Observation of clump structure in transported
particle orbit using an upgraded neutral particle
analyzer during TAE burst in LHD
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公開日: 2021-12-15
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キーワード (En):作成者: KAMIO, Shuji, Fujiwara, Yutaka, NAGAOKA,
Kenichi, OGAWA, Kunihoro, Yamaguchi, Hiroyuki,
NUGA, Hideo, ISOBE, Mitsutaka, OSAKABE, Masaki,
Cheng, C. Z., LHD, Experiment Group
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Observation of Clump Structure in Transported Particle Orbit Using an Upgraded Neutral Particle
Analyzer during TAE Burst in LHD
S. Kamio1, Y. Fujiwara1, K. Nagaoka1,2, K. Ogawa1,3, R. Seki1,3, H. Yamaguchi1, H. Nuga1, M.
Isobe1,3, M. Osakabe1,3, C. Z. Cheng4,5, and the LHD Experiment Group1
1

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki, Gifu 509-5292,

Japan.
2

Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8603, Japan.

3

The Graduate University for Advanced Studies, SOKENDAI, Toki, Gifu 509-5292, Japan.

4

Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 113-0033, Japan.

5

Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA.

kamio@nifs.ac.jp
Abstract
TAE bursts are often observed in relatively low magnetic field experiments in LHD with tangential
NB injection. During TAE bursts, hole-clump pairs in real space were observed in previous studies.
In order to observe the behavior of the energetic particles during TAE bursts in more detail, atangential E-parallel-B type neutral particle analyzer (E||B-NPA) was upgraded to improve the time
resolution up to 100 kilo samples per second by updating its measurement electronic circuits. Using
this high time resolution E||B-NPA, the clump formations are clearly observed in real space. In order1

to analyze the observed particles with high time resolution, conditional averaging technique is used.
The lost energetic particles with 150 keV were initially observed just before the TAE burst, and theenergy decreases faster than the classical slowing down time. The energetic particles transported by
the TAE burst were detected with energy slowing down time of 6-8 ms for more than 6 ms after theTAE burst finished. According to the orbit trace code LORBIT calculation, the particle pitch angle
and the radial location ( = r/a99) of the energetic particles resonating with the TAE mode frequency
are increased by 5 degrees and 0.2, respectively, during TAE bursts. These results are consistent withthe observed downward frequency chirping of the magnetic fluctuation. By comparing the energy ofthe detected particles by E||B-NPA and the corresponding frequency of the magnetic fluctuation, thepitch angles of the resonant particles are considered to be 15-25 degrees at 150 keV before they aretransported by the TAE burst. The frequency chirping of the magnetic fluctuation shows good
agreement with the observed clump structure by considering the pitch angle of the resonant particles.

1. Introduction

Toroidal Alfvèn eigenmodes (TAEs) [1] are being studied numerically [2,3] and experimentally[4-6] because of their practical importance for the future fusion reactor. In burning plasmas,
energetic particles generated by fusion or by external heating can drive the TAE unstable. The TAE
deteriorates fast-ion confinement which adversely affects heating and may cause damage to the firstwall. The spontaneous formation of “clump and hole” phase-space structures have been shown in2

kinetic simulation studies [7,8], and TAE frequency sweeping is often observed in many devices[9-12]. The particle transport due to the TAE has also been investigated in the Large Helical Device(LHD) [13]. Magnetic fluctuations of the TAE bursts are observed in relatively low magnetic field(0.6 T at the magnetic axis) experiments. The ratio of the typical beam velocity and the Alfvèn
velocity is approximately vb/vA=1.5. Therefore, TAE activities can be observed with the TAE
resonance condition of v||=vA by considering the pitch angle and/or the energy slowing down of thebeam ions in this experimental condition.

By measuring the charge exchanged neutral particles using E-parallel-B type neutral particle
analyzer (E||B-NPA) [14] and by measuring the lost ion using scintillator-based fast-ion loss detector(FILD) [15-17], the existence of the hole-clump pairs was suggested in real space. From the slowing
down time analysis, the location of each lost particle orbit was identified. Simultaneous observationof hole-clump formations reveals the enhanced radial transport of energetic particles in plasma by
TAE bursts.

In this paper, we report the results of the TAE burst experiments using upgraded E||B-NPA withimproved time resolution. The energy distributions of the energetic neutrals are clearly observed
together with the magnetic fluctuations. Assuming the resonance condition of v||=vA, the frequency
chirping of the magnetic fluctuations are fitted with the energy slowing down of the energetic
neutrals by adjusting the pitch angle  of the resonance particles.

32. Experimental setup

Figure 1 shows the schematic view of the LHD with the typical plasma flux surfaces (red and pinklines) and the tangential line of sight of the E||B-NPA (blue line). The line of sight of the E||B-NPA
is 50-85 mm below the mid-plane. The E||B-NPA measures the energetic particles injected by neutralbeam injectors (NBIs) #1 and #3. These tangentially injecting NBIs are based on the negative-ion
sources and can inject with energy of up to 180 keV. The location of the E||B-NPA is fixed and theline of sight cannot be altered. The energy range of the E||B-NPA can be changed by changing themagnetic field and the electric field inside the E||B-NPA vacuum chamber [18]. In order to upgrade
the time resolution, new electronics were installed [19]. The upgrades shortened the pulse width of asingle particle from 125 ns to 5 ns and the sampling time was improved from 250 s to 10 s. The
measurement  and the pitch angle  along the line of sight of the E||B-NPA are shown in Fig.2.
Because the NPA measures the energetic particles which exchanged charge with neutral particles, themeasuring region is considered to be the outside region where the neutral density is high. At aroundthe =1 of near side to the E||B-NPA, the  is 23 degrees for the TAE burst experiments with Rax=3.8
m. It is noted that Rax is major radius of the magnetic axis shifted from the vacuum condition of
Rax0=3.6 m.

4

Toroidal and poloidal mode numbers are determined using 6 toroidal and 15 poloidal Mirnov coilswith a sampling rate of 1 MHz. The spatial distributions of the electron temperature and the electron
density are measured by Thomson scattering.

3. Results and discussions

In order to measure the energetic particles transported by TAE bursts using the upgraded E||B-NPA,
NBI #1 is used as the energetic ion source. The magnetic field at the magnetic axis is 0.6 T and the
major radius is 3.8 m. Because of the low magnetic field, electron cyclotron resonance heating(ECRH) cannot be used for the plasma startup. Instead of the ECRH, the initial plasma is generated
by using NBIs [20]. Typical waveforms of TAE burst experiments are shown in Fig.3 (a)-(f). The
timing of 4.4-4.85 seconds sustained by the single co-NBI are used for the investigation of the TAE
bursts. During the period, there was no significant change in the plasma stored energy shown in Fig.3(c), electron density and electron temperature shown in Fig.3 (e). The plasma current Fig.3 (d)gradually increased by the neutral beam current drive (NBCD) during the constant injection of
co-NBI. Fig.3 (f) is the signal of Mirnov coil with high-pass processing at 30 kHz. MHD instabilities
were observed during the timing of co-NBI injection. Figure 4 (a)-(d) focused on the timing of theTAE bursts clearly observed by E||B-NPA. The peak amplitude of the observed magnetic
fluctuations shown in Fig.4 (a) is 2-3x10-5 T, and the spectrogram shown in Fig.4 (b) were calculated5with a FFT window of 200 s. Figure 4 (c) is the time evolution of the energy spectrum of particle
flux  observed by E||B-NPA. The energetic particles which are transported by the TAE burst areclearly observed and the energy is decreasing after the TAE burst. The spatial distributions of theelectron density and the temperature during the TAE burst are shown in Fig. 5. The electron
temperature is approximately 0.7-0.8 keV at the magnetic axis, and the electron density is
1.1-1.4x1019 m-3 with the hollow profile. Figure 6 shows the spectrogram of the magnetic fluctuation
amplitude focused on the single TAE burst and the toroidal distribution of the derivative of themagnetic field at Mirnov coil. Before the large fluctuation at t~4.5009 s, a small fluctuation withsimilar frequency was observed at t~4.5004 s. The toroidal mode number n was 1, and the poloidal
mode number m was a mix of 1 and 2. Figure 7 shows the shear Alfvèn spectrum calculated by the
STELLGAP code [21], which is developed for three-dimensional configurations. The plasma
parameters of at the 4.5 s of #152781 and the magnetic field distribution of the vacuum conditions
are used for the calculation. The TAE gap of n=1 and m=1+2 mode appeared at around =0.4-0.5
with the frequency of approximately 50 kHz. This frequency is similar to the experimentallyobserved 50-80 kHz which is shown in Fig. 6.

Figure 8 (a) shows the dependence of the fluctuation amplitude of the “burst to burst” interval. Theintervals were 5-20 ms. A longer interval induces a larger burst. In the case of a TAE burst with ashort interval, the transported and lost ions are not fully replenished. The fast-ion pressure isconsidered to affect the amount of resonant particles in a TAE burst. The relationship between the6amplitude of the fluctuation and the amount of the increasing flux due to the TAE burst  during
the TAE burst is shown in Fig. 8 (b). Figure 9 shows the time evolution of the amplitude of themagnetic fluctuation, and the  measured by E||B-NPA. Because the TAE bursts are observed at
4.4-4.85 seconds as shown in Fig. 4 (d), the  without TAE burst is measured before 4.4 s and after
4.85 s. The peak of the average counting rate of  is approximately 5-10 counts per 10 s.
Therefore, it is difficult to investigate with high time resolution. In order to investigate the detailed
shape with high time resolution, conditional averaging technique is used to counteract the low countrate. 72 TAE bursts across two similar discharges were averaged. To align the timing of each burst,
the peak amplitude of the magnetic fluctuation of 70 kHz is set to 2.0 ms. By averaging 72 bursts, theclump shape can be seen clearly even with the time resolution of 10 s. The vertical red dashed lines
are the timing of the start and the timing of the end of the TAE bursts. The clump has different
behavior between during the TAE burst and after the TAE burst. During the TAE burst, the energy ofthe  decrease with the slowing down time of 1.0-1.5 ms. This short slowing down time is difficult
to consider as the classical energy slowing down time. This energy slowing down is considered to berelated to the frequency chirping. After the TAE burst, the energy slowing down time is 6-8 ms, andthe  is gradually decreased. However, the clump is still remaining more than 6 ms after the end of
the magnetic fluctuation of the TAE burst. The yellow line in the Fig. 9 indicates the injection energyof the NBI #1. The NBI injection energy is higher than the highest energy of the observed  at 150
keV. Similar fluctuation chirping can be confirmed at 0.5 ms before the large bursting fluctuation
7

between the red dashed lines. As the results of the repeated transportation of energetic particles by
the TAE bursts,  of between the burst and burst is lower than that of without the TAE burst. For thisreason,  is negative at the region between 50-150 keV without clump. Because some of theintervals of burst to burst are shorter than 8 ms, the previous clump can be seen in 0-2 ms at less than
80 keV and in 8-10 ms at more than 100 keV.

In order to investigate the clump shape in more detail, we divided the conditional averaging into
three groups by the amplitude of the magnetic fluctuation at 75-80 kHz. Figure 10 (a) shows the peak
amplitude of the magnetic fluctuations of each frequency. The amplitude of the magnetic fluctuations
are clearly decreased at more than 70-80 kHz and at less than 50 kHz. The TAE coupling frequency
is considered to be 50-80 kHz in this experiment. The large burst group has 14 bursts, the medium
burst group has 23 bursts, and the small burst group has 35 bursts. The numbers of the bursts foreach group were decided to have the same total . The energy distribution of  without TAE burst,
and during the TAE burst of three groups are shown in Fig. 10 (b). As with the conditional averaging
in Fig. 9, the peak amplitude of the magnetic fluctuation of 70 kHz is set to 2.0 ms. The  subsidence
between the burst and burst is approximately 0.2-0.4 counts per 10 s. On the other hand, holeformation can be seen at lower  than between the burst and burst, such as at 160 keV of 2.0-2.5 ms
and at 150 keV of 3.0-3.5 ms. However, the hole formation is difficult to identify because the  ofclump has a much higher counting rate than that of hole. The counting rate of the clump is also
higher than the . Contrary to the frequency distributions of the amplitude in Fig. 10 (a), the8counting rate energy distributions of three groups are similar at the high energy region and different
at the low energy region. Figure 11 shows the time evolutions of the averaged spectrogram of themagnetic fluctuations and the total  and its energy slowing down time fitting curves. The energy
slowing down times are 7.5-8.1 ms and 6.2-6.4 ms for 150 keV and 100 keV particles, respectively.
As shown in Fig. 12, the energy slowing down time of  is approximately 9.7 ms obtained at theturning off timing of the NBI #1 of the same discharge. The slowing down time of the  after theTAE bursts are shorter than that of  before the TAE bursts. These results indicate that the orbit of
the transported particles pass through the outer region where s is very low. The energetic particles
which are resonant with the TAE bursts are transported to the outer orbit, and remain in the outerorbit until energy decay.

Figure 13 shows the results of the Lorenz orbit cord LORBIT [22] calculated for this experimental
condition. Orbit of the energetic particles are tracked with the full gyromotion in the collisionlesscondition. The distribution of the magnetic field in the vacuum condition are used for the calculation.
The orbits are traced from along the line of sight of E||B-NPA. The horizontal axis of the Fig. 13 (a)is the initial location of the orbit trace. We traced the orbit from various LOS on the line of sight, andcalculated the slowing down time using the electron temperatures and densities along the orbit. As
the result of the initial LOS scan, LOS=1.06-1.09 are considered to be the location of the energetic
particles charge exchanging because the slowing down times are similar to the fitting curves in Fig.
11 after the TAE burst. Figure 13 (b) shows the  and the  along the traced orbit with the initial
9

energy of 150 keV and 100 keV. The color contours indicate the time duration while the particle passthrough the  with the . The yellow circles indicate the initial location of the orbit trace. Althoughthe  and  of the resonance position cannot be identified in the orbits, the duration time isequivalent to the possibility to be the  and  of the resonance position. Therefore, we referred to thehigher region to understand the trends. The of the higher region is consistent with the result of theshear Alfvèn spectrum shown in Fig.7. According to the results, the considered to shift to outside
approximately 0.2 and  considered to increase approximately 5 degrees with the resonant particle
energy decrease during TAE burst frequency chirping.

With considering the results of the LORBIT, the peak amplitude of the magnetic fluctuations areover plotted with the  in Fig. 14 (a). The white asterisks are peak of the magnetic fluctuations withthe corresponding energy. The frequencies of the magnetic fluctuations are shown with the energy of
the resonant particles with the relation of v||=vA, written as follows.

1

1

𝐸res = 2 𝑚i 𝑣 2 = 2 𝑚i 𝑣A 2 / cos 𝜃 2 (assuming 𝑣∥ = 𝑣A ),where

𝑣𝐴 = (4𝜋𝑅ax 𝑞TAE )𝑓TAE ,𝑞TAE = (𝑚 + 1⁄2)/𝑛 = 3/2,

10

and  is the pitch angle of the resonance particles. The  of the three cases were chosen to fit thefluctuations to the initial timing of the increase of the in each energy. As the results of the fitting,initial  at 150 keV are 15, 20, and 25 degrees. Because the  increases approximately 5 degrees
during the frequency chirping from the result of the LORBIT, the  for the fitting are changed also in
the Fig. 14 (a). As the result of the conversion of frequency to energy using these , the highest
energies of three groups are 180 keV, and the lowest energies are 110, 100, and 90 keV. These
results are in good agreement with the energy slowing down of the initial . The energetic particles
are not observed at more than 160 keV despite the magnetic fluctuations being observed. However, it
can be considered that the orbit of the energetic particle does not pass through the line of sight at >1.
Actually, the energetic particles at more than 170 keV injected by NBI are not observed by
E||B-NPA. Figure 14 (b) shows the relationship between the peak amplitude of the magnetic
fluctuation and the total  of 0.1 ms after the peak of the fluctuations in each energy. In order tocompare the magnitude of the magnetic fluctuation and the resonated energetic particles observed by
E||B-NPA, the  integration times are shortened to 0.1 ms. The colors of the symbols indicate theenergy of the  and magnetic fluctuation. The symbols of circle, triangle, and diamond are obtained
from large, medium, and small group, respectively. By dividing the resonant particle energies, therelationship between the amplitude of the magnetic fluctuation of the TAE bursts and observed
resonance particles by E||B-NPA could be clarified experimentally in the real space and in the phasespace.
11

4. Conclusion

The TAE burst experiments are demonstrated using an upgraded E||B-NPA with the sampling timeof 10 s. By the conditional averaging technique, the clump formation was clearly confirmed during
and after the TAE burst. In order to investigate the behavior in more detail, we clarified into threesimilar bursting groups. The local resonant  can be estimated by the slowing down time after theTAE burst and the results of the orbit trace calculation by LORBIT. Furthermore, by considering theincrease of the resonant particle pitch angle  during the frequency chirping, the relationship of themagnetic fluctuation frequency chirping and the energy slowing down of  during TAE bursts arewell explained. By comparing the amplitude of the magnetic fluctuations and the observed resonanceparticles by E||B-NPA in each energy, the relationship could be clarified in the real space and in thephase space.

Acknowledgments

This work was supported by NIFS Grant No. ULRR006, ULRR035, and ULRR702.

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References[1] Cheng C. Z. and Chance M. S. 1986 Phys. Fluids 29 3695.
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[19] Fujiwara Y. et al 2019 JINST (to be published).
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Figure 1. Schematic view of the LHD and the line of sight of the E-parallel-B type neutral particle
analyzer (E||B-NPA). E||B-NPA can measure the lost energetic particles injected by NBI #1 and NBI#3. The locations of A and B correspond to A and B in Fig. 2.

15

Figure 2. The radial position  and the pitch angle  of lost particles detected along the line of sightof the E||B-NPA. The  and  of A and B correspond to the location of A and B in Fig. 1.

16

Figure 3. Time evolutions of the (a) injection energies and (b) injection powers of NBIs, (c) stored
energy, (d) plasma current, (e) electron density ne and temperature Te, and (f) magnetic fieldmeasured by magnetic probe.

17Figure 4. Time evolutions of the (a) signal of the Mirov coil, (b) the spectrogram of the magnetic
fluctuations, and (c) the energy spectrum of the particle flux  observed by E||B-NPA. (d) The time
evolution of the particle flux  with wider time range.

18

Figure 5. Distributions of Te and the ne measured by Thomson scattering.

19

Figure 6. The spectrogram of the magnetic fluctuation during the TAE burst. The toroidal mode
number clearly appeared with n=1.

20

Figure 7. The calculated shear Alfvèn spectrum with n=1, the location of the mode coupling is
considered to be around =0.4-0.5, with m=1+2.

21

Figure 8. (a) Amplitude of the fluctuations with the interval of the burst to burst. (b) Amplitude of
the fluctuations compared with the E||B-NPA .

22

Figure 9. The conditional averaged spectrogram of the magnetic fluctuation and the  observed by
E||B-NPA. Red dashed lines are the timing of the start and the end of the TAE bursts. Yellow dashedline indicates the injection energy of the NBI #1.

23

Figure 10. (a) The peak amplitude of the magnetic fluctuations of each frequency. The TAE bursts
are divided into three groups by the amplitude of 75-80 kHz. (b) The  of without TAE burst, andthree groups of each timing.

24

Figure 11. The time evolutions of the spectrogram of the magnetic fluctuations and  measured by
E||B-NPA, conditional averaging with divided into three groups. White dashed lines are the results ofthe energy slowing down time fitting at the edge.

25

Figure 12. The time evolutions of injection powers of the NBIs and the counting rate of the
E||B-NPA for estimating the slowing down estimation. By the fitting after the injection beam power
turning off, the slowing down time is estimated to be 9.7 ms.

26

Figure 13. Results of the orbit trace code LORBIT. (a) The energy slowing down time s of eachtrace started from various LOS. Green hatched s is the energy slowing down time observed by
E||B-NPA. (b) The  and the  of the tracing particles. The color contours are the time duration while
the particle pass through the  with the . The yellow circles indicate the charge exchanged
locations. The red dashed circles indicate the location of the longest time duration.

27

FIG. 14. (a) The conditional averaged  with three groups (color contour), peak of the magnetic
fluctuations with corresponding energy (white asterisk). (b) The amplitude of the magnetic
fluctuation corresponding to each energy, and  counts totaled 0.1 ms after the peak of thefluctuations. is divided by v.

28