 ≤ C ≤ 1) from acoustic to magnetic wave behavior by taking the ratio of the mean magnetic energy flux to the sum of the mean magnetic and acoustic energy flux and compare it to a commonly used theoretical conversion factor. We find that between magnetic field inclinations of 10° to 30° those two methods lie within 40%. For smaller inclinations the absolute deviation is smaller than 0.1.

Analytic equilibrium of “straight tokamak” plasma bounded by a magnetic separatrix

Theoretical and experimental considerations suggest that axisymmetric perturbations that are resonant at the X-point(s) of a magnetic divertor separatrix may play a role in the understanding of Edge Localized Modes in tokamak experiments and their active control via so-called vertical kicks. With this motivation in mind, the first step in the development of an analytical model for resistive axisymmetric X-point modes is presented, i.e., finding an adequate, but at the same time relatively simple analytical magnetohydrodynamic equilibrium for a plasma column with a noncircular cross section bound by a magnetic separatrix. An early example is Gajewski's equilibrium solution [R. Gajewski, Phys. Fluids 15, 70 (1972)], which, however, has the shortcoming that infinite external currents placed at an infinite distance from the X-points produce the elliptical elongation of the plasma column. In this article, Gajewski's solution is extended to the case where external currents are located at a finite distance from the boundary of the plasma current density and the latter is distributed uniformly over a domain bound by a nearly elliptical magnetic flux surface.

Flexible vacuum vessel bolometer camera design in ITER to adapt to the final position of the gaps between Blanket Modules

Bolometer cameras in ITER will be mounted, among others, on the Vacuum Vessel (VV) wall behind Blanket Modules (BMs). For the first assembly phase the platform (Cable fixations and the lower part of the internal signal chain) of VV cameras has to be delivered to fix the cables and protect their termination. During First Plasma, the as-built magnetic axis and magnetic flux surface will be measured and the BMs fixation will be adjusted to align them to the shape of the magnetic flux surfaces. Adjustments of the BMs of up to ±13,3 mm in toroidal and poloidal direction and up to ±20,3 mm in radial direction are foreseen. Accordingly, VV cameras need adjustments, too, to assure a proper view of the plasma.Calculations have been performed to define the impact of the possible BM movements onto the bolometer viewing cones. The toroidal and poloidal movements can be followed by shifting the collimator and the sensor along with the BMs. The radial movement of BMs was transferred to an additional poloidal shift of the sensor and collimator. The resulting concept for camera design with its complex space envelope will be presented. It provides an alignment flexibility of the cameras of ±31 mm poloidally and ±16 mm toroidally. Because of the short period between magnetic measurements and second assembly phase, the number of customizable parts is kept as low as possible.

Physics of toroidal gap heat loading on castellated plasma-facing components

Abstract Because the gaps between plasma-facing components in fusion devices are comparable in size to the ion Larmor radius (of the order of 1 mm), magnetic field line tracing, the so-called approximation, cannot accurately predict the fine scale heat load distribution around the gap edges. Finite Larmor radius effects dominate ion deposition. The poloidal component of the ion flux striking the surface is always in the diamagnetic/EXB drift direction, meaning that ions preferentially load one side of the gap. Usually electrons can be described optically due to their smaller Larmor radius. Depending on the local inclination of magnetic flux surfaces, it is possible that ions and electrons wet the same side of the gap, or opposite sides. Two-dimensional particle-in-cell simulations and dedicated experiments performed in the COMPASS tokamak are used to better understand processes responsible for plasma deposition on the sides of toroidal gaps between castellated plasma-facing components in tokamaks. The different contributions of the total incoming flux along a toroidal gap have been observed experimentally for the first time in COMPASS. These experimental results confirm the model predictions, demonstrating that in specific cases the heat deposition does not necessarily follow the optical approximation. The role played by electric fields in the deposition pattern is marginal, contrary to local non-ambipolarity that can change the asymmetrical plasma deposition from one side of the toroidal gap to the other.

Spatial transport of runaway electrons in axisymmetric tokamak plasmas

An implicit assumption made in the vast majority of studies of runaway electrons is that they are well confined to a given magnetic flux surface, thus allowing the use of slab or bounce averaged formulations that ignore the spatial transport of runaway electrons. While such an assumption is known to break down in the presence of strong 3D magnetic field perturbations, here we show that it can be violated even for an axisymmetric magnetic field under conditions representative of an actively mitigated disrupting plasma. Specifically, the low temperature and large impurity content typical of a post thermal quench plasma are shown to provide a drastic enhancement of the diffusive and convective transport of runaways electrons, where the convective component is found to be dominated by the Ware pinch. This inward convective flux allows runaway electrons to be displaced toward the plasma center, where they are eventually detrapped and reaccelerated, thus focusing populations of runaway electrons in the inner portion of the plasma. The resulting runaway electron distribution is shown to settle into a well-defined spatial eigenmode, whose form is often insensitive to the spatial distribution of the original seed population. The underlying transport processes responsible for determining the width and shape of the spatial runaway electron eigenmode are analyzed under a range of circumstances characteristic of a post thermal quench plasma.

Spatiotemporal evolution of runaway electrons from synchrotron images in Alcator C-Mod

In the Alcator C-Mod tokamak, relativistic runaway electron (RE) generation can occur during the flattop current phase of low density, diverted plasma discharges. Due to the high toroidal magnetic field (B0 = 5.4 T), RE synchrotron radiation is measured by a wide-view camera in the visible wavelength range (λ ≈ 400–900 nm). In this paper, a statistical analysis of over one thousand camera images is performed to investigate the plasma conditions under which synchrotron emission is observed in C-Mod. In addition, the spatiotemporal evolution of REs during one particular discharge is explored in detail via a thorough analysis of the distortion-corrected synchrotron images. To accurately predict RE energies, the kinetic solver CODE (Landreman et al 2014 Comput. Phys. Commun. 185 847–855) is used to evolve the electron momentum-space distribution at six locations throughout the plasma: the magnetic axis and flux surfaces q = 1, 4/3, 3/2, 2, and 3. These results, along with the experimentally-measured magnetic topology and camera geometry, are input into the synthetic diagnostic SOFT (Hoppe et al 2018 Nucl. Fusion 58 026032) to simulate synchrotron emission and detection. Interesting spatial structure near the surface q = 2 is found to coincide with the onset of a locked mode and increased MHD activity. Furthermore, the RE density profile evolution is fit by comparing experimental to synthetic images, providing important insight into RE spatiotemporal dynamics.

Fluctuation characteristics of the TCV snowflake divertor measured with high speed visible imaging

Tangentially viewing fast camera footage of the low-field side snowflake minus divertor in TCV is analysed across a four-point scan in which the proximity of the two X-points is varied systematically. The motion of structures observed in the post-processed movie shows two distinct regions of the camera frame exhibiting differing patterns. One type of motion in the outer scrape-off layer remains present throughout the scan whilst the other, apparent in the inner scrape-off layer between the two nulls, becomes increasingly significant as the X-points contract towards one another. The spatial structure of the fluctuations in both regions is shown to conform to the equilibrium magnetic field. When the X-point gap is wide the fluctuations measured in the region between the X-points show a similar structure to the fluctuations observed above the null region, remaining coherent for multiple toroidal turns of the magnetic field and indicating a physical connectivity of the fluctuations between the upstream and downstream regions. When the X-point gap is small the fluctuations in the inner scrape-off layer between the nulls are decorrelated from fluctuations upstream, indicating local production of filamentary structures. The motion of filaments in the inter-null region differs, with filaments showing a dominantly poloidal motion along magnetic flux surfaces when the X-point gap is large, compared to a dominantly radial motion across flux-surfaces when the gap is small. This demonstrates an enhancement to cross-field transport between the nulls of the TCV low-field-side snowflake minus when the gap between the nulls is small.

In–out impurity density asymmetry due to the Coriolis force in a rotating tokamak plasma

The effect of the Coriolis force due to the impurity toroidal and poloidal rotation on the in–out impurity density asymmetry in a rotating tokamak plasma is investigated. The role of the Coriolis force is figured out explicitly in the toroidally rotating plasma frame. The in–out impurity density asymmetry can be induced by the Coriolis force with , in this case, when moving along the magnetic field line from the outboard side to the inboard side in a magnetic flux surface, one sees a positive Coriolis force. The combined effects of the centrifugal force, the Coriolis force, the poloidal electric field and the ion-impurity friction force on the in–out impurity density asymmetry are discussed. The proposed theoretical model can be applied to improve the understanding of the in–out impurity density asymmetry observed in the tokamak experiments.