Plasma and Fusion Research: Regular Articles

Volume 19, 1402017 (2024)

Evaluation of the Electron Temperature of
the Ablation Cloud for the Small-Size Hydrogen Pellet
Using Paschen Series in Heliotron J
Akihiro IWATA, Shinichiro KADO1) , Gen MOTOJIMA2) , Taiichi SHIKAMA3) ,Minato MURAKUMO3) , Atsuki MORI, Hiroyuki OKADA1) , Takashi MINAMI1) ,Shinsuke OHSHIMA1) , Shigeru INAGAKI1) , Fumiyoshi KIN1) , Shinji KOBAYASHI1) ,Akihiro ISHIZAWA, Yuji NAKAMURA, Shigeru KONOSHIMA1) , Tohru MIZUUCHI1)
and Kazunobu NAGASAKI1)
Graduate School of Energy Science, Kyoto University, Uji 611-0011, Japan
1)
Institute of Advanced Energy, Kyoto University, Uji 611-0011, Japan
2)
National Institute for Fusion Science, Toki 509-5292, Japan
3)
Graduate School of Engineering, Kyoto University, Kyoto 615-8530, Japan(Received 4 September 2023 / Accepted 16 February 2024)
We simultaneously measured the electron temperature (T e ) and electron density (ne ) using a low-dispersion
near-infrared spectrometer in a small-size pellet ablation cloud in Heliotron J, a medium-sized helical-axis heliotron device. We applied the intensity ratio of the Paschen-α, β, and γ to determine T e based on the collisionalradiative model, which was fairly consistent with the partial local thermodynamic equilibrium (LTE) in the upper
principal quantum numbers of 4, 5, and 6. For a typical pellet injection discharge, T e and ne were determined
to be 0.9 eV and 4 × 1021 m−3 , respectively. Our derived generalized empirical calibration curve demonstrates a
weak influence of T e on ne evaluation, particularly in the range of 0.4 - 2.0 eV. Subsequently, we determined theregion where the LTE is achieved for the Paschen series.
c 2024 The Japan Society of Plasma Science and Nuclear Fusion Research⃝

Keywords: pellet ablation cloud, near-infrared spectroscopy, collisional-radiative model, partial LTE, electron
temperature measurement, Heliotron J
DOI: 10.1585/pfr.19.1402017

1. Introduction
The injection of the hydrogen ice pellet is one of themost important methods for fueling fusion plasma. The
physics of pellet ablation must be clarified to develop the
optimal fueling scenario. The neutral gas shielding (NGS)[1] and neutral gas and plasma shielding (NGPS) [2] models have been proposed to predict pellet ablation behavior
and are being compared with observations of pellet trajectories and lifetimes based on strong Balmer-α emissions
from the ablation cloud. However, for a more quantitative
comparison between models and observations, it is desirable to measure the plasma parameters used in these models, namely the electron temperature (T e ) and the electron
density (ne ).
The Stark broadening of the hydrogen atomic spectrum emitted from the ablation cloud was used to measure
ne in the cloud in LHD [3], and the intensity of the radiative continuum spectrum was employed to evaluate T e .
In that case, the ne of the ablation cloud was determined
to be of the order of 1023 m−3 through the Stark broadening of the Balmer-β (Hβ , 486.135 nm) in the visible (VIS)
region. Simultaneously, T e was estimated to be approxiauthor’s e-mail: iwata.akihiro.73c@st.kyoto-u.ac.jp

mately 1 eV [4]. However, when the pellet is small and,
consequently, the ne value in the cloud is relatively low(∼ 1021 m−3 ) [5], the intensity of the radiative continuum
spectrum is also low. Thus, it becomes diﬃcult to evaluate
T e . In our previous work, the Paschen-α (Paα , 1875.13 nm)
line in the near-infrared (NIR) region, which has a wider
Stark width than Hβ , was used to measure the lower nevalue in the Heliotron J [6]. The Stark width has a strong
dependence on ne ; however, it also demonstrates a weak
dependence on T e . In Ref. [6], the plasmoid of the ablation cloud was assumed to be in the local thermodynamic
equilibrium (LTE) state. Hence, the T e value was set to
1 eV, which is typically valid for LTE plasma. Although
the Stark broadening of the atomic hydrogen line emission
from the ablation cloud is highly dependent on ne , its value
can be modified by T e . Therefore, it is important to evaluate the range of T e and its eﬀect on the ne measurement.
In this study, instead of using the radiative continuum
spectrum, we measure the intensity ratio of the Paschen-α,β and γ to determine T e based on the collisional-radiativemodel, using a simple low-dispersion NIR spectrometer.
This measurement can be taken simultaneously with the
Stark broadening measurement reported in Ref. [6]. Sub-

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Science and Nuclear Fusion Research

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sequently, we assess the parameters at which we can assume (at least partially) the local thermal equilibrium indetermining T e . Finally, we discuss the population balancein the ablation cloud.

2. Experimental Setup
Pellet injection experiments were conducted in Heliotron J, a medium-sized helical-axis heliotron device.
The pellet injection system and the NIR spectroscopy system were installed in the # 11.5 port, as shown in Fig. 1.
The pellet injection system produces a cylindrical solid hydrogen pellet with a diameter of 0.7 mm and ejects it at a
speed of approximately 250 m/s. In the NIR spectroscopy
system, the emission from the pellet ablation cloud is focused by the objective lens (THORLABS F220SMA-A, acollimator lens with a focal length of f = 10.92 mm, numerical aperture NA = 0.25) and then transmitted to thespectrometer (Ocean Optics, Inc., NIRQuest 512-2.2) via
a 16-m long low-OH fiber (THORLABS FT400EMT, acore diameter of 400 µm and a NA value of 0.39). The
spot diameter of the sight line is approximately 12 mm
at the plasma center. The spectrometer is a compact andlow-dispersion crossed Czerny-Turner-type spectrometerequipped with a thermoelectrically cooled (−20◦ C) InGaAs linear sensor (Hamamatsu G9206-512W, 512 channels, pixel dimension of 10 × 250 µm2 , horizontal pixel
pitch of 15 µm, sensitivity range of 800 - 2150 nm), a grating of 100 lines/mm, and a 100-µm slit without a long-passfilter that absorbs light in the visible region. The measurement range is approximately 905 - 2140 nm, and thereciprocal linear dispersion is 96.49 nm/mm at the centerof the detector. Note that the second and even the thirdorder diﬀraction light may overlap in the NIR region whenthe emission line has high intensity. The absolute sensitivity calibration of the spectrometer was performed using atungsten-halogen lamp (USHIO, JC100V500W) as a standard light source, cutting the second-order diﬀracted lightfrom the visible region (525 - 800 nm) using an external
1050 nm long-pass filter [7].

Fig. 1 Cross section at the # 11.5 port in Heliotron J. The pellet
injection system and the NIR spectroscopy system were
installed in this port.

3. Results
Figure 2 shows the temporal evolution of the monitoring parameters (Shot # 75847). Deuterium plasma in a
low-toroidicity magnetic field configuration was generated
through electron cyclotron resonance heating (ECH) andmaintained via neutral beam injection (NBI). In this discharge, the pellet was injected at 244 ms in the NBI phase.
Then, the plasma underwent radiative collapse. The intensity of Hα peaked at the pellet injection, and a fringe jumpoccurred in the line-averaged electron density. We also
monitored the impurity lines with monochromators (Nikon
P-250) that had a wavelength resolution of 0.06 nm and awavelength accuracy of 0.3 nm. The impurity oxygen OV(1s2 2s3s3 S − 1s2 2s3p3 Po ; 278.1 nm) intensity increased
after pellet injection and then rapidly decreased with Wp ,indicating plasma cooling during the radiation collapse.
The carbon CIII (1s2 2s3s3 S − 1s2 2s3p3 Po ; 464.7 nm) intensity increased to an over-range value, indicating thepresence of low T e plasma below the ionization barrier.
The exposure time for NIR spectroscopy was set to
10 ms, which included the pellet injection time. Therefore,
the obtained signal reflects the brightest spectrum in timeand space of the observation. Figure 3 shows the NIR spectra in shot #75847 without the visible light cut-oﬀ filter.
Paα , Paβ , Paγ , and the second and third-order spectra of Hα
were observed. The electron density determined from the
Stark broadening of Paα , 1.5±0.3 nm was (4±1)×1021 m−3when T e = 1 eV was assumed.
In the evaluation of T e , we applied the collisionalradiative (CR) model for neutral hydrogen [8, 9]. This

Fig. 2 Time evolution of the target plasma (Shot #75847). The
pellet was injected at 244 ms in the NBI phase. a) Heating
via ECH and NBI. b) Hα intensity at the #11.5 port (Hα )and the plasma stored energy (Wp ). c) The line-averaged
electron density (ne ). The fringe jump occurred at the
moment when the pellet was injected. d) Beryllium-like
oxygen (OV) and carbon (CIII). e) Gas puﬀ signal of deuterium.

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Fig. 3 NIR calibrated spectra in shot #75847. Paα , Paβ , Paγ , andthe second and third-order spectra of Hα were measured.

model considers various atomic processes at each excitation level of a neutral hydrogen atom in the rate equation,and the steady-state solution gives the population density
n(p) at the excitation level p as:n(p) = R0 (p)ne ni + R1 (p)ne n(1) + R2 (p)ne nH2 . (1)R0 , R1 , and R2 are referred to as the population coeﬃcientsand are functions of ne and T e . ni represents the ion density, n(1) is the ground state atomic density, and nH2 isthe molecular density. Note that the last term in Eq. (1)is ignored here, because the formation of molecular H2 isnot considered in the pellet ablation process. For atomic
hydrogen without considering the fine structure, p can beinterpreted as the principal quantum number. Therefore,
the upper states of the Paschen-α, β, and γ correspond to
p = 4, 5, and 6, respectively.
The line intensities of the Paschen series were obtained via fitting with a Voigt profile. Subsequently, thepopulations per degeneracy, i.e., the reduced population
densities, were plotted against the excitation energy, as
shown in Fig. 4. In calculating the CR model under theconditions of ne = 4 × 1021 m−3 and T e = 0.9 eV, the relative intensities of the calculated results for levels p = 4, 5,
and 6 best matched the experimental results. In such a pellet ablation process, the recombining component was dominant. Here, n(1) is assumed to be 1 × 1021 m−3 , which is of
the same order as ne , as deduced from the Saha-Boltzmann
equation for ne = 4 × 1021 m−3 and T e = 0.9 eV. In actuality, n(1) has no eﬀect on the recombining component
and little eﬀect on the line ratio for the ionizing component. We confirmed that the sensitivity of this assumption
is suﬃciently low. The reduced population densities obtained from the CR model calculations form approximately
a straight line from the high excitation levels, indicating
the establishment of a partial LTE (pLTE) state for levels
above p = 4 under these electron density and temperature
conditions.
In the LTE state, the reduced population densities andthe excitation energies have the proportional relationshipFig. 4 Reduced population densities of the Paschen series measured in shot #75847. The upper level p is shown on
the excitation energy axis. The blue cross points represent CR model results under the conditions of ne =4 × 1021 m−3 , and T e = 0.9 eV. The red solid line denotes
the linear Boltzmann plot. The electron temperature wasdetermined to be 0.9 ± 0.3 eV from its slope.

expressed in Eq. (2):
(
)
E(p)
n(p)
∝ exp −
,
g(p)
kB T

(2)

where n(p), g(p), and E(p) are the population density, degeneracy, and excitation energy, respectively. kB is theBoltzmann constant, and T is the electron temperature.
Through the linear fitting of the semi-logarithmic plot,
known as the Boltzmann plot (BP), the electron temperature T e _BP(p = 4 - 6) was determined to be 0.9 ± 0.3 eVfrom the reciprocal of its slope.
To evaluate the levels at which the LTE state can beconsidered valid, we evaluated the Griem’s boundary, pG ,for hydrogen using Eq. (3) [10]. This boundary represents
the lower limit above which the LTE approximation isvalid.
pG ≃ 1.6 × 103 /n2/15
.
e

(3)

To assess the practically applicable boundary of BP, wecalculated T e _BP(p−1, p) from the slope between each adjacent pair of levels in the CR model results using Eq. (4).
T e _BP(p − 1, p) = −E(p − 1) − E(p)][ n(p) ] .
[ln n(p−1)g(p−1) − ln g(p)(4)

We calculated the reduced population densities under theconditions of ne = 4 × 1021 m−3 and ne = 1 × 1020 m−3 at
T e = 0.9 eV using the CR model, as shown in Fig. 5 (a).
Figure 5 (b) shows the T e _BP(p − 1, p) evaluated using
these results. For p ≥ 4, which is higher than pG ∼ 2.1
at ne = 4 × 1021 m−3 , the T e _BP(p − 1, p) was approximately 0.9 eV. p = 4 seems to be marginal for the LTE
treatment in this condition. If ne is lower, pG increases,
and the threshold level of the LTE state may be higher.
The pG value for ne = 1 × 1020 m−3 , which falls below

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Fig. 6 Electron temperature from the Boltzmann plot for levels
p = 4 - 6 (T e _BP(p = 4 - 6)) from the CR model in therange of 0.1 - 3.0 eV. The red circle represents the caseof ne = 4 × 1021 m−3 , and the blue square represents thecase of ne = 1 × 1020 m−3 . The black solid line denotes
the electron temperature assuming LTE.

4.1

Fig. 5 (a) Reduced population densities of the CR model calculation and (b) T e evaluated from the adjacent level, p
and p − 1 (T e _BP(p − 1, p)) using Eq. (4) in cases where
ne = 4 × 1021 m−3 and ne = 1 × 1020 m−3 at T e = 0.9 eV.

the lower limit of the ablation cloud density, was approximately 3.4. As shown in Fig. 5 (b), the deviation of theevaluated temperature from 0.9 eV increases as the levels become lower. The reduced population densities corresponding to lower levels in Fig. 5 (a) deviate from thestraight line of the 0.9 eV Boltzmann temperature. Figure 5 (b) suggests that levels p ≥ 4 for the density of theablation cloud can be treated as pLTE, whereas the lower
density violates the pLTE assumption. This can be confirmed by the slope, i.e., T e _BP, between p = 3 - 4 and4 - 5 in Fig. 5 (a). In these cases, the CR model needs to be
applied. A comparison of the CR model and BP (p = 4 5) may confirm the validity of p = 4 as a marginal level.
Although, the eﬀect on the density measurement is suﬃciently small, the results of the Boltzmann plots and the
CR model calculations are consistent, suggesting that theobserved pellet ablation plasma was in a pLTE state above
p = 4. In low ne cases, the population is inverted at p = 2.
However, one does not need to consider this as long as using a Paschen series, i.e., p − 1 ≥ 3.

4. Discussion
In this section, we discuss the sensitivity of the ne determination to the T e value. Then, a strategy for determining T e is proposed, depending on the T e region.

Influence of T e on the ne evaluation

As done in ref [6] for the fixed T e of 1 eV, we deduced
the ne calibration curves for diﬀerent values of T e . Then,
we obtained the generalized empirical calibration curve
equation in the range of 0.4 - 2.0 eV as:ne ≃ (2.44 − 0.0791T e ) × 1021 × S tark width1.48 . (5)The T e dependence is apparently weak in this T e range,
with a variation of approximately 5 % over this T e range.
This means that the eﬀect is not severe, suggesting thatknowing only the approximate value of T e is suﬃcient.
Particularly when the LTE approximation is valid, the interpretation of the phenomenon is straightforward. Thiscondition will be satisfied when one measures the integrated spectra over time and space, following the methodology presented in this work.
However, if the population distribution deviates from
LTE, we should be careful in determining T e , particularly
when only a limited number of lines can be obtained. Thissituation occurs when one tracks the spatial and temporal
behavior of the ablation cloud because the ablation cloudis homogenized into a high-temperature bulk plasma. Considering these facts, the categorization of the T e range isdiscussed.

4.2

LTE-like region

We examine the T e range where the pLTE state isvalid. We calculated n(p)/g(p) from the CR model fora given T e value in two cases: ne = 1 × 1020 m−3 andne = 4 × 1021 m−3 , representing two typical scenarios.
Then, T e _BP was evaluated from p = 4 - 6 using the Boltzmann plot. For pLTE, we can expect T e = T e _BP. Figure 6
shows the electron temperature from the Boltzmann plot
for p = 4, 5, and 6 (T e _BP(p = 4 - 6)) from the CR model
results in the electron temperature range of 0.1 - 3.0 eV. In

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this calculation, we assumed ne = ni , n(1) = 1 × 1020 m−3 ,and n(1) = 1 × 1021 m−3 for each ne . In the range of 0.4
to 1.4 eV at ne = 4 × 1021 m−3 and for that of 0.4 to 1.3 eV
at ne = 1 × 1020 m−3 , the T e _BP(p = 4 - 6) values fromthe CR model are almost consistent with the straight line,
assuming that these levels are in the LTE state. We refer tothis region and the lower region (region A) as the LTE-likeregion. We refer to the temperature region higher than the
LTE-like region (region B) as the higher-T e region.
In the LTE-like region, T e is determined using theBoltzmann plot for p = 4 - 6 (T e _BP(p = 4 - 6)). Subsequently, we create a calibration curve at the determined
T e and evaluate ne . For higher ne , LTE must be established
for p = 4 - 6. However, for lower ne , p = 4 may graduallystop satisfying the LTE assumption, suggesting that moreaccurate T e values can be obtained by using only p = 5
and 6. In this case, a visible light cut-oﬀ filter is needed
to measure Paβ without the influence of the second-orderdiﬀraction of Hα .

4.3 Higher-T e region
In the higher-T e region, the ionizing component isdominant. In this case, pLTE will not be satisfied anymore, meaning that the slope of the BP cannot reflect theT e . Therefore, we can obtain the best fit T e (T e _CR) by
comparing the relative intensities of the spectra with theresults of the CR model calculated with ne evaluated fromthe Stark width. This procedure can be repeated with new
T e values until the values converge.
Figure 6 shows that the slope exhibits an inverse dependence on T e in the ranges of 1.5 eV to 3.0 eV (in cases
where ne = 4 × 1021 m−3 ) and 1.4 eV to 2.5 eV (in cases
where ne = 1 × 1020 m−3 ). Thus, fitting the CR model tothe emission line intensity ratios may lead to multiple solutions for T e . Note that when the number of measurable
spectral lines is limited to a few, particularly when including marginal levels, such as p = 4, it is diﬃcult to verify
that the CR model’s best fit temperature T e _CR indicatesT e . Figure 6 shows that under the condition of a fixed electron density, the slope of BP can give two values of T e forT e ≥ 1.5 eV.
In this case, we should determine whether the population satisfies LTE, depending on whether T e is higher thanthe critical temperature between regions A and B.

ments in the ablation cloud formed by relatively small-sizehydrogen ice pellets, T e was evaluated using the relative
intensities of the Paschen series spectra in the Heliotron
J. From observation, we evaluated T e ∼ 0.9 eV, which isconsistent with the assumed value in the previous work [6].
The CR model calculation indicates that the plasmoid of
the ablation cloud is in the LTE state, even if the ne is low(T e = 0.4 - 1.4 eV for ne = 4 × 1021 m−3 and T e = 0.4 1.3 eV for ne = 1 × 1020 m−3 ).
Regarding the influence of T e on the determination of
ne , we derived and established the generalized empiricalcalibration curve equation over the range of 0.4 - 2.0 eV,
showing a weak dependence of ne on T e (∼ 5% variation
over this range). This suggests that T e does not significantly impact the ne evaluation.
For ablation cloud plasmas formed by the injectionof small-size pellets, T e can be determined by using theBoltzmann plot, which is a simple analysis that assumes
LTE. Subsequently, ne can be evaluated from the Stark
broadening of Paα in the LTE-like region. However, as
the ablation progresses and the cloud homogenizes into ahigh-temperature bulk plasma, we should be careful in determining T e . An investigation into the spatiotemporal behavior of the ablation cloud is left for future work.

Acknowledgments
The authors are grateful to the staﬀ of Heliotron J
for performing the experiment. This work was supportedby the NIFS Collaborative Research Program (Grant Nos.
NIFS10KUHL030 and NIFS16KUHL073) and the JSPS
Core-to-Core Program, A. Advanced Research Networks,“PLADyS”.
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5. Conclusion
To enhance the reliability of the ne and T e measure-1402017-5