Plasma and Fusion Research: Rapid Communications

Volume 19, 1201021 (2024)

Determination of Parallel and Perpendicular Ion Temperatures
Based on Selective Ion Transmission in a Retarding Field Analyzer
Shigetaka KAGAYA, Hiroyuki TAKAHASHI, Tomohiro SEINO, Keigo YOSHIMURA,
Ryota NISHIMURA, Akihiro KANNO, Yusaku TAKAHASHI, Tomoya HARA, Tetsutarou OISHI,
Akinobu MATSUYAMA1) and Kenji TOBITA
Department of Quantum Science and Energy Engineering, Tohoku University, Sendai 980-8579, Japan1)
Graduate School of Energy Science, Kyoto University, Uji 606-8501, Japan(Received 9 February 2024 / Accepted 3 April 2024)
This work reports a novel approach employing a retarding field analyzer (RFA) to simultaneously measure
parallel and perpendicular ion temperatures. I-V curves obtained by the RFA were analyzed considering theinfluence of selective ion transmission, and the ion temperatures were evaluated. The RFA analysis yieldedparallel and perpendicular ion temperatures of 1.2 eV and 2.1 eV, respectively. The perpendicular ion temperature
obtained by an ion sensitive probe was 2.0 eV, demonstrating good agreement with that evaluated by the RFA.
c 2024 The Japan Society of Plasma Science and Nuclear Fusion Research⃝

Keywords: retarding field analyzer, selective ion transmission, ion temperature, radio-frequency plasma,DT-ALPHA
DOI: 10.1585/pfr.19.1201021
In open magnetic systems, such as SOL-divertor plasmas, convective losses of parallel components of ion energy typically exceed those of the perpendicular components unless collisional relaxation progresses suﬃciently.
This potentially leads to anisotropy in ion temperatures.
Kinetic and fluid simulations for SOL-divertor plasmas
have demonstrated the emergence of significant temperature anisotropy [1–3]. This anisotropy is believed to influence heat loads and the physical sputtering of plasmafacing components. However, experimental investigations
focusing on such temperature anisotropy are limited due tochallenges associated with simultaneous measurements ofparallel and perpendicular ion temperatures (T i|| and T i⊥ ).
This study aims to develop a novel technique allowing simultaneous measurements of the two ion temperature components using a retarding field analyzer (RFA).
RFAs were originally developed to measure T i∥ andhave been utilized in tokamaks and stellarators [4–6].
RFAs typically feature narrow entrance slits at the plasmafacing sections. However, for use in small linear devices,a diﬀerent type of RFAs equipped with a circular aperture has been proposed.[7, 8]. Recently, the influence ofion Larmor motion on use of these aperture-type RFAs
has been investigated based on simple numerical calculations [9]. The results indicate that the ion Larmor motion
results in selective ion transmission, deforming the I-Vcurves. Furthermore, Ref. [9] has proposed the concept ofevaluating T i∥ and T i⊥ from a single I-V curve utilizing selective ion transmission. This concept potentially enables
observations of anisotropic ion temperatures with an RFA.
However,owing to the lack of experimental investigations,author’s e-mail: shigetaka.kagaya.q7@dc.tohoku.ac.jp

the feasibility of the concept remains unclear. This paper
presents the results of the first experimental implementation of this concept, as well as a comparison between T i⊥
obtained by an RFA and an ion sensitive probe (ISP).
In this study, experiments were conducted within theradio-frequency (RF) plasma device DT-ALPHA [10]. Helium plasma was produced by 13.56 MHz RF discharge.
The cross-section of the RFA mounted within the DTALPHA device is illustrated in Fig. 1 (a). The RFA comprises an aperture (6 mm in diameter), three grids, and acollector. Figure 1 (b) depict the potential structure within
the RFA. In addition to the RFA, an ISP was also mountedwithin the DT-ALPHA device. Details regarding the ISP
can be found in Ref. [11]. The RFA and ISP measurements were conducted in the central region of the cylindrical plasma. To mitigate the space-charge limitations,low-density plasma was employed in this experiment. The
magnetic field strength in this region was 0.13 T. A Lang-Fig. 1 (a) Cross-section of the RFA, and (b) potential structure
within the RFA.

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c 2024 The Japan Society of Plasma⃝Science and Nuclear Fusion ResearchPlasma and Fusion Research: Rapid Communications

Volume 19, 1201021 (2024)

muir probe mounted near the plasma production region
yielded an electron temperature of approximately 14 eV
and a density of 4.5 × 1015 m−3 .
When considering ion Larmor motion, the collector
current of an RFA (IC ) can be described as follows [9]:∫∫ ∞∫ ∞IC = 2πqni rdr
f (v∥ , v⊥ )v∥ v⊥ dv∥ dv⊥ , (1)0vmin∥

where ni and q denote the ion density and the ion charge,respectively. f (v∥ , v⊥ ) represents the Maxwellian distribution function of parallel and perpendicular velocities(v∥ , v⊥ ). vmin
represents the minimum parallel velocity of∥detectable ions. In conventional RFA analyses, vmin
is de∥
termined by the ion retarding potential. However, when
considering the ion Larmor motion, vmin
also depends on∥
the ion Larmor radius and the position of the ion guidecenter (r). This eﬀect limits the ranges of parallel and perpendicular velocities of detectable ions, resulting in the deformation of I-V curves corresponding to T i⊥ . Using thischaracteristic, T i⊥ can be determined by identifying the T i⊥value that best reproduces the experimentally obtained I-Vcurve.
Figure 2 (a) presents a typical I-V curve obtained by
the RFA. Vret represents the eﬀective ion retarding poten-Fig. 2 (a) I-V curve obtained with the RFA, (b) comparison withcalculations, (c) fer defined in Eq. (2) as a function of T i⊥ ,and (d) I-V curve obtained with the ISP.

tial (grid three potential minus plasma potential). The collector current exhibits an exponential decrease above theplasma potential, where Vret = 0 V. T i|| evaluated fromthe slope of the curve was approximately 1.2 eV. Notably,
the ion saturation current was significantly smaller than
the space-charge-limited current derived using the formula
proposed in Ref. [12], indicating that the measurement was
not aﬀected by space-charge limitations. Using this T i|| andvarious T i⊥ values, I-V curves were calculated and compared with the experimentally obtained curve. Figure 2 (b)summarizes the results. Here, the vertical axis represents
the normalized collector current at the plasma potential. As
depicted in Fig. 2 (b), the calculation with T i⊥ = 2.0 eV reproduces the experiment better than those with 1.0 eV and
3.0 eV. The most reasonable T i⊥ was evaluated using anevaluation function defined as follows:∑ ( Iexp − Icalc )2
fer =,
(2)
Iexp
V
G3

where Iexp and Icalc represent the experimentally obtained
and calculated collector currents. Figure 2 (c) depicts theevaluation function fer as a function of T i⊥ . As depictedin Fig. 2 (c), fer was minimized at T i⊥ = 2.1 eV, indicatingthat the calculation with T i⊥ = 2.1 eV yields the best reproduction. To validate this T i⊥ , ISP measurements were conducted. Figure 2 (d) presents an I-V curve obtained with
the ISP. The exponential decay part of this curve indicates that T i⊥ = 2.0 eV, exhibiting good agreement withthe value obtained by the RFA analysis.
In summary, parallel and perpendicular ion temperatures were evaluated using an RFA, and results were compared with those obtained using an ISP. Analysis of theRFA considering the influence of selective ion transmission yielded value of T i∥ = 1.2 eV and T i⊥ = 2.1 eV. The
perpendicular ion temperature obtained with the ISP was2.0 eV, exhibiting good agreement with that evaluated by
the RFA. These results substantiate the potential utility ofthis technique for investigating ion temperature anisotropy
predicted by numerical calculations and its impact on divertor heat load and sputtering.
This work was supported by the Japan Society for
the Promotion of Science JSPS KAKENHI (Grant Nos.
JP20H01883, JP22K18699, and JP24K00607). This work
was also supported by the NIFS Collaboration Researchprogram (No. NIFS23KIIP018) and Collaborative Research Program of Research Institute for Applied Mechanics, Kyushu University (No. 2023CR-FP-22).
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