Plasma and Fusion Research: Regular Articles

Volume 14, 3402053 (2019)

Dependence of Plasma Parameters in Hydrogen Pellet Ablation
Cloud on the Background Plasma Conditions∗)
Motoshi GOTO1,2) , Hiroya UYAMA3) , Takuya OGAWA4) , Khanit MATRA5) ,Gen MOTOJIMA1,2) , Tetsutarou OISHI1,2) and Shigeru MORITA1,2)
1)

National Institute for Fusion Science, Toki 509-5292, Japan
Department of Fusion Science, SOKENDAI (The Graduate University for Advanced Studies),
Toki 509-5292, Japan
3)
National Institute of Technology, Toyama College, Toyama 939-8630, Japan
4)
Department of Electrical and Electronic Engineering, Utsunomiya University, Utsunomiya 321-8505, Japan
5)
Department of Electrical Engineering, Srinakharinwirot University, Ongkharak, Nakhonnayok, 26120, Thailand
2)(Received 25 December 2018 / Accepted 28 January 2019)
UV-visible spectra of the radiation from hydrogen pellet ablation clouds have been measured in the Large
Helical Device. The temporal development of the Balmer-α line intensity shows a peaked profile with FWHM
(full width at half maximum) of approximately 150 µs. The electron temperature T e , electron density ne , andplasma volume V are evaluated by fitting of the measured spectra with a complete LTE (local thermodynamic
equilibrium) model. The results shows that T e is almost unchanged, while ne and V increases and decreases
monotonically, respectively, in the dominant time period around the intensity peak. The same analyses madefor several diﬀerent magnetic configurations have revealed that ne has a tendency to become higher when themagnetic field strength is higher, while no clear dependence on the magnetic axis position has been observed. On
the other hand, T e shows little dependence either on the magnetic field strength or the magnetic axis position.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: hydrogen pellet injection, ablation cloud, Stark broadening, radiative recombination continuum, radiative attachment continuum, complete LTE
DOI: 10.1585/pfr.14.3402053

1. Introduction
The hydrogen pellet injection is considered to be an
essential method for the particle fueling of fusion plasma[1]. Understanding the characteristics of the pellet ablation mechanism is indispensable for optimizing the fuelingeﬃciency.
The hydrogen pellet is surrounded by localized highdensity plasma, the so-called ablation cloud, immediately
after plunging into the background plasma. The ablation
cloud emits intense radiation which helps us obtain clues
for revealing plasma states in the pellet ablation cloud.
Emission lines of neutral hydrogen obviously exhibit the
Stark broadening, from which the electron density ne canbe evaluated. The electron temperature T e is inferred fromthe continuum radiation profiles and the discrete line intensities.
In our previous study [2], it has been verified that thecomplete LTE (local thermodynamic equilibrium) is approximately established in the ablation cloud. In that case,the entire Balmer-series spectrum including the discretelines and the continuum is determined only by T e and ne
author’s e-mail: goto@nifs.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

aside from the absolute intensity. We have actually derived
T e and ne from spectra measured in the Large Helical Device (LHD).
The parameters obtained in that study are representative values of the ablation cloud. The actual ablation
cloud should have a spatial structure in it, and it is unclear whether the LTE is established in the entire regionof the ablation cloud. Although some eﬀorts have been
made for a spatially resolved measurement inside the ablation cloud [3,4], no definitive conclusion has been obtained
to date.
It is also unclear, and interesting, whether the derived
representative parameters are the universal parameters irrespective of the background plasma conditions, i.e., themagnetic configuration and the magnetic field strength. In
this study, we focus our interest on measuring representative T e and ne values for diﬀerent magnetic configurations
in LHD and on deriving dependence of T e and ne in theablation cloud on the plasma condition.

2. Experimental Setup
The measurement has been made for discharges in
LHD. Pellets are injected from the outboard side of thevacuum vessel on the equatorial plane [5]. The pellet hasa cylindrical shape having the diameter and the length of

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c 2019 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 14, 3402053 (2019)

Fig. 1 Top view of LHD vacuum vessel around the pellet injection port. The pellet trajectory is drawn by the blue solid
arrow, and the approximate field of view of the present
observation is indicated by the area colored orange.

roughly 3 mm. The number of atoms contained in a pellet
is in the order of 1021 . The pellet is injected by a pneumatic
pipe-gun type accelerator into the plasma with the velocity
of approximately 1 km s−1 , which has been measured witha time-of-flight method.
Figure 1 shows the top view of the vacuum vessel
where the pellet trajectory is indicated by the blue solid
arrow.
An optical fiber end is placed at an observation port
near the pellet injection port and observes the radiationfrom the ablation cloud. The approximate field-of-view,which is determined by the numerical aperture of the optical fiber of 0.2, is shown with the area colored orange in
Fig. 1. It is confirmed that the ablation cloud always stays
inside the field-of-view.
The light received by the optical fiber is transferred
to a UV-visible spectrometer having a focal length of
50 cm (Chromex 500is). The spectrometer is equippedwith a grating of 100 grooves/mm which gives the reciprocal linear dispersion of 19.984 nm/mm. The instrumental
function is approximated with a Gaussian function having
FWHM of 1.64 nm with the entrance slit width of 50 µm
which is fixed throughout the present measurement. A
CCD (charge coupled device) which has 1024 × 255 pixels
with each pixel size being 26 × 26 µm2 (Andor DU-420 V)
is used for the detector. The sensitivity of the entire system has been absolutely calibrated with a standard lamp
(Labsphere USS-600C).
The fast kinetic mode is used for recording high tem-

Fig. 2 Example of typical discharges for the present pellet injection experiment. The top panel shows the stored energy
WP , NBI power PNBI , and ECH power PECH . The middle
panel shows the central electron temperature T e0 and theline-averaged electron density ne , and the bottom panel
shows the Balmer-α line intensity IHα .

poral resolution spectra, i.e., the horizontal direction with
1024 pixels is used for recording a spectrum and its temporal development is stored in the vertical direction. The
time resolution is determined by the vertical charge shift
speed of the CCD, which is 16 µs in the present case. The
maximum observation time length is simply determined as
16 µs/pixel × 255 pixels = 4080 µs. Intense radiation fromthe ablation cloud lasts roughly 400 µs. Because the observable time period is rather short (∼ 4 ms), the CCD isgiven a trigger from the pellet injection system for synchronizing the data acquisition start with the pellet injection.
Figure 2 shows an example of the discharges for thehydrogen pellet injection experiment. The plasma is initiated by the electron cyclotron heating (ECH) and is sustained by the neutral beam injection (NBI). No gas fuelingis made in this case, thus the plasma is made with the residual gas in the vacuum vessel.
Twelve pellets are sequentially injected betweent = 3.5 s and t = 5 s in this case, which can be recognizedby the Balmer-α line intensity signal IHα at the bottom
panel in Fig. 2. It is also observed that the line-averaged
electron density ne and the central electron temperature
T e0 increases and drops, respectively, by each pellet injection. While the number of pellets injected in a discharge ischanged depending on the purpose of the experiment, thepresent observation always targets on the first pellet.
An example of the measured spectra is plotted withthe red crosses in Fig. 3. This spectrum has been taken attrel = 80 µs, where trel is the time relative to the intensity

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Fig. 3 An example of spectra measured in the present study (redcrosses) and the fitted curve with the model spectrum(black solid lines). The T e and ne values are the resultof the fitting.

peak of the Balmer-α line center as explained later. Fourdiscrete lines, i.e., Balmer-α, β, γ, and δ, are observed, andall the discrete lines are found to be noticeably broadened.
Because the line profile observed for the pellet ablation cloud is known to be dominated by the Stark broadening eﬀect [2], this result suggests that ne can be evaluated through an analysis of the line profile. Moreover, it isfound that the broadening width and thus ne change withtime as shown in Fig. 4 (a). It is also noticed that the line
width, or ne , is diﬀerent even at the same observation timing when the magnetic field strength is changed as shownin Fig. 4 (b).
In the actual analysis, the measured spectra are fittedwith a model spectrum which will be discussed in detail in
the next section, and T e , ne , and the plasma volume V are
derived.

3. LTE Spectrum
Under the complete LTE, the population of any levelp, which includes the ground state, is expressed by the
Saha-Boltzmann equation [6] as


3/2

R
h2
2
exp 2
(1)
ne ni ,
n(p) = p
2πmkT ep kT ewhere h, R, k, and m are the Plank constant, Rydberg constant, Boltzmann constant, and electron mass, respectively,
and p and ni are the principal quantum number of neutralhydrogen and the proton density, respectively. Althoughn(p) is generally a function of T e , ne , and ni , ni = ne should
be a reasonable assumption in the present case because
pure hydrogen plasma is expected in the ablation cloud,Fig. 4 Examples of the measured Balmer-β profiles at diﬀerent observation timings (a) and for diﬀerent magnetic
field strengths (b). The black dashed lines show the fitted curves. The corresponding ne values are 3.9 × 1022 ,9.6×1022 , and 1.8×1023 m−3 for trel = −48, 32, and 80 µs,
respectively, in (a), and 1.8 × 1023 and 8.3 × 1022 m−3 for
Bax = 2.75 and 1 T, respectively, in (b).

and, consequently, n(p) is determined only by T e and ne(or ni ).
The Balmer series lines of neutral hydrogen correspond to transitions from levels p > 2 to p = 2 level. Theline profile of a transition from level p is here denoted as
line
ρline
p (λ), where λ is the wavelength, and ρ p (λ) is normalized as

(2)
ρline
p (λ)dλ = 1.
In the present study, ρline
p (λ) is dominated by the Stark
broadening and other broadening eﬀects, such as the
Doppler broadening, are negligible. The convolution of
the Stark broadening and the instrumental function is evaluated when the synthetic line profile is compared with themeasured profiles.
The database of Ref. [7] is adopted for calculating the
Stark broadening profiles. Although the Stark broadening
generally depends on ne and T e , the dependence on T e issmall. Thus T e = 1 eV, which is the representative value
found in the previous study [2], is used throughout.
The continuum radiation spectrum, which is also an
essential part for constructing the entire spectrum, dominantly consists of two components, i.e., the radiations accompanying the radiative recombination and the radiative
attachment processes. The radiative attachment is a pro-

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Volume 14, 3402053 (2019)cess in which a hydrogen atom turns into a negative hydrogen ion by capturing an electron. It is confirmed that theBremsstrahlung is negligibly small in the plasma condition
considered here.
The radiation power density spectrum due to the radiative recombination process to level p, ρrecp (λ), is expressedas [6]

3/2
12 2 h4 c2
rec
p
σion
ρ p (λ) = 2p (λ)π m3/2 λ5 kT ehc/λ − χ p
× exp −
(3)
ne ni ,
kT e
where σion
p (λ) is the cross section of the photoionization,
which is the inverse process of the radiative recombination,and χ p is the ionization potential of level p. The values ofσion
p (λ) are evaluated by the method in Ref. [8].
The radiation power density spectrum for the radiative
attachment process is obtained in a similar manner to thecase of the radiative recombination as


3/2
1
2 h4 c2
σdet (λ)ρatt (λ) =π m3/2 λ5 kT ehc/λ − χH−× exp −
(4)
ne n0 ,
kT e
where σdet (λ) is the cross section of the photodetachment,
which is the inverse process of the radiative attachment,χH− is the detachment potential of the negative ion, and n0
is the ground state atom density. The values of σdet (λ) aretaken from Ref. [9].
The entire spectrum ρ(λ) is obtained as a superposition of all the components discussed above as

rec
att
n(p)ρline(5)
ρ(λ) =
p (λ) + ρ (λ) + ρ (λ).
pWhat we obtain in the measurement is the radiation power
integrated over the radiation volume in the ablation cloud.
Here, a homogeneous plasma having the volume V is assumed and P(λ) = ρ(λ)V is used for fitting the measured
spectra. It is finally emphasized that P(λ) is determined
only by T e , ne , and V under the complete LTE, which is assumed throughout the present study. More specifically, ne
is dominantly determined by the Stark broadening width of
discrete lines, and T e is mainly derived by the spectral profile of the continuum radiation and the continuum radiation
intensity relative to that of the discrete lines.
Figure 3 shows the fitted curve of the measured spectrum with the black solid line as an example. The Balmerδ line is completely omitted in the analysis because thepresent ne values are close to the Inglis-Teller limit [10]and are sometimes out of range of the Stark broadening
database used here. The central part of the Balmer-α line
is also excluded from the wavelength range used for the fitting because this line is known to be often aﬀected by the
self-reabsorption eﬀect [2].

The maximum wavelength of the radiative recombination continuum corresponds to the ionization potentialof the p = 2 level, which is translated into the wavelengthof ∼ 364.7 nm. In high density plasmas, however, due tothe ionization limit lowering eﬀect, the continuum radiation spectrum continuously extends beyond that maximum
wavelength. It is known that the extended part of the spectrum is expressed by the same equation as Eq. (3) but withσion
p (λ) evaluated with the bound-bound Gaunt factor [6].
In the present analysis, calculation of the radiative recombination continuum spectrum is extended up to 400 nm.
The fitted curves for the measured Balmer-β line profiles in Fig. 4 are also shown with the black dashed lines
in the same figure as another example of the fitting. It is
confirmed that the measure line profiles are well explainedby the Stark broadening.

4. Results and Discussion
The measurement was first made for two groups ofdischarges for which Rax is fixed at 3.6 m but the magnetic field strength is diﬀerent. One group consists of
14 discharges with Bax = 2.75 T and the other is madeup of 5 discharges with Bax = 1 T. Although Rax of thesecond group is actually changed from 3.53 m to 3.6 m
shot by shot, they are treated as a single group labeled as
Rax = 3.6 m (1 T). When more than one pellet is injected ina single discharge, the first pellet is always the observation
target as mentioned above.
Figure 5 (a) shows the temporal development of theintensity at the line center of the Balmer-α, IHα (0), takenfrom the measured spectra for Rax = 3.6 m (red) andRax = 3.6 m (1 T) (gray). The time resolution is 16 µs perframe as mentioned in Sec. 2. The data plotted are the average of the values at the same timing of all the discharges
in the same group, and the error bar indicates their standard deviation. The values of IHα (0) are normalized by its
integral over the time period displayed in Fig. 5.
The horizontal axis, trel , denotes the time relative tothe timing at the maximum IHα (0). Although the data acquisition is started by the trigger signal at the pellet injection, the actual timing of the signal detection in the observable time window of 4 ms is randomly shifted shotby shot. Therefore, trel has been adjusted in advance foreach discharge such that the maximum IHα (0) takes placeat trel = 0 µs. It is readily noticed in Fig. 5 (a) that the temporal development of IHα (0) for Rax = 3.6 m (1 T) is almost
identical to that for Rax = 3.6 m.
We have carried out least-squares fittings with themodel spectrum described in Sec. 3 for the spectra taken
at all the timings of all the discharges. Figures 5 (b), (c),and (d) show T e , ne , and V obtained as the result of thefittings. The values plotted are again the average of the results at the same timing of all the discharges in the samegroup, and their standard deviations are given as the error
bars.

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Fig. 5 Intensity of the Balmer-α line center (a) and parameters
obtained in fittings of the measured spectra; (b) T e , (c) ne ,and (d) V. The red, blue, and green symbols correspondto Rax = 3.6 m, 3.75 m, and 3.9 m, respectively. The graysymbols show the results for Rax = 3.6 m but with a low
magnetic field strength (1 T). The errors are the standard
deviation evaluated from all the spectra in each Rax groupused for the analysis. The dashed lines show the resultsof the least-squares fittings.

In both the Rax = 3.6 m and Rax = 3.6 m (1 T) cases,
T e first takes several electronvolts and decreases down toapproximately 1 eV with increasing IHα (0), and then keeps
to be almost unchanged for a certain period. After IHα (0)takes the maximum, T e starts to increase up to values similar to those at the beginning while IHα (0) decreases. On
the other hand, ne is found to remain increasing even afterIHα (0) takes the maximum.
It is found that ne for Rax = 3.6 m (1 T) is significantly
lower than that for Rax = 3.6 m at all times. Intuitively,
this result is understandable because in the low magnetic
field case, it is expected that the confinement in the ablation
cloud is worse so that the plasma is swelled in the direction
perpendicular to the magnetic field lines. As a result, ne islowered. The plasma volume V for Rax = 3.6 m (1 T) actually appears slightly larger than that for Rax = 3.6 m. For aquantitative understanding of the present results, however,
the assistance of simulation studies of the pellet ablation

phenomena would be necessary.
It is here noted that a sudden decrease is observed inT e and V at around trel = 0 µs especially for Rax = 3.6 m(1 T). This change seems to be caused by small but significant increase in the radiative attachment continuum whichleads to lowering of T e in the fitting. When T e is lowered,excited level populations relative to ni become larger as
expected from Eq. (1), and then V is decreased as compensation.
We have also made measurements for discharges with
diﬀerent magnetic axis positions, i.e., Rax = 3.6 m, 3.75 m,
and 3.9 m. The maximum magnetic field strength isadopted for each Rax , i.e., Bax = 2.75 T, 2.64 T, and 2.54 T
for Rax = 3.6 m, 3.75 m, and 3.9 m, respectively. The
Rax = 3.75 m and 3.9 m groups consist of 21 and 13 discharges, respectively, and the Rax = 3.6 m group is thesame as that used for investigating the Bax dependence.
The values of IHα (0) and the fitting results are plottedin Fig. 5 with blue symbols for Rax = 3.75 m and green
symbols for Rax = 3.9 m. It is found that the peak width ofIHα (0) in Fig. 5 (a) becomes narrower when Rax is shifted
outward, which indicates that the ablation is completed
more quickly for larger Rax cases. No clear diﬀerence isfound in T e derived in the fittings among the three Rax
cases. At the final stage of the ablation process, ne appears to behave diﬀerently depending on Rax . However, nodefinitive statement can be made due to their large uncertainties.
In conclusion, it has been found for the first time thatne in the ablation cloud depends on the magnetic fieldstrength while T e shows no significant dependence, andthat the ablation takes a longer time when Rax is inward
shifted. These results suggest a relationship concerning
the plasma confinement characteristics between in the ablation cloud and in the background plasma. Although detailed mechanisms which determine the plasma parametersin the pellet ablation cloud remain open, the present results
should have noticeable significance in the pellet ablation
study for the fusion plasma.

Acknowledgments
We are grateful to all members of the LHD experimentgroup for their help in accomplishing the discharges andthe measurements. This work is partly supported by JSPS
KAKENHI Grant Number 18K03588 and by the National
Institute for Fusion Science grant administrative budgets(ULHH028).
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83, 093506 (2012).
[4] G. Seguineaud, G. Motojima, Y. Narushima and M. Goto,
Atoms 6, 34 (2018).

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Volume 14, 3402053 (2019)[5] R. Sakamoto, H. Yamada, K. Tanaka et al., Nucl. Fusion 41,
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