Evaluation of Spatial Profile of Local Emissions from W¹⁷⁺–W²³⁺ Unresolved Transition Array Spectra

Abstract

Tungsten (W) spectroscopy has attracted significant attention because W is one of the major impurities in ITER and future DEMO reactors. W²²⁺–W³³⁺ spectra at 15–45 Å have been useful for impurity diagnostics. Unresolved Transition Array (UTA) spectra around 200 Å, which contain W¹⁷⁺–W²³⁺, have potential for diagnostics tungsten ions in even lower charge states. Because multiple charge states overlap with very similar wavelengths, it is challenging to evaluate impurity spatial profiles from UTA spectra around 200 Å. In this study, we conducted tungsten pellet injection experiments in Large Helical Device (LHD) and attempted to evaluate the spatial profiles of UTA spectra around 200 Å, observed at 0.3–0.8 keV of central electron temperature. The results indicated that tungsten ions around W²⁰⁺ were locally profiled in a radial region, r_eff = 0.38 m, where the local electron temperature decreases by 30% to 40% with respect to more central and outer temperatures. These results suggested that the UTA spectrum around 200 Å would be useful for diagnostics of tungsten impurities in lower charge states than the charge states contained in UTA spectra around 15–45 Å.

1. Introduction

Tungsten (W) is planned for use as a plasma-facing component in the divertor and first wall of ITER [1] and future demonstration (DEMO) [2] reactors. Tungsten, one of the major impurity species released from metal surfaces, can penetrate high-temperature plasma. In such cases, a large amount of plasma-stored energy is lost through ionization, excitation, and radiation. Thus, it is essential to measure tungsten impurities for steady-state operation without impurity accumulation.

Tungsten impurities are distributed as charged ions in fusion plasma with extremely low charge states in the divertor, low-to-intermediate charge states in the edge plasma, and highly charged states in the core plasma.

Spectroscopic measurements are useful for determining the ionization balance and spatial profiles of W impurities. Emission lines from tungsten impurities have been observed in tokamaks [3,4,5,6,7,8], and also in stellarators [9,10,11]. These studies have contributed to our understanding of the behavior of tungsten impurities in magnetically confined plasma.

However, tungsten spectral data remain limited, especially for W⁸⁺–W²⁶⁺ in the Atomic Spectra Database of the National Institute of Standards and Technology (NIST-ASD) [12,13]. In order to accumulate tungsten spectral data, Electron Beam Ion Trap (EBIT) measurements were conducted [14,15,16]. The spectra of ions in specifically charged states were observed in the EBIT device. In addition, collisional-radiative modeling (CRM) was carried out [17,18]. By comparing the results of EBIT and CRM, atomic processes such as the transition, collisional strengths, electron impact (de)excitation, ionization, and recombination can be identified. In recent years, spectroscopic studies on tungsten ions in low-to-intermediate charge states have attracted significant attention. For example, Pm-like W¹³⁺ [19], In-like W²⁵⁺, and Sn-like W²⁴⁺ [20] have been successfully identified. In our previous study, an Unresolved Transition Array [21,22,23] (UTA) spectrum from W¹⁷⁺–W²⁵⁺ around 200 Å was observed in the Large Helical Device (LHD) and Compact EBIT (CoBIT) device [24], and identified using CRM on Flexible Atomic Code (FAC) [25], as well as a UTA spectrum around 300 Å [26,27]. It is very important to experimentally evaluate the spatial profile of tungsten ions around W²⁰⁺, because it allows us to verify the radiation power distribution, and impurity transport, such as the tungsten screening effect, in the edge plasma. The purpose of this study is to describe a method for experimentally evaluating the impurity spatial profile, and to evaluate the spatial profile of tungsten ions around W²⁰⁺ from UTA spectrum around 200 Å. This is expected to be useful for diagnosing ions in low-to-intermediate charge states that are difficult to measure because of the lack of spectral data.

2. Experimental Setup

2.1. Large Helical Device and Measurement System

The tungsten pellet injection experiments were conducted in LHD [28]. The experimental scheme is shown in Figure 1. Five Neutral Beam Injection (NBI) systems were used to heat the plasma.

In Figure 1, n-NBI(#1–3) and p-NBI(#4,5) represent the negative and positive ion source NBI, respectively. A tungsten pellet was injected at t = 4.1 s. Figure 2a–e show the discharge waveforms of the plasma heating power P_H, central electron density n_e0, central electron temperature T_e0, plasma stored energy W_P, and radiation power P_rad, respectively, where n_e0 and T_e0 were measured using the Thomson scattering system [29], and P_rad was measured using a bolometer [30].

Plasma was initiated by Electron Cyclotron Heating (ECH) and maintained at n_e0 = 2 × 10¹⁹ m⁻³ and T_e0 = 3 keV by n-NBI heating. A tungsten pellet was injected at t = 4.1 s. P_rad abruptly increased, and then stabilized at a high level because of the radiation of tungsten impurities, whereas W_p gradually decreased. The parameter n_e0 increased from 2 × 10¹⁹ m⁻³ to 4 × 10¹⁹ m⁻³, whereas T_e0 decreased from 3 keV to a few hundred eV at t = 4.1–5.3 s. In the tungsten pellet injection experiments, emissions from highly charged tungsten ions were first observed, followed by emissions from lower-charged states as the electron temperature decreased. Emissions from W¹⁷⁺–W²⁵⁺ were observed at t = 5.00–5.30 s, where T_e0 was 0.8–0.3 keV.

2.2. Space-Resolved Spectroscopic System in EUV Wavelength

Two space-resolved spectrometers, called “EUV Short2” and “EUV Long2” [31,32] were used to evaluate the spatial profile of tungsten impurities. Both spectrometers had an entrance slit, spatial-resolution slot, varied-line-spacing holographic grating, and CCD detector with 1024 × 255 pixels and a pixel size 26 × 26 μm². In fact, the pixels of the CCD were binned, and 204 × 128 channels (CHs) were available along the space and wavelength directions. The groove densities of the varied-line-spacing holographic gratings for the EUV Short2 and EUV Long2 spectrometers were 2400 and 1200 grooves/mm, respectively. The observable wavelength ranges of EUV Short2 and EUV Long2 were 5–130 and 30–650 Å, respectively. In this study, the wavelength ranges were set to 24.2–37.8 and 183.7–234.3 Å. The interval time for obtaining the spectra was 100 ms, of which approximately 61.21 ms was allocated for exposure and the rest for data processing.

In this study, the magnetic axis and toroidal magnetic field strength were set at a major radius of R = 3.6 m and B_t = 2.75 T (clockwise in the top view). The spatial profile of the effective minor radius r_eff and line of sight of EUV Short2 and EUV Long2 are shown in Figure 3. Here, r_eff is defined by an equation, S = πr_eff², where S is the averaged area of the poloidal cross-section along the toroidal angle.

2.3. Method to Evaluate Impurity Spatial Profile

A space-resolved spectrometer was used to observe the line-integrated intensity along the line of sight. The spatial profile of the local emissivity for tungsten was obtained using a line-integrated intensity profile. An inverse Abel transform [33,34,35] has been used to obtain the local emissivity from the line-integrated intensity. However, as the inverse Abel transform typically assumes axisymmetry, it is unsuitable for the non-axisymmetric geometry of LHD. This section describes the method for evaluation of the local emissivity profile of LHD.

Generally, the local ionic state strongly depends on the electron temperature T_e and electron density n_e, and it is assumed that the local emissivity is a function of T_e and n_e. This implies that the local emissivity can be defined on a magnetic surface with the same T_e and n_e. The principle for evaluation of the local emissivity is shown in Figure 4.

Here, $I_j$ and ${\epsilon }_k$ are the line-integrated intensity along the line of sight $\#j (j=1-204)$ and local emissivity on the magnetic surface $\#k (k=1-204)$, respectively. And $L_{jk}$ is the length along which line of sight $\#j$ passed the magnetic surface $\#k$. For $j=k$, $L_{jk}$ is the length of the dark arrow in Figure 4. On the other hand, for $j\ne k$, $L_{jk}$ is expressed as

$$L_{jk}=L_{jk}^{\prime }+L_{jk}^{\prime \prime } \left(j\ne k\right).$$

(1)

In many cases, the values of $L_{jk}^{\prime }$ and $L_{jk}^{\prime \prime }$ are different, because of the Shafranov shift. Therefore, $L_{jk}$ was obtained by numerical calculations using the measurements shown in Figure 3. Then, $I_j$ is expressed as

$$I=L\epsilon \to \left[\begin{array}{c}{I}_1\\ I_2\\ I_3\\ ⋮\\ I_N\end{array}\right]=\left[\begin{array}{ccccc}{L}_{11}& 0& 0& \cdots & 0\\ L_{21}& L_{22}& 0& \cdots & 0\\ L_{31}& L_{32}& L_{33}& \cdots & 0\\ ⋮& ⋮& ⋮& \ddots & 0\\ L_{N1}& L_{N2}& L_{N3}& \cdots & L_{NN}\end{array}\right]\times \left[\begin{array}{c}{\epsilon }_1\\ {\epsilon }_2\\ {\epsilon }_3\\ ⋮\\ {\epsilon }_N\end{array}\right].$$

(2)

The component of matrix L, L_jk, is shown in Figure 5.

A line of sight passes along the length of a specific magnetic surface. Thus, the local emissivity of a specific magnetic surface can be evaluated.

Typically, Gaussian distribution is used to determine the functional shape of a local emissivity profile [36,37]. In addition, Demura et al. reported that the fractional abundance would be Gaussian for high-Z elements, such as tungsten, in T_e < 10 keV [38]. On the other hand, it is suggested that the functional shape is a non-symmetric Gaussian from a spatial profile of W²⁴⁺ of 32.28–32.39 Å [39]. Thus, a non-symmetric Gaussian distribution was used in this study. The non-symmetric Gaussian distribution is expressed as

$$\epsilon (r_{eff})=\left\{\begin{array}{c}\exp \left[-{\left({\displaystyle \frac{r_{eff}-r_c}{\Delta r_{in}}}\right)}^2\right], \mathrm{f}\mathrm{o}\mathrm{r} r_{eff}<r_c\\ \exp \left[-{\left({\displaystyle \frac{r_{eff}-r_c}{\Delta r_{ot}}}\right)}^2\right], \mathrm{f}\mathrm{o}\mathrm{r} r_{eff}\geqq r_c\end{array}\right.$$

(3)

where r_c, Δr_in, and Δr_ot are the profile center and function broadenings for inner and outer r_c, respectively. The parameters r_c, Δr_in, and Δr_ot were determined using numerical calculations so that the cross-correlation coefficient, $\alpha$, between observed line-integrated intensity and calculated line-integrated intensity is greater than 99.5%. The typical results of the calculated local emissivity, experimentally observed line-integrated intensity, and evaluated line-integrated intensity profiles are shown in Figure 6a,b.

In Figure 6b, there is a region around r_eff = 0.6 m where the measured profile cannot be reproduced. This may be due to the tungsten ions localized in the edge plasma. Although a tiny signal was observed at r_eff = 0.5–0.6 m, it was difficult to determine whether the signal was from the emission of tungsten or other signals, such as bremsstrahlung, or emissions from other impurities. However, this was neglected in this study because the emission intensity was relatively low compared to the intensity of r_eff < 0.5 m.

3. Results and Discussion

The UTA spectrum around 200 Å contains line emissions from multiple states with very similar wavelengths. The structure of the UTA spectrum around 200 Å is shown in Figure 7a–c.

Here, the detector readout noise was subtracted in Figure 7a. The bremsstrahlung component was included in the observed EUV spectrum. Although the intensity of Bremsstrahlung depends on the wavelength, the level is much smaller than the intensity of tungsten ions. Therefore, the effect of bremsstrahlung on the analysis of the tungsten spatial profile was neglected. The spectra shown in Figure 7b,c were calculated using FAC [25], including electron collision excitation, de-excitation, and ionization between the 4f^m (m = 11–5), 4f^m−1 5l (l = 0–3), 4d⁹ 4f^m 5s, 4d⁹ 4f^m+1, 4f^m−2 5s²/5s5p/5p²/5s5d, and 4f^m−1 configurations. Quasi-continuum peaks around 192, 197, 201, 207, 213, and 221 Å contain 5s-5p and 5s²-5s5p emissions from several charge states. The transition wavelengths of 5s-5p and 5s²-5s5p shift towards longer wavelengths with decreasing charge states. It is necessary to verify whether the spatial distribution of tungsten ions can be evaluated from the UTA spectra of such complex structures.

The measured space-resolved spectra of 23.6–38.0 Å and 183.7–234.3 Å are shown in Figure 8a,b.

Here, the horizontal label, Z_R3600, in Figure 8a,b, means the vertical location of the observation chord at the major radius of 3600 mm. Emissions from W²²⁺ at 35.9 Å (4f-5g), W²³⁺ at 34.2 Å (4f-5g), and W²⁴⁺ at 32.6 Å (4f-5g) were observed using the EUV Short2 spectrometer. No clear emission lines from ions below W²²⁺ were observed at λ = 23.8–38.0 Å. Emissions from W²⁰⁺–W²³⁺ (W²⁰⁺(5s²-5s5p)+W²¹⁺(5s-5p, 5s²-5s5p)+ W²²⁺(5s-5p, 5s²-5s5p)+W²³⁺(5s-5p)), W²⁰⁺(5s²-5s5p)+W²²⁺(5s-5p), W¹⁹⁺(5s²-5s5p)+W²¹⁺(5s-5p), W¹⁸⁺(5s²-5s5p)+W²⁰⁺(5s-5p), W¹⁷⁺(5s²-5s5p)+W¹⁹⁺(5s-5p), and W¹⁶⁺(5s²-5s5p)+W¹⁸⁺(5s-5p) were observed at λ = 191.7, 196.3, 201.0, 207.3, 213.3, and 221.4 Å, respectively, using the EUV Long2 spectrometer. A quasi-continuum peak included in the UTA spectrum around 200 Å consists of emission lines from 5s-5p and its satellite line from 5s²-5s5p of different charge states, in addition to 5p-5d transitions [26]. Emissions from the 5s-5p and 5p-5d transitions have been experimentally observed in EBIT device [24]. The intensity from 5p-5d was relatively small. For the spectrum around 200 Å, emission lines from 5s²5s5p have not yet been directly observed in plasma and EBIT devices. The transition wavelengths of 5s-5p and 5s²-5s5p lines are very close. In plasma, because multiple charge states are included, it may be difficult to separate the 5s-5p and 5s²-5s5p lines. This means that it would be difficult to obtain a spatial profile of tungsten ions in separated charge states from a 200 Å spectrum. Therefore, the effect of the 5s²-5s5p line on the tungsten spatial profile must be revealed. For that purpose, W²²⁺ and W²³⁺ spectra at 34.2 and 35.9 Å are useful, because the spatial profiles of separated charge states can be evaluated from these spectra. By comparing the spatial profiles of two UTA spectra around 15–45 and 200 Å, the difference in peak position and broadening of the profiles will be revealed. The UTA spectrum around 15–45 Å would include ions in lower charge states than W²²⁺ [15,18]. However, no peaks were observed in LHD because of very low intensity and overlap with C and O lines. We first evaluated the spatial profiles of the 34.2 and 35.9 Å lines and the 191.7, 196.3 Å lines. Figure 9 shows the electron temperature and electron density profile measured by Thomson scattering and the evaluated local emissivity of 34.2, 35.9 Å lines, and the 191.7, 196.3 Å lines. The local emissivity profiles were normalized such that a maximum value of 1 was achieved.

The local emissivity profiles of W²²⁺ and W²³⁺ evaluated from Figure 8a peak at the plasma center, with W²²⁺ slightly distributed on the outer side. However, the local emissivity profiles of W²⁰⁺+W²²⁺ and W²⁰⁺–W²³⁺ peak around r_eff = 0.35 m, and are more widely distributed in the plasma than the profiles at 34.2 and 35.9 Å. This means that the peak position and broadening of 196.3 and 191.7 Å profiles are thought to have shifted toward r_eff = 0.4 m, where the electron temperature locally decreased, due to the inclusion of multiple charged states with very close wavelengths.

Finally, the local emissivity profiles of 191.7 (W²⁰⁺–W²³⁺), 196.3 (W²⁰⁺+W²²⁺), 201.0 (W¹⁹⁺+W²¹⁺), 207.3 (W¹⁸⁺+W²⁰⁺), 213.3 (W¹⁷⁺+W¹⁹⁺), and 221.4 (W¹⁶⁺+W¹⁸⁺) Å are summarized in Figure 10.

The spatial profiles of 207.3 (W¹⁸⁺+W²⁰⁺), 213.3 (W¹⁷⁺+W¹⁹⁺), and 221.4 (W¹⁶⁺+W¹⁸⁺) Å are localized around r_eff = 0.35 m, where the electron temperature is locally lower, while the 191.7 (W²⁰⁺–W²³⁺), 196.3 (W²⁰⁺+W²²⁺), and 201.0 (W¹⁹⁺+W²¹⁺) Å profiles are broadly distributed at r_eff = 0–0.35 m. This suggests that the tungsten impurity density is relatively high, at approximately r_eff = 0.35 m. The local emissivity profiles of 191.7 (W²⁰⁺–W²³⁺), 196.3 (W²⁰⁺+W²²⁺), 201.0 (W¹⁹⁺+W²¹⁺), 207.3 (W¹⁸⁺+W²⁰⁺), 213.3 (W¹⁷⁺+W¹⁹⁺), and 221.4 (W¹⁶⁺+W¹⁸⁺) Å have similar functional shapes, but the spatial broadening of emission lines on the short wavelength side tend to be slightly larger. The profiles of 207.3 (W¹⁸⁺+W²⁰⁺), 213.3 (W¹⁷⁺+W¹⁹⁺), and 221.4 (W¹⁶⁺+W¹⁸⁺) Å are consistent with the electron temperature profile, which has obvious dips at r_eff = 0.38 m. Although the UTA spectrum around 200 Å contains multiple charged states with very close wavelengths, we obtained W¹⁷⁺–W²³⁺ profiles with different peak positions and broadenings. Furthermore, the profiles of W¹⁷⁺–W²³⁺ and the observed electron temperature profile are consistent. This means that the UTA spectrum around 200 Å would be useful for diagnostics of tungsten impurities in lower charge states than the charge states contained in UTA spectra around 15–45 Å.

In this study, we evaluated the local emissivity profiles of W¹⁷⁺–W²³⁺. If the charge exchange processes could have been negligible, the ion density profile would be evaluated using reliable Photon Emissivity Coefficient, PEC, as

$$\epsilon ={\mathrm{P}\mathrm{E}\mathrm{C}}^{\mathrm{e}\mathrm{x}}{n}_e{n}_W{f}_q+{\mathrm{P}\mathrm{E}\mathrm{C}}^{\mathrm{r}\mathrm{e}\mathrm{c}}{n}_e{n}_W{f}_{q+1}.$$

(4)

where $\mathrm{P}\mathrm{E}{\mathrm{C}}^{\mathrm{e}\mathrm{x}}$, $\mathrm{P}\mathrm{E}{\mathrm{C}}^{\mathrm{r}\mathrm{e}\mathrm{c}}$, $n_W$, and $f_q$ are the PEC of electron collision excitation, recombination, total tungsten density, and fractional abundance. Fractional abundance is determined by the balance of ionization and recombination [40]. Currently, only PEC^ex is still evaluated in the CR model [26,27]. The evaluation of a reliable PEC is a kye issue in ion density diagnostics, $n_W{f}_q$. In addition to PEC, the evaluation of $n_W$ is one of the most important issues. For a long time, it has been established that the spatial profile of heavy impurities, such as tungsten, is determined by ionization equilibrium within the existing uncertainties in rate coefficients of ionization and dielectronic recombination [41]. The ratio of ionization rates to recombination rates is the parameter of the ion density profile [42]. In tungsten-contaminated plasma of LHD, $n_W$ has been evaluated using visible M1 lines from W²⁶⁺ and W²⁷⁺ [37]. The radial profile was evaluated using the STRAHL code [43], a standard diffusive-convective transport model for many impurities, and compared with ionization equilibrium. The two profiles were well matched. In addition, Fujii et al. reported that the fractional abundance ratios evaluated using STRAHL are consistent with the standard diffusive-convection model without transport [36]. Pütterich et al. evaluated the tungsten ionization balance based on ionization equilibrium [44]. These reports assist that the tungsten ions are in ionization equilibrium. On the other hand, Shurygin recently proposed an impurity transport model as an alternative model to the standard diffusive-convective transport model [45]. The Markov Chain Monte Carlo method was applied to source/sink term of ionization and recombination, which is incompatible with the radial dynamics and charge kinetic analysis of impurities. Therefore, the obtained profiles are different from standard diffusive-convective models. These efforts have contributed to the understanding of impurity transport processes. From an experimental standpoint, it is essential to expand the tungsten spectral database to make it useful for diagnostics and to align it with modeling.

4. Conclusions

In this study, tungsten pellet injection experiments were conducted in LHD. Two spatial profiles of UTA spectra around 15–45 Å and 200 Å, which contained W²²⁺–W²⁴⁺, and W¹⁷⁺–W²³⁺, respectively, were compared. The local emissivity profiles of W²²⁺ and W²³⁺, evaluated from 35.9 and 34.2 Å, had a peak position at the plasma center, r_eff = 0 m. On the other hand, local emissivity profiles of W¹⁶⁺+W¹⁸⁺, W¹⁷⁺+W¹⁹⁺, W¹⁸⁺+W²⁰⁺, W¹⁹⁺+W²¹⁺, W²⁰⁺+W²²⁺, and W²⁰⁺–W¹⁸⁺, evaluated at 221.4, 213.3, 207.3, 201.0, 196.3, and 191.7 Å, had a peak position at r_eff = 0.38 m, where the local electron temperature decreases by 30% to 40% with respect to more central and outer temperatures. Furthermore, the profiles of W¹⁷⁺–W²³⁺ and the observed electron temperature profile are consistent. These results suggest that the UTA spectrum around 200 Å would be useful for diagnostics of tungsten impurities in lower charge states than the charge states contained in UTA spectra around 15–45 Å. The impurity spatial profile analysis method and spectral data for tungsten ions in low-to-intermediate charge states described in this paper could assist in future impurity diagnostics and transport modeling. For future work, an evaluation of a reliable PEC database and total tungsten density, $n_W$, will be required. By accomplishing these tasks, we will contribute to the understanding of the impurity transport processes.