Observation of carbon impurity flow in the edge stochastic magnetic field layer of Large Helical Device and its impact on the edge impurity control

The parallel flow of carbon impurity in a thick stochastic magnetic field layer called the ‘ergodic layer’ located at the edge plasma of the Large Helical Device (LHD) is studied by space-resolved vacuum ultraviolet (VUV) spectroscopy, using a 3 m normal incidence spectrometer. A full vertical profile of C3+ impurity flow is evaluated from the Doppler shift of the second order of CIV line emission (2  ×  1548.20 Å) at a horizontally-elongated plasma position of LHD. The carbon flow at the top and bottom edges in the ergodic layer has the same direction toward the outboard side along the major radius direction. The observed flow quantitatively agrees with the simulation results calculated with a 3D simulation code, EMC3-EIRENE. It experimentally verifies the validity of edge parallel flow driving the impurity screening.

Studies on the edge stochastic magnetic field in helical systems have also been intensively conducted. A thick stochastic magnetic field layer called the 'ergodic layer' of the Large Helical Device (LHD) consists of stochastic magnetic fields with a 3D structure intrinsically formed by helical coils, while well-defined magnetic surfaces exist inside the last closed flux surface [9]. It is therefore extremely important to study the impurity behaviour and transport in the ergodic layer and to compare with those in the scrape-off layer of tokamaks. The effect of impurity screening has also been compared between the scrape-off layer of a tokamak and the ergodic layer of a helical device [10]. An impurity transport simulation based on a 3D simulation code, EMC3-EIRENE [11,12], has been applied to the ergodic layer of LHD [13]. In the simulation, a transport model that considers the parallel momentum balance on impurity ions along a magnetic field line, connecting the core plasma and the divertor plate, has been proposed based on the following equation; where the five terms at the right-hand side are contributions of impurity ion pressure gradient, parallel electric field, friction force between bulk ions and impurity ions, electron thermal force and ion thermal force, respectively. The impurity transport which is perpendicular to magnetic field lines is also important; therefore, the perpendicular transport is modelled by defining a perpendicular impurity diffusivity. The effect of the perpendicular diffusivity was studied. A reasonable parameter range for the diffusivity was found in [14]. In this paper, the discussion is focused on the parallel transport. Among the terms in the right-hand side of equation (1), the friction force term and the ion thermal force term are the dominant terms. When the ion density gradient increases, the friction force  also increases, resulting in an impurity flow directed towards the divertor plates; this refers to the impurity screening. On the other hand, when the ion temperature gradient increases, the ion thermal force increases, resulting in an impurity flow directed towards the core plasma, which leads to impurity accumulation. In LHD, it is found that carbon impurities are screened by the presence of the ergodic layer [15], iron impurities are also more effectively screened. Effective screening for iron can be explained by the parallel transport with following reasons; the first ionization energy of iron is lower than that of carbon as well as the velocity of iron ions is slower than that of carbon. Therefore, iron is ionized at the outer region of the ergodic layer where the friction force is more dominant due to the lower temperature, which results in the more effective screening for iron. As a result, the iron density in core plasmas of LHD is found to be extremely low despite the stainless-steel vacuum vessel [16]. The precise measurement of impurity behaviour is very important to develop a deeper understanding of the impurity transport in the edge ergodic layer. However, the impurity flow in the ergodic layer has not yet been measured experimentally, even though it is considered to be a key mechanism to determine impurity distributions. Therefore, a profile measurement of the impurity flow is truly required to examine the validity of the theoretical modelling on the impurity transport in stochastic magnetic field layer.
This paper mainly describes impurity flow measurement based on a vacuum ultraviolet (VUV) spectroscopy technique in LHD for the contribution to the impurity transport study in the edge stochastic magnetic field layer. In section 2, impurity screening in LHD characterized by carbon line emissions is briefly introduced. In section 3, the space-resolved VUV spectro meter system is explained with the measurement results of emission intensity, ion temperature and flow velocity of the carbon impurity. In section 4, interpretation of a physical meaning of the measured flow profile is discussed assisted by an impurity transport simulation based on a 3D simulation code, EMC3-EIRENE. The paper is summarized in section 5.

Impurity screening evaluated by carbon line emissions in LHD
The LHD coil system consists of a set of two continuous superconducting helical coils with poloidal pitch number of 2 and a toroidal pitch number of 10 and three pairs of superconducting poloidal coils. Figure 1 shows schematic drawings of toroidal plasma with helical coils and a horizontally-elongated poloidal cross section of LHD. Poincare plots of stochastic magnetic fields in the ergodic layer under vacuum condition are shown for poloidal cross sections at horizontally-elongated plasma positions of LHD, for different magnetic axis configurations of R ax = 3.6 m and 3.9 m. The stochastic magnetic fields in the edge ergodic layer are plotted with colour scale indicating the magnetic field connection length in addition to the magnetic surfaces. The ergodic layer mainly consists of stochastic magnetic field lines with connection lengths from 10 to 2000 m, which correspond to 0.5-100 toroidal turns in the LHD. Radial thickness of the ergodic layer varies toroidally and poloidally. When the magnetic axis shifts outwardly, the ergodic layer is wider and the plasma size within the LCFS is smaller.
In order to evaluate the impurity screening effect, due to the existence of the ergodic layer, impurity spectroscopy was widely employed [15]. Figure 2 shows a typical waveform of a discharge with a magnetic configuration with R ax = 3.6 The averaged electron density n e was scanned from 0.8 to 6.1 × 10 13 cm −3 . Intensities of carbon line emissions are monitored as an indicator of the impurity screening. CIII (977.03 Å, 2s 2 -2s2p) and CIV (1548.02 Å, 2s-2p) are measured using a 20 cm normal incidence VUV spectrometer [17], while CV (40.27 Å, 1s 2 -1s2p) and CVI (33.73 Å, 1s-2p) are measured using a grazing incidence EUV spectrometer [18]. The ionization potential, E i , for C 2+ , C 3+ , C 4+ , and C 5+ is 48 eV, 65 eV, 392 eV, and 490 eV, respectively. Therefore, CIII and CIV radiation is emitted by carbon ions with low E i located at the outer region of the ergodic layer, while CV and CVI radiation is emitted by carbon ions with high E i located at inner region of the ergodic layer. Figure 3 shows the electron density dependence of line intensity of (a) CIII, (b) CIV, (c) CV, and (d) CVI nor malized by the line-averaged electron density and (e) a line ratio of (CV + CVI)/(CIII + CIV) as an indicator of the impurity screening effect. Smaller values of the ratio leads to enhancement of the impurity screening effect. The line ratio decreases with the electron density, because carbon lines emitted from the outer region of the ergodic layer (CIII, CIV) increase, while those from inner region (CV, CVI) decrease. It indicates enhancement of the impurity screening in the high density regime. Figure 3(e) also shows a comparison of the line ratio between the inward-shifted magnetic configuration with R ax = 3.6 m and the outward-shifted magnetic configurations with R ax = 3.9 m. The impurity screening effect is more obvious in the outward-shifted configuration. It has been known that the edge density profile is flat in the outwardshifted magnetic configuration for the same line-averaged electron density. Therefore, the friction force becomes dominant in the thick ergodic layer, which results in more effective impurity screening [15].

Measurements of emission intensity, ion temperature and flow velocity of the carbon impurity
Space-resolved VUV spectroscopy using a 3 m normal incidence spectrometer is utilized to measure impurity emission profile in the edge and divertor plasmas of LHD in wavelength range of 300-3200 Å [19]. A 3 m normal incidence VUV spectrometer (McPherson model 2253) is installed on an outboard midplane diagnostic port, as shown in figure 4. A back-illuminated CCD detector (Andor model DO934-BN: 1024 × 1024 pixels) is placed at the position of the exit slit of the spectrometer for measuring a focal image of VUV line emissions. A high wavelength dispersion of 0.037 Å/pixel enables the Doppler profile measurement of the impurity lines over the whole wavelength range [20]. The viewing angle can be switched between the 'full profile measurement' mode to cover an entire vertical region of the elliptical LHD plasma at horizontally-elongated poloidal plasma cross section to measure the top-to-bottom vertical profile and 'edge profile measurement' to focus the viewing angle on the bottom edge with a high spatial resolution for observations of vertical impurity profile in the ergodic layer, as shown in figure 4.
The CCD signals are summed up every 10 vertical pixels and replaced into single vertical channels. The CCD image with 1024 × 1024 pixels is then changed into 102 × 1024 channels. The observable region is resolved by 102 observation chords. Each profile image is taken with a time interval of 200 ms.  the discharge, as shown in figure 2. Signal intensities in the figure are normalized to be a unit for simplicity. We successfully observed the Doppler-shift which corresponds to the flow of C 3+ ions in observation chords located at both the top and bottom edges of the ergodic layer, as shown in figures 5(a) and (c). The flow velocity along the sightline, v, is given by v = c (Δλ/λ), where c is the speed of light, Δλ is the Doppler-shift and λ is the wavelength of line emission. Presently, a spectral peak of the CIV spectrum in a recombination phase at the plasma termination, as shown in the hatched region in the discharge waveform from 5.4 to 5.6 s in figure 2, is regarded as the reference of the Doppler-shift because the plasma temperature is extremely low and any plasma flow seems to have already disappeared. It is known that the spatial profile of the CIV intensity has a steep peak in the ergodic layer [21]. CIV emission is released only in the outermost region of the ergodic layer in LHD plasmas, because the low ionization energy of 65 eV for C 3+ ions causes less fractional abundance in the core plasma. Therefore, the peak of the intensity profile outside the LCFS shown in figure 6(a) is a result of line integration in a long path along the sightline through the ergodic layer at the bottom and top edge of the horizontally-elongated elliptical plasma. The intensity peak around Z = 0 mm in figure 6(a) is a superposition of emissions from inboard and outboard divertor trajectories. Emission peaks from the top and bottom edges have an asymmetry depending on the direction of the toroidal magnetic field. In the present study, the bottom peak has a larger intensity so that that it appears clearer than the top peak [22]. The T i profile also indicates the edge T i in the ergodic layer at corresponding vertical position. Figure 6(c) shows a flow profile of C 3+ impurity. The measured flow velocity in figure 6(c) is a projection of the flow along the observation chord which can approximately be the direction of the plasma major radius. Therefore, a variable of v R is used to indicate the measured flow value. Positive and negative sign in the horizontal axis of figure 6(c) corresponds to the outboard and inboard direction along the plasma major radius, respectively. From the figure, it is found that the flow direction is the same, i.e. the outboard direction, for both the top (Z = 480 mm) and bottom (Z = −480 mm) edges of the ergodic layer. A synthetic profile of the C 3+ flow calculated with the impurity transport simulation based on a 3D simulation code, EMC3-EIRENE, is also plotted with solid line in figure 6(c). To obtain a synthetic vertical profile of the flow, v R , local value of the calculated flow projected in the major radius direction, v R,loc , is line-integrated weighted by emission intensity along each observation chord as follows, v R = v R,loc εn C 3+ n e dl/ εn C 3+ n e dl , where ε is an emission coefficient of the CIV line, n C 3+ is density of C 3+ ion, and n e is the electron density. The experiment and simulation exhibit excellent agreement with each other. The simulation code employs an impurity transport model, where the impurity flow is driven by a momentum balance on the impurity ions along the magnetic field line. The friction force term is much larger than the ion thermal force term in the momentum balance in the present case, which will be discussed later in the next section. Figure 7 shows the flow at the top and bottom edges of the ergodic layer as a function of density. It indicates that the flow, which has the same direction as the friction force, increases with the density. The result supports a prediction by the simulation that the friction force becomes more dominant in the force balance in the higher density regime, which results in the increase of impurity flow causing the impurity screening. The edge flow profile is investigated with high spatial resolution by using the viewing angle of the edge profile measurement of the VUV spectroscopy. Figure 8 shows vertical profiles at the bottom edge of the ergodic layer of (a) CIV line intensity, (b) ion temperature, and (c) flow velocity derived from CIV 1548.20 × 2 Å line emission measured by VUV spectroscopy for n e = 2.9, 4.2, and 6.0 × 10 13 cm −3 with a magnetic configuration with R ax = 3.6 m and B t = 2.75 T. The observation range of the edge profile measurement of the VUV spectroscopy is also shown in figure 8(d). By increasing the electron density, the flow velocity toward the outboard direction develops clearly with the maximum value at Z = −480 mm. We compared the results with a magnetic configuration of R ax = 3.9 m and B t = 2.539 T, as shown in figure 9. Figure 9(c) indicates that the flow is directed toward the inboard direction with the maximum value at Z = −480 mm. This direction is also the same as the friction force in the parallel momentum balance for R ax = 3.9 m calculated with EMC3-EIRENE code which will be described below, even though it is the opposite direction to that of the R ax = 3.6 m case. The maximum values of the flow did not depend on the electron density within the density range employed in this experiment.

Comparison of the impurity flow between experiment and simulation
The carbon flow measured with spectroscopic methods is compared with the impurity transport simulation based on the EMC3-EIRENE code for the first time. The simulation is carried out with the electron density at the LCFS, n e, LCFS , of 6.0 × 10 13 cm −3 and the auxiliary heating power, P in , of 10 MW, which is the same discharge condition as the result in figure 6. Figure 10 shows a colour contour of the simulation result for the flow component of C 3+ impurity flow parallel to magnetic field lines projected to the major radius direction. The yellow and blue colour indicates that the flow has a major radius component in outboard and inboard directions, respectively. The magnetic field lines at the top and bottom edges of the ergodic layer are illustrated by the black solid arrows as B top and B bottom , respectively. The green thick dashed arrows indicate the flow velocity and direction parallel to the magnetic field line, V // , at the top and bottom edges. In this calculation result, the absolute value of V // is about 50 km s −1 both at the top and bottom edges. It should be noted here that the toroidal component of V // has an opposite direction between the top and bottom edges, while the major radius component of V // has the same direction towards the outboard side. The detailed studies of the impurity flow direction are presented in the paper [23]. A synthetic profile of the simulated flow is also shown in figure 6(c) with a solid line, which is obtained by integrating the Doppler-shifted CIV intensities along the observation chord. The excellent agreement between  experiment and simulation in the present study concludes that the parallel flow in the ergodic layer can be well explained by the presently used theoretical modelling on the edge impurity transport. Therefore, the impurity parallel flow can be mainly determined by the momentum balance along the magnetic field line. In particular, the friction force between impurity and bulk ions to the ion thermal force driven by the ion temperature gradient are dominant terms in the momentum balance. The calculated friction force, which is expressed as the third term of the right-hand side of equation (1), has the maximum value at both the top and bottom edges of the ergodic layer, where the impurity parallel flow also takes the maximum value. The impurity screening driven by the friction force can be more effective at the higher electron density range. The density dependence of the flow in the modelling can also be clarified by the experimental result shown in figures 7 and 8(c).
On the other hand, figure 11 shows the simulation results for a different magnetic configuration of R ax = 3.9 m and B t = 2.539 T for 4.0 × 10 13 cm −3 and P in of 10 MW. When the magnetic axis is shifted outward, the ergodic layer is wider and the plasma size within LCFS is smaller. It should be noted that here, the toroidal component of V // has an opposite direction between the top and bottom edges, while the major radius component of V // has the same direction, namely, the direction toward the inboard side for outward-shifted configuration with R ax = 3.9 m. It agrees with the experimentally observed flow direction toward the inboard direction as shown in figure 9(c) for R ax = 3.9 m. The agreement concludes that    the parallel flow in the ergodic layer can be well explained by the presently used theoretical modelling on the edge impurity transport.
Finally, the electron density dependence of the maximum value of measured flow is summarized in figure 12. We now understand that all plots in the figure have the same directions as the friction force even though the flow directions are opposite between R ax = 3.6 m and R ax = 3.9 m. In the case of R ax = 3.9 m, the flow has a large value even in the low density regime. The reason why flow velocity is almost constant with electron density for R ax = 3.9 m has not yet been clarified. This may have some relationship with the fact that the impurity screening effect for R ax = 3.9 m is larger than R ax = 3.6 m. It has been known that the edge density profile is flat in the outward-shifted magnetic configuration for the same line-averaged electron density. Therefore, the friction force becomes dominant in the thick ergodic layer, which results in the more effective impurity screening. Further simulations in the low density regime are needed to clarify the density dependence of the impurity flow, which remains a future study.

Summary
The parallel flow of carbon impurity in a thick stochastic magnetic field layer called the 'ergodic layer' located at the edge plasma of the LHD is studied by space-resolved VUV spectr oscopy using a 3 m normal incidence spectrometer. A full vertical profile of C 3+ impurity flow is evaluated from the Doppler-shift of the second order of CIV line emission (2 × 1548.20 Å) at a horizontally-elongated plasma position of LHD for a hydrogen discharge with R ax = 3.6 m, B t = 2.75 T, n e = 6.0 × 10 13 cm −3 and P in = 10 MW. It is found that the the carbon flow at the top and bottom edges in the ergodic layer has the same direction towards the outboard side along the major radius direction. The flow velocity increases with the density at both the top and bottom edges of the ergodic layer.
The simulation result of C 3+ impurity flow parallel to the magnetic field lines calculated with a 3D simulation code, EMC3-EIRENE indicates that the major radius component of the flow has the same direction towards the outboard side at the top and bottom edges in the ergodic layer. The experiment and simulation agree with each other quantitatively, thus we may conclude that the parallel flow in the ergodic layer can be explained by the presently used theoretical model. In particular, the impurity screening driven by the friction force between impurity and bulk ions can be more effective at higher electron density ranges. The density dependence of the flow in the modelling can also be clarified by the experimental result.