Plasma and Fusion Research: Regular Articles

Volume 9, 1401056 (2014)

Validation of Spectroscopic Model for Fe Ions in Non-Equilibrium
Ionization Plasma in LHD and Hinode∗)
Izumi MURAKAMI1,2) , Tetsuya WATANABE3,4) , Chihiro SUZUKI1) , Shigeru MORITA1,2) ,Chunfeng DONG1) , Naoki TAMURA1) , Norimasa YAMAMOTO5) , Daiji KATO1,2) ,Hiroyuki A. SAKAUE1) , Hirohisa HARA3,4) , Nobuyuki NAKAMURA6)
and Shigeru SUDO1,2)
1)2)

National Institute for Fusion Science, Toki, Gifu 509-5292, Japan
Department of Fusion Science, The Graduate University of Advanced Studies (SOKENDAI), Toki, Gifu 509-5292, Japan
3)
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
4)
Department of Astronomical Science, The Graduate University of Advanced Studies (SOKENDAI), Mitaka, Tokyo
181-8588, Japan
5)
Center of Applied Superconductivity and Sustainable Energy Research, Chubu University, Kasugai, Aichi
487-8501, Japan
6)
Institute for Laser Science, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan(Received 25 September 2013 / Accepted 16 February 2014)
We measured extreme ultraviolet spectra of Fe ions for plasmas produced in the Large Helical Device(LHD) at the National Institute for Fusion Science (NIFS). Iron was injected into the plasmas by using a tracer–
encapsulated pellet. By controlling the neutral beam injection pattern, we could produce plasma with a central
electron temperature of approximately 500 eV, which was suitable for producing Fe XVII ions. We measured
seven Fe XVII lines. The intensity ratio for λ of 20.468 to 25.493 nm was consistent with the theoretically calculated value of 1.1. This calculated value was determined purely from the branching ratio due to the common
upper level of these transitions, although Warren et al. [Astrphys. J. 685, 1277 (2008)] reported a larger ratio of
approxinately 2 from Hinode EIS measurements. The other five ratios for Fe XVII lines in our LHD measurements were also consistent with the theoretical ratios calculated with a collisional–radiative model. A preferredatomic dataset for Fe XVII is suggested to obtain better agreement between the measured and calculated ratios.
c 2014 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: Fe XVII spectral lines, spectroscopic diagnostics, EUV spectrum, solar plasma, fusion plasma
DOI: 10.1585/pfr.9.1401056

1. Introduction
In solar physics, one of the major issues to be solved
is the identification of the heating mechanism that keeps
the hot and diﬀuse corona, extending above the Sun’s cool
atmosphere at its high temperature of a few million degrees. Since 2006, the Hinode spacecraft has been in orbit to study the heating mechanism and dynamics of theactive solar corona, the origin of strong magnetic fields,
and the trigger mechanism for solar flares [1]. Hinode isequipped with a solar optical telescope (SOT), an X-ray
telescope (XRT), and an extreme ultraviolet (EUV) imaging spectrometer (EIS). The EIS takes EUV images of the
Sun as well as EUV spectra in the wavelength regions of
17.0 - 21.0 nm and 25.0 - 29.0 nm [2]. In these regions, Fe
VIII–XXIV lines are measurable and are expected to provide information on the solar plasma in the wide electron
temperature range 4.7 < log T e [K] < 7.2.
author’s e-mail: murakami.izumi@nifs.ac.jp∗) This article is based on the invited talk at the 29th JSPF Annual Meeting(2012, Fukuoka).

Several models have been proposed to explain coronal heating by acoustic waves, Alfvén body waves, microflares, etc [3]. Conventional one-fluid MHD plasma
in thermal equilibrium has been used for modeling solar plasma. Typical ions observed in the solar transition
region and the corona have long ionization and recombination timescales, and non-equilibrium ionization has
been suggested especially for plasma with flow [4] or solar flares [5]. When the ionization timescale is longer than
the time required for an ion to traverse a temperature scaleheight, the degree of ionization is delayed behind the equilibrium value under local conditions. In the solar transition region, the electron temperature and density change
drastically, and non-equilibrium conditions can result fromdownflows or outflows in the transition region. Dupree etal. [4] showed that the electron temperature dependencesof O IV, N IV, and C IV spectral-line intensity ratios arealtered when plasma is in non-equilibrium with outflows
in the transition region. Imada et al. [6] found that the Fe
ion state distribution is quite diﬀerent from that for ion-

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ization equilibrium when time-dependent ionization andrecombination processes are considered in the shock region caused by magnetic reconnection. Thus, when analyzing the spectroscopic data, we need to focus on physical conditions of plasma, such as flows and shocks. In
addition, non-thermal velocities measured as an excess ofline thermal broadening are thought to be caused by turbulence, waves, or velocity gradients; those velocities provide important information for examining the coronal heating mechanism [7]. Doscheck et al. [7] and Imada et al. [8]estimated non-thermal velocities in the solar active region
by using Fe XII and Fe XVI lines, and obtained values of
30 - 60 km s−1 and approximately 13 km s−1 , respectively.
Such estimates depend on the accuracy of thermal condition determination for plasmas.
The accuracy of the analyzed results from spectroscopic measurements depends on that of the spectroscopic
model and the atomic data used in the model. As Hinode EIS measures Fe VIII–XXIV lines for plasma diagnostics as good indices for the solar transition region overa wide electron temperature range, we have constructed
collisional–radiative (CR) models for Fe7+ –Fe23+ ions toanalyze both solar and laboratory plasmas [9–14]. We havecarefully examined atomic data of Fe ions to be used in the
CR models [15, 16], and so far, have applied the models to
the measurements of laboratory plasmas to validate the CR
models and atomic data for Fe XIII [9,14], Fe XIV [14], Fe
XV [14], Fe XXI [12], and Fe XXII [13].
The Large Helical Device (LHD) in the National Institute for Fusion Science (NIFS) was used to validate theCR models and atomic data of Fe ions. The LHD canmaintain stable plasmas even after impurity elements are
injected by an impurity pellet or a tracer-encapsulated pellet (TESPEL) [17, 18]. The LHD has various diagnostic
systems for measuring electron temperature, density, andother plasma properties. LHD plasmas have electron temperature distributions from a few electron volts in the peripheral region to approximately 4 keV in the plasma center. We can produce plasmas in the LHD with electron
temperatures similar to those in the solar transition region
and the corona. Thus, we used a TESPEL to inject iron
into LHD plasmas and measured EUV spectra to comparewith the model calculations [9, 12, 13]. The CR model for
Fe XIII evaluated using the LHD experiments [9] has been
applied to analyze solar spectra measured by Hinode EIS
to estimate the electron density distribution in the solar active region [11].
We also used an electron beam ion trap (EBIT) device
and compact EBITs (CoBITs) at the University of ElectroCommunications (UEC) and NIFS [19, 20]. An EBIT ionizes ions by an electron beam and traps them with an electric field of the electron beam. It produces diﬀuse plasma
with an electron density of approximately 1010 cm−3 . It
controls the ion charge distribution by choosing the electron beam energy, and the charge states of spectral lines
can be identified easily as only ions with ionization po-

tentials smaller than the electron beam energy are produced. EUV spectral lines of Fe XIII, Fe XIV, and Fe XV
were measured by the CoBIT at the UEC and comparedwith the CR model calculations [14]. Electron density dependence of line ratios for Fe XIII and Fe XIV agreed
very well with the CR model calculations, but the Fe XV
23.39 nm/24.38 nm ratio was a factor 1.5 - 2 larger than thatobtained from the model calculation. To find the causeof this discrepancy, we need to examine measurements,
atomic data, and the CR model even more carefully.
Here we focus on Fe XVII. Recently, Fe XVII spectral lines were measured by Hinode EIS and discrepancies
from theoretical predictions were reported for the intensity
ratios of Fe XVII 20.4675 nm (2p5 3s 1 P1 –2p5 3p 1 S0 ) and25.4885 nm (2p5 3s 3 P1 –2p5 3p 1 S0 ) [21]. The upper levelsof both transitions are the same (2p5 3p 1 S0 ), so the intensity ratio is determined by the branching ratio of 1.1 anddoes not depend on plasma conditions for optically thinplasma. However, the measured ratio was 2.5. In addition,other Hinode EIS results for this line ratio for the solar
active region also show this discrepancy; the ratio tends
to increase with decreasing electron temperature [22]. The
same lines were measured previously in solar-flare spectra by Skylab and the ratio was 1.1, which agreed with thetheoretical prediction [23]. Del Zanna and Ishikawa [24]made a list of Fe XVII EUV lines based on two Hinode
EIS measurements, and also reported a discrepancy withrespect to theoretical calculations for this line ratio. Theysuggested that the 20.466-nm line was blended with anunidentified line at 20.472 nm, with the same morphology
as the Fe VIII line in the monochromatic images taken by
Hinode EIS.
In order to use the Fe XVII lines for diagnosing hightemperature solar active region, the validation of theatomic data for Fe XVII is needed. Jönsson et al. [26]performed theoretical calculations for the Fe XVII atomic
structure by using the GRASP2K code, which is widelyused for theoretical studies of atoms and is believed tohave a high accuracy [25]. Relativistic eﬀects were carefully considered in configuration interaction calculations.
The results obtained for the branching ratio of the two Fe
XVII lines agreed with the previous prediction [26].
In this study, we used LHD plasmas to measure the Fe
XVII spectral lines for validation of the atomic data andthe CR model for Fe XVII experimentally and to investigate the discrepancy in the Fe XVII line ratio between theoretical predictions and Hinode EIS measurements. These
two Fe XVII lines are very weak and were not detected using CoBIT. In Sec. 2, we briefly introduce the CR model,
followed by an explanation of the measurements with the
LHD and the analysis in Sec. 3. In Secs. 4 and 5, we discuss the results of validation of the CR model and Hinode
EIS measurements. This study is summarized in Sec. 6.

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2. Collisional–Radiative Model

3. LHD Experiments

The spectral line intensity of the transition from leveli to level j is proportional to the product of the population
density of the upper level; radiative transition probability;and energy diﬀerence of the transition, n(i)Ar (i, j)ΔE(i, j).
We constructed a CR model to calculate the population
densities of excited states for an Fe ion using the quasisteady-state approximation. We assumed that population
densities of excited states relax fast enough, compared tothe timescales for changes in plasma properties and ion
densities, and solved the rate equations for population densities as dn(i)/dt = 0. Excited states up to the principal
quantum number n = 5 were considered, and a total of 157
fine-structure levels were included. The rate equation is
written as

EUV spectra in the 10 - 30 nm wavelength range were
measured for plasmas in LHD using a flat-field EUV spectrometer [32]. The spectrometer can cover a wavelength
range of 5 - 50 nm using a laminar-type holographic grating. Spectral resolution of approximately 0.02 nm wasachieved at 20 nm. A 0.15 µm thick aluminum filter wasplaced in front of the grating to screen out emissions inwavelengths below approximately 17 nm. This successfully reduced the contamination of higher-order emission
lines, especially the second-order emission line of Fe XXII
at 10.22 nm, which could overlap with the Fe XVII line at
20.468 nm. The exposure time of one frame was 5 ms. A
new technique for absolute intensity calibration was conducted using bremsstrahlung continuum radiation and abranching ratio of C IV lines [33].
We analyzed the spectra measured for the plasma ofshot number 107802. Figure 1 shows the temporal distribution of the discharge. Three tangential neutral beams(NBIs) were injected at t = 3.3 - 4.3 s, and two perpendicular neutral beams were injected at t = 4.2 - 6.2 s. Due tothese changes, the stored energy Wp and the central electron temperature started decreasing drastically at t = 4.3 s,reached their minimum at around t = 5 s, and increased
again. The minimum central electron temperature was

dn(i)
dt 

{C( j, i)ne +Cp ( j, i)np }n( j) +Ar ( j, i)n( j)
=
ji

−



j>i

{C(i, j)ne + Cp (i, j)np + S (i)ne }n(i)

ji

−



Ar (i, j)n(i).

(1)

j<i

We included radiative decay (Ar (i, j)), electron-impact excitation and de-excitation (C(i, j)), electron-impact ionization (S (i)), and proton-impact excitation and de-excitation(Cp (i, j)) processes. Recombination processes were not included in this model because LHD plasmas are mostly inan ionizing plasma phase, and in such cases, recombination processes are not important for the spectral analysis.
Energy levels, transition probabilities, and electron-impact
excitation and ionization cross sections were calculatedwith the HULLAC atomic code [27]. Proton-impact rate
coeﬃcients were taken from recommended data [15].
For comparison, we also calculated population densities and photon emissivity coeﬃcients using the ADAS
package [28]. ADAS contains various atomic datasetsfor one ion; for comparison, we selected three diﬀerent atomic datasets for energy levels, transition probabilities, and electron-impact excitation eﬀective collision strengths. Specifically, the selected datasets were“chv6” whose atomic data are taken from CHIANTI ver.6(245 levels) [29], “cpb06” whose excitation eﬀective collision strengths are obtained by the Dirac-Fock R-matrix
method (139 levels) [30], and “lgy09” whose excitationeﬀective collision strengths are obtained by the ICFT Rmatrix method (209 levels) [31]. In the CHIANTI dataset,electron-impact excitation rate coeﬃcients are calculatedby the distorted wave method and are included only for certain selected transitions. The same atomic data of “cpb06”
were used for the intensity calculations in [24].

Fig. 1 Temporal evolution of shot 107802 discharge for NBI
power PNBI , stored energy Wp , line-averaged electron
density ne , electron temperature at geometrical center
T e (0), and total radiated power Prad .

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Fig. 2 Electron temperature distributions (top) and electron density distributions (bottom) measured by Thomson scattering at t = 4.3 s (solid circles) and 4.9 s (open diamonds).

about 500 eV. Figure 2 shows the electron temperature anddensity distributions at t = 4.3 and 4.9 s. At t = 4.3 s, thecentral electron temperature was about 2 keV with a peaky
distribution; at t = 4.9 s, the distribution flattened witha central electron temperature of approximately 500 eV.
This temperature is suitable for Fe XVII measurements.
At t = 3.8 s, a TESPEL doped with iron powder was injected. This instantly caused a large radiation power loss,
but soon the loss became less eﬀective. The electron temperature and density in the outer region were not aﬀectedby the changes in the central region.
Figures 3 (a) and 3 (b) show the EUV spectra at t = 4.4
and 5.0 s for wavelength regions 18 - 22 nm and 25 - 29 nm,
respectively. At t = 4.4 s, the central electron temperature was high, as shown in Fig. 2, and Fe ions in higher
charge states were observed, such as Fe XXIII and Fe
XXIV. However, when the central electron temperature
decreased to approximately 500 eV at around t = 5.0 s, thehigher charged ions disappeared and Fe XVII at 20.468
and 25.493 nm were clearly detected. Lower charged Fe
ions such as Fe XII and Fe XIII were constantly observed
as these ions exist in the peripheral region at lower electron
temperatures of approximately 100 eV.
As listed in Table 1, a total of seven Fe XVII lines appear in Fig. 3. The measured wavelengths were calibrated
with known prominent Fe XXIV lines and other impurity
lines. Errors for the line wavelengths measured in the LHD
in Table 1 were obtained by fitting to a Gaussian profile.
The pixel size of the measurements corresponds to about

Fig. 3 EUV spectra at 4.4 s (dotted line) and 5.0 s (solid line) (a)for 18 - 22 nm wavelength region and (b) for 25 - 29 nm
wavelength region of shot 107802. Forty frames (Δt =200 ms) were added to obtaine the spectra. Wavelengths
shown in bold face for identified lines were measured;
others were taken from the NIST ASD database [35].

0.02 nm, but high S/N ratios in the measurements allow
smaller errors for the line fits. The wavelengths of all Fe
XVII lines roughly agree with those measured by Hinode
EIS, those in the NIST database [34], and those calculatedby the GRASP code [26]. We follow the identifications of
the transitions for the λ 26.646-nm and 27.564-nm lines in
the NIST database and the GRASP calculation. The identifications of these two lines are exchanged in the list of
Warren et al. [21]. The upper levels of these transitions are
mixed with 1 D2 and 3 F2 levels due to configuration mixing, and similarly, the lower levels are mixed with 1 P1 and3
D1 levels.
The lower level of the transition for λ of 28.021 nm(no.6 in Table 1) is mixed with 2s2 2p5 3p 1 D2 and 3 D2levels due to configuration interactions. The term identification of this level in the NIST database [34] diﬀers fromthat in the GRASP calculation [26], but because the mixing coeﬃcients are almost the same, the levels in the NIST
database and the GRASP calculation are expected to bephysically identical. The energy levels calculated with the
HULLAC code used in our CR model are described with jj

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Table 1 Observed Fe XVII lines.

Fig. 5 Temporal evolution of Fe XVII line ratio for λ 20.468 nm
and λ 25.493 nm (solid circles) and the central electron
temperature (solid squares).
Fig. 4 Temporal evolution of Fe XVII line intensities for shot
107802.

coupling, so no LS terms were specified in the HULLAC
calculation.
Figure 4 shows the temporal distribution for Fe XVII

line photon intensities; all lines show the same evolution.
Forty frames (Δt = 200 ms) of the spectra were summed
to determine line intensities by fitting to a Gaussian profile. Figure 5 shows the energy intensity ratio for Fe XVII

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Fig. 6 Fe XVII line ratios as functions of electron temperature. (a) Fe XVII 20.468/25.493, (b) Fe XVII 26.646/25.493, (c) Fe XVII
26.949/25.493, and (d) Fe XVII 28.021/25.493. Solid dots with error bars are our measurements in LHD. Other measured values
are from Hinode EIS measurements (open triangles and open squares [22] and plus symbol [21]) and the Skylab measurements(crosses [23]). Theoretical calculations are from our CR model (solid line), ADAS calculations with chv6 atomic dataset (dashedline), ADAS calculations with cpb06 atomic dataset (dot-dashed line), and ADAS calculations with lgy09 atomic dataset (dottedline).

20.468-nm and 25.493-nm lines and the central electron
temperature as functions of time. Figure 6 (a) shows themeasured energy intensity ratio as a function of central
electron temperature. There are time variations in the intensity ratio, and the average intensity ratio is 1.35 ± 0.16,
which is slightly larger than the theoretically obtained
value of 1.1. The observed 20.468-nm line is possibly
blended with Fe XIII 20.43-nm and 20.494-nm lines, asother Fe XIII lines such as the 20.383-nm line constantly
appeared just after pellet injection until t = 6.4 s when the
Fe XVII 20.468-nm line disappeared. Such lower charged
Fe ions exist in the lower-temperature peripheral region,
which intersects the line of sight. We need to subtract thecontribution of these blended Fe XIII lines to estimate thecorrect Fe XVII 20.468-nm line intensity. Electron density and temperature of the Fe XIII emitting region were
estimated using intensity ratios for Fe XII 18.66-nm and19.51-nm lines, Fe XII 19.66-nm and Fe XIII 19.65 nm
lines, and Fe XIII 20.38-nm and Fe XII 20.37-nm lines;
the Fe XVII 20.468-nm line intensity was estimated bysubtracting the intensities of the Fe XIII 20.43-nm and20.49-nm lines. The corrected average intensity ratio becomes approximately 1.1, which agrees well with the theoretical calculation [35]. Therefore, the branching ratioof Fe XVII 20.468 and 25.493 nm, obtained by atomic
physics, is confirmed by these LHD experiments. Details

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Volume 9, 1401056 (2014)of the analysis for subtracting the contributions of Fe XIII
lines are described by Watanabe et al. [36].

4. Model Validation
As described above, we confirm that the measured intensity ratio for Fe XVII 20.468 and 25.493 nm is consistent with the theoretical prediction. Now we compare
measured energy intensity ratios for other Fe XVII lines
listed in Table 1 with theoretical calculations by the CR
model. Some of the results are shown in Fig. 6. Measured
ratios are plotted as solid dots with error bars; other datameasured for the solar plasma by Skylab [23] (crosses) and
Hinode EIS [21, 22] (squares and triangles) are also plotted for comparison. In Fig. 6 (a), measured line ratios for20.468 and 25.493 nm before the calibration are plotted.
To compare with the measured 28.021-nm line intensity,
the calculated intensities of two lines (nos. 6 and 6’ in Table 1) were summed. Basically, the diﬀerences between
the four theoretical calculations are mainly due to diﬀerent atomic data, i.e., transition probabilities and electronimpact excitation eﬀective collision strengths.
All measured ratios in the LHD plasma are roughly
consistent with the calculated ratios, but ratios from Hinode EIS measurements are larger than the theoretical calculations, as seen in Fig. 6. Ratios from our CR model
calculations are marginally consistent with the LHD measurements, but tend to be lower than the measurements. As
described in Sec. 3, the measured ratios for λ of 20.468 to
25.493 nm are slightly larger than the theoretical calculations (Fig. 6 (a)), because the λ 20.468-nm line is blended
with the Fe XIII line. After subtracting the latter contribution, the ratio becomes consistent with the theoretical prediction. Similarly, our measured ratios for λ of
26.949 to 25.493 nm, whose average is 0.382 ± 0.055(Fig. 6 (c)), are marginally consistent with our CR model
calculation but larger than the three ADAS calculations,perhaps because the λ 26.949-nm line is possibly blended
with the Fe XIV 26.9357-nm line. As seen in Fig. 4, theline intensities of λ 26.949 and 26.646 nm increased at
t = 4.8 - 5.0 s, but other lines decreased. These behaviors of intensity also suggest contamination of other lines
to λ 26.949-nm and λ 26.646-nm lines. The measured ratios for λ 26.646-nm to 25.493-nm lines, whose average is
0.202 ± 0.051 (Fig. 6 (b)), are roughly consistent with calculated ratios, but the candidate for line blending is the Fe
XV 26.6377-nm line. The measured ratios for λ of 28.021
to 25.493 nm, whose average is 0.604 ± 0.102 (Fig. 6 (d)),
show better agreement with all ADAS calculations thanwith our CR model calculation. The measured ratios for
λ of 27.564 to 25.493 nm, whose average is 0.134 ± 0.027,
and those for λ 28.121-nm to 25.493-nm lines, whose average is 0.202 ± 0.028 show tendencies similar to that of
the ratio for λ of 28.021 to 25.493 nm in Fig. 6 (d).
These results show that our CR model is marginallyconsistent with the LHD measurements for the Fe XVII

line ratios. The ADAS calculations with the lgy09 atomic
dataset show better agreement with the measurements thanours, except for the λ 26.949-nm line. For constructing
a better CR model, the lgy09 atomic dataset is therefore
preferred. The reason is that the electron-impact excitation rate coeﬃcient is calculated with the R-matrix method,which includes the resonance eﬀect and is better than the
distorted wave method in the lower collision-energy region, and many excited levels are considered. This atomic
dataset can be obtained from the OPEN-ADAS website at
http://open.adas.ac.uk/.

5. Discussion
The LHD measurements of the Fe XVII lines are almost consistent with the theoretical predictions from ourCR model, as described in Sec. 4. However, Hinode EIS
measurements still remain inconsistent with the theoretical predictions. For the λ 20.468-nm line, Del Zanna andIshikawa [24] suggested a blend with an unidentified line
at 20.472 nm, which showed the same morphology as the
Fe VIII line in monochromatic images taken by Hinode
EIS. This unidentified line could originate from the transition regions with lower temperatures at T e = 4 - 6 × 105 K(34 - 54 eV). For an active region core and a small flaring event on June 2, 2007, Watanabe et al. [35] reanalyzed
the intensity ratio for λ 20.468-nm and 25.493-nm lines byconsidering the contribution of the unidentified line originating from the transition region; the intensity ratio wassignificantly reduced to approximately 1.5 - 1.6. Nevertheless, the ratio is higher than the theoretical prediction. This
inconsistency indicates the need for re-examining the inflight intensity calibration of Hinode EIS instruments using two CCDs for the wavelength regions of 17 - 21 nm
and 25 - 29 nm [37]. For the other five intensity ratios, thelines were measured with the same CCD and the inconsistency cannot be attributed to the intensity calibration of the
instruments. The intensity for λ of 25.493 nm seems systematically smaller than the theoretical prediction, but it isdiﬃcult to explain. In the future, we will need to examine
Hinode EIS measurements in more detail.

6. Summary
We measured EUV spectra for LHD plasmas in whichiron was injected by a TESPEL. NBI heating was well controlled, and we successfully produced plasmas with a central electron temperature of approximately 500 eV, which
is suitable for producing Fe XVII ions. We detected sevenFe XVII lines whose wavelengths are consistent with Hinode EIS measurements, NIST database, and GRASP calculations. The measured intensity ratios for Fe XVII lines
are consistent with the CR model calculations. Especially,
the intensity ratio for Fe XVII 20.468-nm and 25.493-nm
lines, after subtracting the eﬀects of line blending, is consistent with the theoretical prediction of 1.1. This prediction was determined purely from the branching ratio due

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to the common upper level, although Warren et al. [21] reported a larger ratio from Hinode EIS measurements. The
agreement of our LHD measurements and theoretical calculations for these ratios imply that the atomic data and the
CR model are valid to be used for diagnostics. We suggest
a preferred atomic dataset to obtain better agreement in theintensity ratios.

Acknowledgments

We acknowledge the LHD experimental group for
their assistance. This work is partly supported by the NIFS
Collaborative Research Programs (NIFS10KLPF008 and
NIFS12KLPF027), the NINS Inter-institute collaborative
program for Creation of New Research Area (Head Investigator: T. Watanabe), NIFS/NINS under the project of Formation of International Network for Scientific Collaborations (Head Investigator: H. Yamada). The authors would
like to thank Enago (www.enago.jp) for the English language review.
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