Electron temperature profile collapse induced bydouble-odd-parity MHD mode in the Large Helical
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公開日: 2021-07-14
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キーワード (En):作成者: Kobayashi, Tatsuya, IDA, Katsumi, SUZUKI,
Yasuhiro, TAKAHASHI, Hiromi, TAKEMURA, Yuki,
YOSHINUMA, Mikiro, TSUCHIYA, Hayato, Sanders, M.,
LHD, Experiment Group
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1Electron temperature profile collapse induced bydouble-odd-parity MHD mode in Large Helical
DeviceT. Kobayashi1,2 , K. Ida1 , Y. Suzuki1,2 , H. Takahashi1,2 , Y. Takemura1 ,M. Yoshinuma1 , H. Tsuchiya1 , M. Sanders3 , and LHD ExperimentGroup
1National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292,

Japan
2

SOKENDAI (The Graduate University for Advanced Studies), Toki 509-5292, Japan3

Eindhoven University of Technology, Eindhoven, 5600 MB, Netherlands

E-mail: kobayashi.tatsuya@nifs.ac.jp

Abstract.

In this paper, we report new results of a beam switching experiment aiming at areversed magnetic shear profile formation for the study of an MHD mode induced profile collapse
event. A transient MHD mode whose oscillation frequency chirps down is observed. The electron
temperature profile collapse is induced by the mode activity, leading to the flattening of thecentral electron temperature profile. The radial mode structure is the double-odd-parity at the
beginning, but it transits to the even-parity in its final stage. The central electron temperature
profile recovers after the radial mode structure changes to the even-parity, even though the mode
itself does not disappear.

2
1. Introduction

In order to produce a suﬃciently high temperature plasma in fusion devices toward
the reactor, it is crucially essential to understand the physics of the plasma profile
formation. One of the key elements is how the rotational transform ι, 2π/ι = q where
q is the safety factor, impacts on the electron temperature profile formation. There
have been a number of investigations related to this issue, e.g., the relation between
the low order rational surface and the internal transport barrier location [1, 2, 3], thetransport barrier enhancement by the electron cyclotron current drive (ECCD) [4, 5] or
the lower hybrid current drive (LHCD) [6], and the profile collapse induced by MHD
modes [7, 8, 9, 10, 11] including disruptions [12]. In particular, transient global MHD
activities often limit the plasma performance by terminating the profile growth or leading
to disruptions. Therefore, much attention is paid to avoid these MHD events by various
active control techniques [13].
In heliotron devices such as the Large Helical Device (LHD), there are generally
no disruptions, therefore investigations for the profile collapse events induced by thetransient MHD modes can be safely performed. In LHD, the rotational transform profileat the core can be varied by the plasma current induced by the tangentially injected
neutral beam (NB) or the electron cyclotron current drive (ECCD). In particular,
the beam switching from the co-beam to the counter-beam enhances flattening of therotational transform profile and even produces a reversed shear profile [14, 15]. This
operation was used for studying the static island formation in LHD, and it was revealed3that the island property was highly sensitive to the local magnetic shear [16]. The
MHD mode activity when the magnetic shear is weakened or the reversed shear profile
is formed under the beam switching operation is the next topic of interest.
In this paper, we report new results of a beam switching experiment aiming at
a reversed magnetic shear profile formation for the study of an MHD mode induced
profile collapse event. A transient MHD mode whose oscillation frequency chirps down
is observed. The electron temperature profile collapse is induced by the mode activity,
leading to the flattening of the central electron temperature profile. The radial mode
structure is the double-odd-parity at the beginning, but it transits to the even-parity inits final stage. The central electron temperature profile recovers after the radial mode
structure changes to the even-parity, even though the mode itself does not disappear.
The present observations contribute to the literature by exemplifying a profile collapse
event induced by a peculiar MHD mode in the stellarator devices.

2. Experimental results

2.1. Time evolution of the electron ITB collapse event
The experiments were conducted in the Large Helical Device (LHD). The magnetic
axis in the vacuum configuration is set to Rax = 3.6 m, the so-called inward shifted
configuration, with the toroidal field of Bt = 2.75 T directed clockwise when viewed
from the torus top. The plasma minor radius is defined by the averaged minor radiusin which 99 % of the plasma kinetic energy is confined, to be a99 ∼ 0.6 m. In the

4vacuum configuration, the rotational transform profile ι/2π typically has a 1/2 rationalsurface in the mid-minor radius of reﬀ ∼ 0.3 m, where reﬀ indicates the eﬀective minor
radius [17], and monotonically increases towards the edge. Although the confinement
magnetic field is mainly generated by the external helical coils, various plasma current
components including the currents driven by the neutral beam injection (NBI) andthe electron cyclotron current drive (ECCD) alter the vacuum rotational transformprofile. In particular, by performing the beam switching operation from the co-directed
NBI to the counter-directed NBI, flattening or reversal of the rotational transformprofile is observed [14, 15]. Here, the co-direction corresponds to the direction of thetoroidal magnetic field and hence the direction of the equivalent plasma current in LHD.
Therefore, a stationary co-directed plasma current increases the rotational transformfrom its vacuum value. Figure 1 shows the time evolution of the target discharge.
At t = 5.5 s, the NBI is switched from the co- to counter-direction, which overturns
the direction of the total plasma current drive. The abrupt change of the oﬀ-axis NB
driven counter-directed current excites the co-directed current in the core region that
decelerates the total plasma current change slower than the resistive time scale. This cocurrent at the core leads to the increase of the rotational transform value at the core andtherefore enhances the flattening or reversal of the rotational transform profile. Before
the beam switching, the two co-ECCDs focused in the plasma core region are appliedboth to realize the peaked electron temperature profile and to drive the co-directed
plasma current at the core. The line averaged density is kept approximately constant at

5slightly below 1 × 1019 m−3 . Note that the double-odd-parity mode discussed below is
not observed in the discharges in which the line averaged density exceeds 1.5×1019 m−3 .
The electron temperature profile drastically evolves in time after the beam switching
as shown in Fig. 1 (c). A gradual reduction of the central electron temperature starts
approximately one hundred milliseconds after the beam switching, and continues untilt ∼ 5.81 s, in which a sharp collapse of the central electron temperature occurs.
Immediately after the collapse, the central electron temperature turns to recover, andpeaked electron temperature profile is regenerated at t ∼ 5.92 s. Time evolutions of
the electron density profile, the electron temperature profile, and the ion temperature
profile are shown in Figs. 1 (d)-(f). The profile flattening is seen not only in theelectron temperature profile but also in the ion temperature profile, although it is rather
ambiguous. The profile collapse does not occur in the electron density profile since it
is almost flat in the core region. According to the saddle loop magnetic coil arraymeasurement, the static magnetic island dynamics is not responsible for the electron
temperature profile collapse, unlike the case in Ref. [10, 11].

2.2. Double-odd-parity MHD mode that induces electron temperature profile collapse
The temperature profile collapse is considered to be induced by a MHD mode activity.
Figure 2 (a) shows time evolution of the squared cross coherence between an on-vessel
magnetic probe and a chord of the ECE array at reﬀ ∼ 0.15 m as the representative
dynamics of the MHD mode. The coherent fluctuation mode first appears at t0 ∼ 5.7 s

6and f ∼ 4.5 kHz whose frequency chirps down stepwise as time progresses. Finally, themode frequency becomes f ∼ 1 kHz and disappears at t ∼ 5.9 s. By performing thepoloidal and toroidal mode structure analysis with the magnetic probe arrays, the mode
number is determined to be m/n = 2/1, where m and n are the poloidal and toroidal
mode numbers. The squared cross coherence γ 2 and the cross phase α are calculated
at the various radial position of the ECE measurement with respect to the magnetic
probe yielding the three-dimensional variables γ 2 (t, reﬀ , f ) and α(t, reﬀ , f ). From Fig. 2(a), the time evolution of the mode peak frequency is defined as fpeak (t). Taking values
at f = fpeak (t) from γ 2 (t, reﬀ , f ) and α(t, reﬀ , f ) provides the evolution of the mode
radial structure, as shown in Figs. 2 (b) and (c). For the sake of visual clarity, the crossphase is only plotted in the case that the squared cross coherence is high enough. As
time progresses and the frequency decays, the mode radial structure expands gradually,
finally reaching the peripheral region of reﬀ ∼ 0.5 m. As shown in the phase profile,the mode structure is identified as the double-odd-parity until t ∼ 5.84 s, which has
two diﬀerent phase inversion radii, at reﬀ ∼ 0.1 m and at 0.25 m. Figure 2 (d) presents
the time evolution of the relative electron temperature gradient profile with respect tothe value at t0 = 5.7 s, defined as δ[−∇Te (t, r)] = −∇Te (t, r) + ∇Te (t0 , r). When themode appears at t0 = 5.7 s, the electron temperature gradient begins to decay at thetwo diﬀerent phase inversion radii, reﬀ ∼ 0.1 m and 0.25 m, which are indicated by two
arrows. These two flattening regions broaden as the mode evolves, and are connected toeach other at t ∼ 5.81 s, at which the sharp reduction of the central electron temperature

7
is observed. Interestingly, the outer phase inversion radius approaches toward the inner
inversion radius after the central electron temperature collapse, at t ∼ 5.81 s, and they
are connected to each other at t ∼ 5.85 s. This evolution makes the mode even-parity.
After t ∼ 5.81 s, the central electron temperature increases again while the mode exists.
In order to quantitatively discuss the dynamics of the mode and the electron
temperature profile, time averaged cross coherence analysis is performed. Figures 3
rows (a) to (c) show the imaginary part of the cross spectrum that corresponds to themode eigen function, the squared cross coherence, and the cross phase, respectively. The
time averaging is performed in 5.72 < t < 5.75 s (first column), 5.75 < t < 5.82 s (second
column), 5.82 < t < 5.84 s (third column), and 5.86 < t < 5.90 s (fourth column). Slicesof the squared cross coherence and the cross phase at the peak frequency are shown in
Fig. 3 row (d). Here, the mode width wmode is defined as the maximum radial rangethat has the squared cross coherence larger than 0.5. The evolution of the electron
temperature profiles are shown in Fig. 3 row (e) with those before the profile collapse
occurs plotted by the dashed curves (first column of Fig.3). When the mode appears at
the frequency of ∼ 4.5 kHz, the mode width wmode is ∼ 0.23 m and the phase inversion
width winv , i.e., the radial width between two phase inversion radii, is ∼ 0.18 m. No clear
flattening is seen in the electron temperature profile. As time progresses and the mode
frequency decays down to ∼ 3 kHz (second column of Fig.3), the mode width broadens
while the phase inversion width shrinks. The flattened electron temperature profile
seems to appear in 0.1 < reﬀ < 0.2 m. In the next stage of the mode evolution (third8column of Fig.3), the mode frequency becomes ∼ 1.5 kHz and further expansion of themode width and further shrinking of the phase inversion width are observed. This stage
corresponds to the time period shortly after the sharp central electron temperature decay
at t ∼ 5.81 s in Fig. 1 (c), so that a wide flattening region arises in 0.1 < reﬀ < 0.3 m. In
the last stage before the mode disappears (fourth column of Fig.3), the mode becomesthe even-parity having no phase inversion layer. Even though the mode itself still exists,
the electron temperature profile recovers comparable to that before the mode is driven.
Figure 4 shows how the mode width wmode and phase inversion width winv. depend on
the frequency. As the frequency decreases stepwise, wmode increases while winv. decreases
both approximately linearly. In the last stage, winv. becomes zero and wmode saturates
at ∼ 0.37 m.
By use of the obtained mode properties, i.e., the poloidal mode number m = 2,
the mode amplitude A(reﬀ ), and the radial phase structure Φ(reﬀ ), the eigen functionof the mode can be reconstructed as Ψ(reﬀ , θ) = A(reﬀ ) cos[−mθ − Φ(reﬀ )]. Figure 5
shows the time evolution of the reconstructed mode structure. As the mode evolves, themode radial width expands and the phase inversion layer shrinks. In the final stage ofthe evolution, the phase inversion layer disappears and the mode parity becomes even.

2.3. Electron cyclotron current drive direction scan experiment
In order to investigate the impact of the ECCD on the mode appearance, we performed
the ECCD scan experiment on the discharge scenario described in Fig. 1.

The9Table 1. Relation between the ECCD directions and the mode appearance. Number of injectedbeams in each direction is shown in the parentheses.

Shot number n̄e [1019 m−3 ] co-ECCD [MW]counter-ECCD [MW]Mode appearance

1506721.3

2.3 (3)

0 (0)

Yes

150673

1.3

1.5 (2)0.8 (1)

Yes

1506741.3

0.8 (1)

1.5 (2)

No1506761.30 (0)2.3 (3)No

ECCD from three launchers is injected to the base discharge with the beam switching.
Combinations of the injection directions are scanned in the shot-to-shot manner. Table 1
shows the shot status regarding the ECCD direction and the mode appearance. Whenthe number of the co-injected ECCDs surpasses that of the counter-injected ECCDs,
the mode appears and the central electron temperature collapse occurs after the beamswitching.
It is worthwhile to compare the rotational transform profile in these discharges
measured by the motional Stark eﬀect (MSE) spectroscopy [15] with an advanced
analysis technique [18]. In the MSE spectroscopy system, the polarization angle ofthe probe beam emission is measured, from which the local magnetic pitch angle isevaluated. Change of the rotational transform from its vacuum value is estimated by
the relative polarization angle from the reference shot, δγpol . Here, the reference shot is
produced by injecting the balanced co- and counter-NBs and by keeping the density as
low as possible for minimizing a net plasma current. The plasma current profile in the10shot of interest that is consistent with δγpol is then chosen from a set of predetermined
plasma current profiles. The radial profile of the relative polarization angle δγpol in#150672 is plotted in Fig. 6 as an example. Symbols show measured δγpol and curves
represent the polarization angles derived from the chosen current profiles. As time
progresses, the polarization angle increases, which corresponds to increasing ι/2π intime.
Figure 7 shows the time evolutions of the rotational transform profiles ι/2π derived
from the relative polarization angle profiles measured by the MSE technique in eachdischarge. A quantitative discussion regarding the MHD mode onset and ι/2π profile
shape evolution is still challenging due to poor temporal resolution and relatively large
uncertainty in the core region, therefore we abandon to identify the magnetic shear
reversal. Nevertheless, a clear qualitative diﬀerence in ι/2π profile evolution between the
co-ECCD dominant cases and the counter-ECCD dominant cases is seen. In the cases of#150672 and #150673, the central ι/2π increases in time that makes the profile flattenedor reversed near the rational surface of ι/2π = 1/2. The transient beam switching fromthe co-NB to the counter-NB tends to increase the core ι/2π and to decrease the edge
ι/2π [14, 15]. The co-injected ECCDs that have a more localized deposition in the core
likely assist the increment of ι/2π in the core. In the other cases, ι/2π stays almost
unchanged. The counter-injected ECCDs seem to compensate the NB-driven current
change, which help to prevent the MHD mode appearance. Therefore, the counterECCD is an eﬀective control tool for this MHD mode induced electron temperature

11
profile collapse.

3. Discussion

Now we discuss the origin of the double-odd-parity mode. One possibility is the resistive
interchange mode, which can be unstable in the magnetic hill of the LHD inward shiftedmagnetic axis configuration. The beam switching operation can trigger such a mode
by weakening the magnetic shear or making a reversed shear iota profile with two
rational surfaces. Although the eigen mode function of the resistive interchange mode
is considered to be the even-parity in general, it is predicted that the odd-parity is also
possible as the secondary eigen mode function [19]. Since the radial mode structure
observed is the double-odd-parity possibly having a tearing mode nature, the double
tearing mode driven by external current drive would be another candidate. As discussed
in [20], even in heliotron devices a tearing mode can be excited in the reversed iota
profile. However, the mode is predicted to be solely at the inner ι/2π = 0.5 surface,
while the observation shows a much wider mode structure being inconsistent with thetheoretical model [20]. The tearing mode excitation was observed in W7-AS stellarator
by an intense ohmic current [8].
In the later phase of the mode evolution the mode parity transits to the evenparity, implying a diﬀerent driving mechanism of the mode. Since the central iota is
continuously increasing and the ι/2π = 0.5 rational surface is considered to eventuallydisappear keeping the magnetic shear very small. This situation resembles to the12condition in which the ‘infernal’ mode emerges [21]. One of the keys for the mode
identification is the accurate rotational transform profile measurement in the core witha high time resolution, which is still very challenging with the current MSE system in
LHD.

4. Summary

In this paper, we reported new results of a beam switching experiment aiming at areversed magnetic shear profile formation for the study of an MHD mode induced profile
collapse event. A transient MHD mode whose oscillation frequency chirps down wasobserved. The electron temperature profile collapse was induced by the mode activity,
leading to the flattening of the central electron temperature profile. The radial mode
structure was the double-odd-parity at the beginning, but it transited to the evenparity in its final stage. The central electron temperature profile recovered after theradial mode structure changes to the even-parity, even though the mode itself did notdisappear.

Acknowledgments

The authors acknowledge all the members of the LHD Experiment Group for theirassistance.

The authors also thank Professors S. Sakakibara, K. Y. Watanabe,

Y. Narushima, and K. Ichiguchi for strong support and useful discussions. This work is
partly supported by the National Institute for Fusion Science grants (17KLPH031 and13
ULHH033) and by the Grant-in-Aid for Scientific Research of JSPS (17K14898).

14
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Fig. 1 Time evolution
16#150701
PNB,co(a)
PNB,ctr

PNB,p

PECH

(e)

(f)

ne [1019 m3]
Te [keV]

(d)

0.07
0.15
0.23
0.30
0.39

Ti [keV](c)reff [m](b)ECH0+4
19382
5.7s5#0+
5.82s5# 7/
7/ ')5.92s(3 ,$i/2pi=0.3

Figure 1. Time evolutions of (a) heating power, (b) line averaged density and plasma current,(c) electron temperature, (d) electron density profile, (e) electron temperature profile, and (f)ion temperature profile.

17
reff = 0.15 m

(a)

(b)
(c)

(d)

Figure 2. Time evolutions of (a) squared cross coherence spectrum between the ECE signal
and the magnetic probe signal, (b) squared cross coherence profile, (c) cross phase profile, and(d) electron temperature gradient profile.

18
(a1)

(b1)

(a2)

(b2)

wmode

(a3)

(b3)

(a4)

(b4)

(c1)

(c2)

(c3)

(c4)

(d1)

(d2)

(d3)

(d4)

(e2)

(e3)

(e4)

γ2
winv

α [2π rad](e1)

Figure 3. Radial profiles of various MHD mode related parameters in t = 5.72 − 5.75 s (firstcolumn), t = 5.75−5.82 s (second column), t = 5.82−5.84 s (third column), and t = 5.86−5.90 s(fourth column): (a) imaginary part of the cross spectrum density, (b) squared cross coherence,(c) cross phase, (d) slices of the squared cross coherence and the cross phase at the peak frequency,and (d) electron temperature profile. Dashed curves in (e) show the electron temperature profile
before the profile collapse occurs.

wmode

winv

Figure 4. Mode width and phase inversion layer width plotted against the mode frequency.

19
(a)

(b)

(c)

(d)

Figure 5. Reconstructed mode structure in the arbitrary poloidal cross section in (a) t =5.72 − 5.75 s, (b) t = 5.75 − 5.82 s, (c) t = 5.82 − 5.84 s, and (d) t = 5.86 − 5.90 s.

#150672(a)(b)

Figure 6. Radial profiles of the relative polarization angle from the reference shot at (a) t = 5.8 s
and (b) t = 6.4 s for # 150672. Symbols show the measured data point and curves represent thepolarization angle profiles derived from the chosen current profiles.

20(a) #150672(b) #150673(c) #150674(d) #150676

ctr-ECCD
co-ECCD

Figure 7. Radial profiles of the rotational transform and the ECCD deposition in (a) # 150672,(b) # 150673, (c) # 150674, and (d) # 150676.