Plasma and Fusion Research: Regular Articles

Volume 11, 2402051 (2016)

Direct Observation of Electron Heating by Electron Landau
Damping of Alfvén Ion Cyclotron Waves Using Thomson
Scattering System in the Tandem Mirror GAMMA 10/PDX∗)
Masayuki YOSHIKAWA, Ryuya IKEZOE, Koichi OHTA, Xiaolong WANG, Junko KOHAGURA,Yoriko SHIMA, Masayuki CHIKATSU, Kazuya ICHIMURA, Mizuki SAKAMOTO,
Makoto ICHIMURA, Tsuyoshi IMAI, Ryutaro MINAMI,Kohei TSUMURA and Yousuke NAKASHIMA
Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan(Received 16 November 2015 / Accepted 9 March 2016)
In the hot ion mode of the tandem mirror GAMMA 10/PDX experiments, increases in the flux and temperature of end-loss electrons were observed after the excitation of Alfvén ion cyclotron (AIC) modes. The increaseof the electron temperature in the central cell is directly observed using a Thomson scattering system, confirming
electron heating due to the electron Landau damping of AIC modes.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: GAMMA 10/PDX, Thomson scattering, electron temperature, Alfvén ion cyclotron wave
DOI: 10.1585/pfr.11.2402051

1. Introduction
In the tandem mirror GAMMA 10/PDX, ion cyclotron
range of frequency (ICRF) waves have been used forplasma production, heating, and sustaining magnetohydrodynamic stability [1, 2]. A maximum ion temperature of 10 keV and a temperature anisotropy (defined as
the temperature ratio between directions perpendicular,T ⊥ , and parallel, T // , to the magnetic field line) of morethan 10 have been achieved. In such a strong temperature anisotropy condition, slow Alfvén ion cyclotron (AIC)
waves were spontaneously excited in the central cell of
GAMMA 10/PDX [3–6]. The AIC mode is normally observed using magnetic probes [7] and reflectometers [8, 9].
Diamagnetism increases with increased power of heating,and the anisotropy becomes strong. Saturation of the diamagnetism is observed in some experiments. The excitation of AIC modes that can scatter hot ions confined in
the magnetic mirror field into the loss cone of the velocity
space in the central cell is a possible confinement degradation mechanism. On the other hand, the parametric decay of heating ICRF waves was discussed for the saturation
mechanism of diamagnetism [4]. Low-frequency magnetic
fluctuations with beat frequencies between heating ICRF
waves and discrete peaks of AIC modes were clearly detected in GAMMA 10/PDX along with diﬀerent frequencies of AIC modes [10].
AIC modes exhibit several discrete peaks in the frequency spectrum just below the ion cyclotron frequency.
Although no resonance with ions has been observed, resauthor’s e-mail: yosikawa@prc.tsukuba.ac.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

onant interaction with electrons can be extracted. Accelerated electrons at the machine end of GAMMA 10/PDX
were directly detected, and the eﬀects of AIC modes onelectrons were examined using the loss electron energy(LEE) analyzer [5, 6]. An AIC mode leads to increases
in the end loss electron flux and electron temperature thatwere measured using the LEE analyzer. Based on the analysis of the transient feature of the end loss electron temperature, this interaction was attributed to electron Landau
damping [6]. However, electron temperatures measured
using the LEE analyzer may include the eﬀects of the potential diﬀerence between the central and end regions.
In this study, the first direct observation of electron
heating by the interaction of AIC waves is reported. Electron temperatures were directly measured using a Thomson scattering system with changing laser injection time
every 10 ms per shot. This is unlike the previous reports ofrefs. 5 and 6, where electron temperatures were estimatedindirectly using LEE signals.

2. Experimental SetupThe tandem mirror GAMMA 10/PDX consists of acentral cell, two anchor cells located at both ends of thecentral cell, and two mirror cells connected to the anchorcells. Detailed description of GAMMA 10/PDX has been
provided elsewhere [1–12]. The magnetic field strength
at the midplane of the central cell is 0.405 T, and the mirror ratio of the central cell is 5. A segmented limiter witha diameter of 0.36 m is set near the midplane. Plasma
is produced by applying RF1 (9.9 - 10.3 MHz) in combination with short-pulse-gun-produced plasmas from both

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c 2016 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 11, 2402051 (2016)

Fig. 1 Schematic of GAMMA 10/PDX.

ends and hydrogen gas injection near RF antennas. Moreover, plasma is heated by applying RF2 (∼ 6.36 MHz) witha fundamental ion-cyclotron resonance layer near the midplane of the central cell. The RF1 frequency is selected tobe a fundamental ion-cyclotron resonance frequency near
the midplane of an anchor cell. Two types of antennas areinstalled at both (east and west) ends of the central cell.
Figure 1 shows a schematic of the GAMMA 10 coil system and magnetic field profile in the axial direction. Thex and y axes are perpendicular to the magnetic field in thevertical and horizontal directions, respectively. The z axis
is parallel to the magnetic field.
A microwave reflectometer (RM) was constructed forstudying high-frequency fluctuations in the plasma core region [9]. This system consists of two simple heterodyne
reflectometers. The relevant microwave frequency range
is 8.2 - 12.4 GHz (X band), which covers a wide range of
GAMMA 10/PDX plasma (ne ∼ 2 × 1012 cm−3 ).
Plasma touches the end plates electrodes along themagnetic field. End plates are made of stainless steel andare located at both ends of GAMMA 10/PDX [10]. These
plates consist of several plates that are radially divided into
five sections and are connected to the ground though a cement resistor. We measured the floating potential of eachend plate using a 50-Ω pick-up resistor set between the1.111-MΩ resistor and ground by a high-speed analog-todigital converter (1 MSa/s). The floating potential is usually negative.
Several microwave interferometers for density measurements are present in GAMMA 10/PDX [12]. A movable microwave interferometer is set at z = −60 cm forelectron line density radial profile measurements, and its
movable horn position is changed shot-by-shot. We canobtain electron density radial profiles in the y direction using the Abel transform technique.

To measure the electron temperature, we installed ayttrium–aluminum–garnet Thomson scattering system atz = 60 cm for the radial measurement in the x direction[13, 14]. This system can measure the electron temperature and density at several radial positions in a single period for single laser and plasma shots. Unfortunately, wecould not obtain the radial profile of the electron temperature and density in this experiment. The Thomson scattering system measures the perpendicular component of theelectron temperature. In GAMMA 10/PDX, the electron
collision time is less than 10 µs and the electron temperature is normally isotropic.
We measure the radial profiles of soft X-ray (SX) intensities using two SX diagnostic system sets constructedusing a 16-channel semiconductor X-ray detector (XSD)
array [15]. Two XSD arrays separated by 135◦ in the azimuthal direction are placed at z = −120 cm.
End-loss electrons are measured using a multigridtype LEE analyzer installed on the end wall of the vacuum vessel [5, 6]. End-loss electrons enter the analyzer
through a small hole on the electrically floating end plate
located in front of the end wall. The collector current of
the analyzer represents the electron current flowing into theend plate. The electron repeller voltage of the analyzer isswept, and current–voltage characteristics of the end loss
electrons can be obtained in one shot. The LEE analyzer
measures the parallel component of the electron temperature.

3. Experiments
Plasma is heated and maintained by applying ICRF
waves; RF1 is applied for t = 51 - 240 ms, and RF2 isapplied for t = 53 - 240 ms. The rise time of RF2 inthese experiments is set to 90 ms. RF3 is applied fort = 190 - 240 ms. Figure 2 (a) shows the electron line den-2402051-2

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Fig. 3 AIC wave spectra measured using the RM system.

increases from t = 115 ms to 130 ms (light blue hatchedregion in Fig. 2). The line density then further increased
until t = 150 ms. The maximum value of the SX intensity is obtained at approximately t = 140 ms, which is almost identical to the time of maximum diamagnetism. The
maximum value of the EP potential is obtained at approximately t = 125 ms, prior to the time of maximum diamagnetism. Together with the increase of the AIC fluctuation
intensity in the light blue hatched region of Fig. 2, the electron temperature also increases with the AIC amplitude up
to 90 eV. The electron temperature then decreases to about
half of the maximum value. High AIC amplitudes fromt = 140 ms correspond to decreasing electron temperature
as well as decreases in diamagnetism, LEE, and EP values. Changes in the SX intensity follow changes in diamagnetism values.
In Fig. 3, we show the AIC spectrum obtained using
the RM system. For t = 115 - 130 ms, AIC waves wereclearly observed at three frequencies and show a frequency
peak at approximately t = 120 ms. Starting at t = 135 ms,
the startups of the frequency of AIC waves are observed
again.
Fig. 2 (a), (b), (c) and (d) show diamagnetism and line density,
electron temperature and end loss electron current (LEE),
soft X-ray intensity (SX) and end plate potential (EP),and AIC amplitude, respectively.

sity (blue solid line) and diamagnetism (red dotted line).
The time evolution of the electron temperature measured
using the Thomson scattering system for diﬀerent laser injection times shot-by-shot is shown in Fig. 2 (b) together
with the end loss electron current obtained using the LEE
analyzer. Figure 2 (c) shows the SX intensity and end plate#1 potential (EP), and Fig. 2 (d) shows the AIC amplitude
measured via reflectometry. Diamagnetism increases withincreased electron temperature from t = 100 ms to 130 ms.
The maximum electron temperature value at t = 120 130 ms is obtained faster than the maximum diamagnetism
value at t = 140 ms. The electron line density slightly

4. Discussion
An AIC mode is excited when a drive term β(T ⊥ /T // )2exceeds a threshold value [16]. In GAMMA 10/PDX, thevalue of β is equal to a few percent. Usually, the AIC modeexhibits several peaks in the frequency spectrum. As thediamagnetic signal increases at about 0.3 × 10−4 Wb, anAIC mode is excited. The electron temperature increases
significantly with the excitation of the AIC mode but gradually decreases with time. Without the AIC wave, the electron temperature increases with the electron drag poweron the hot ions. Figure 4 shows the relationship between
T e and ne D/T e1.5 [5, 6] and the electron drag line. Here,ne D/T e1.5 is proportional to the electron drag power, and ne ,T e and D represent the electron density, electron temperature and diamagnetism, respectively. The electron dragline is obtained by linear fitting of T e versus ne D/T e1.5 except for the data collected for t = 70 - 80 ms and AIC heat-2402051-3

Plasma and Fusion Research: Regular Articles

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Fig. 4 T e versus ne D/T e1.5 . Electron drag is obtained by linear
fitting from t = 60 to 110 ms and t = 160 ms, except for
t = 70 and 80 ms and AIC heated periods.

ing periods of t = 115 - 130 ms. Some of the T e values att < 110 ms are due to the direct heating of electrons by theRF electric field. The significant increase of electron temperature with the start of AIC mode condition for t = 115 130 ms is clearly observed. The electron temperature decreases gradually for t = 130 - 160 ms. The mechanism of
the increased direct electron heating by the AIC mode isthought to be due to electron Landau damping [5, 6]. Theelectron temperatures of electron drag by the hot ions andfrom AIC waves are about 40 eV and 90 eV, respectively.
Unfortunately, T e values measured using the LEE analyzer
could not be obtained. This makes it diﬃcult to determine
the anisotropy of the electron temperature. As the driving
term β(T ⊥ /T // )2 increases, the AIC mode changes its character from a traveling wave to a standing wave like andthe absorption power of the electron Landau damping decreases [6]. This is the origin of the gradual decrease in theelectron temperature to the level expected for conditionsin the presence of the AIC wave excitation when only thedrag power eﬀect is present after reaching the maximum
value of electron temperature.
Figures 5 (a) and 5 (b) show the radial profiles of electron densities and SX intensities, respectively, at t = 100,130, and 160 ms. Electron density radial profiles weremeasured using the microwave interferometer system. The
full widths at half maximums (FWHMs) of electron density radial profiles are almost constant during the AICmode. The FWHM of the SX intensity radial profile at
t = 160 ms is larger than those at t = 100 ms and 130 ms.
Moreover, the FWHMs of these profiles at t = 100 and
130 ms are almost the same. The SX intensity at the coreregion is mainly increased at t = 130 ms. Comparison of
the radial profiles of the electron density and the SX intensity shows that the AIC mode electron temperature heating

Fig. 5 Radial profiles of electron densities (a) and soft x-ray intensities (b) at t = 100, 130, and 160 ms, respectively.

is carried out in the core plasma region.

5. Summary
We carried out the direct observations of electron heating by the AIC wave interaction using the Thomson scattering system. The electron temperature increases up toabout 90 eV at the initial excitation phase of the AIC waves
when the Landau damping condition is satisfied. Using
the Thomson scattering system, the electron temperature
behavior in the central cell was directly observed and thepreviously reported electron heating by Landau dampingof the AIC waves was confirmed.

Acknowledgments
The authors thank the members of the GAMMA
10 group of the University of Tsukuba for their collaboration. This study was conducted with the supportand under the auspices of the NIFS Collaborative Research Program (NIFS11KUGM056) and the Bidirectional

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Collaboration Research Programs (NIFS14KUGM086,
NIFS14KUGM088).
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