Isotope effect in transient electron thermaltransport property and its impact on the electroninternal transport barrier formation in LHD
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公開日: 2021-07-15
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キーワード (En):作成者: Kobayashi, Tatsuya, IDA, Katsumi, TANAKA,
Kenji, YOSHINUMA, Mikiro, Tsujimura, Ii Toru,
INAGAKI, Shigeru, TOKUZAWA, Tokihiko, TSUCHIYA,
Hayato, TAMURA, Naoki, IGAMI, Hiroe, YOSHIMURA,
Yasuo, ITOH, Sanae -I., ITOH, Kimitaka, LHD,
Experiment Group
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1

Isotope eﬀect in transient electron thermal transport
property and its impact on the electron internaltransport barrier formation in LHD
T. Kobayashi1,2 , K. Ida1 , K. Tanaka1 , M. Yoshinuma1 , T. Ii Tsujimura1 ,S. Inagaki3,4 , T. Tokuzawa1 , H. Tsuchiya1 , N. Tamura1 , H. Igami1 ,Y. Yoshimura1 , S.-I. Itoh4,3,5,† , K. Itoh6,1,4 and LHD Experiment Group
1

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

Japan
2

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

3

Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan

4

Research Center for Plasma Turbulence, Kyushu University, Kasuga 816-8580, Japan

5

Graduate School of Engineering, Chubu University, Kasugai 487-8501, Japan

6

Institute of Science and Technology Research, Chubu University, Kasugai 487-8501, Japan†

Deceased July 18, 2019

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

Abstract.

In this study, we perform a comprehensive comparison of the transport hysteresis

width in deuterium (D) plasmas, hydrogen (H) plasmas, and D-H mixed plasmas. The corefocused modulation electron cyclotron resonance heating (MECH) is applied as the heat source
perturbation, and the heat flux is evaluated using the energy conservation equation with themeasured electron temperature response and the ECH deposition profile calculated by the raytracing scheme. Systematic density scan in plasmas with diﬀerent ion mass reveals that there
is no significant isotope eﬀect in their hysteresis width. It is found that plasmas with heavier
isotope mass can easily form the electron internal transport barrier. As the hysteresis width is2insensitive to the isotope mass, the classical part of the diﬀusivity is considered to be responsible
for the isotope eﬀect in the transport barrier formation.

1. Introduction

One of the long-standing mysteries in magnetically confined fusion plasma research is
the hydrogen isotope eﬀect [1, 2, 3, 4, 5]. In the simplest scaling model, i.e., the Bohm
scaling model or the gyro-Bohm scaling model [6, 7, 8], it is predicted that the heavier
the fuel particles are the worse the confinement becomes. However, the experimental
investigations showed the opposite tendency. Many of these studies were based on
the transport analysis using the steady state confinement time or the power balance
diﬀusivity. As another technique, the thermal transport property can be analyzed fromthe plasma response with respect to a fractional perturbation applied on the heating
source, which we call the transient transport analysis [9, 10, 11]. It is known thatthe transport coeﬃcients obtained by the power balance analysis and by the transienttransport analysis diﬀer when nonlinearities exist in the flux-gradient relation, e.g., thecritical gradient [10, 11, 12, 13]. All of these analyses implicitly assume that the plasma
thermal transport is uniquely determined by the local plasma parameters.
However, some counter examples for those local transport models have beenreported in particular when the plasma heat source or sink are subject to transient
perturbations, e.g., by the local and intense electron heating [14, 15, 16, 17, 18, 19]
or by the edge plasma cooling [20, 21, 22]. These phenomena are called the nonlocal

3thermal transport [23], and considered to be of great importance for predicting future
reactor performance [24]. Recently, a direct impact of the heating source on the plasma
turbulence and thus on the turbulent transport was experimentally pointed out [18, 19].
Because of this ingredient, the turbulence amplitude is allowed to change immediately
after an additional heat source is applied and before the local parameters change.
This response results in the bifurcation of the trajectory in the flux–gradient diagram
depending on the applied ECH power [25, 26, 27]. In particular, under a modulation
ECH (MECH) application, the trajectory in the flux–gradient diagram draws a loop,
which we call the transport hysteresis. When the transport hysteresis emerges, a single
scalar transport coeﬃcient is found to be no longer valid for representing the transport
property of the high temperature plasmas [28, 29, 30, 31]. A theoretical model predicts
that the magnitude of the hysteresis is more enhanced in lighter isotope mass plasmas,
which results in the confinement degradation and therefore explains the isotope eﬀect[27].
To date, there are few experimental assessments for the isotope eﬀect on thetransient thermal transport such as the transport hysteresis. In this study, in addition
to the recent phenomenological investigations for the heating power dependence [18]or the density dependence [19] of the hysteresis width, we perform a comprehensive
comparison of the transport hysteresis width in deuterium (D) plasmas, hydrogen (H)plasmas, and D-H mixed plasmas. The core focused MECH is applied as the heat source
perturbation, and the heat flux is evaluated using the energy conservation equation with4
the measured electron temperature response and the ECH deposition profile calculatedby the ray-tracing scheme. Systematic density scan in plasmas with diﬀerent ion mass
reveals that there is no significant isotope eﬀect in their hysteresis width. In the low
density plasmas, the internal transport barriers (ITBs) [32] are dynamically formed in
the electron temperature profile with the MECH. It is found that plasmas with heavier
isotope mass can form ITBs with higher density at a fixed heating power similar to thecase of ITBs in the ion temperature profile [33]. As the hysteresis width is insensitive
to the isotope mass, the classical part of the diﬀusivity is considered to be essential forthe isotope eﬀect in the density threshold of the ITB.
This paper is organized as follows. Section 2 is dedicated to a brief review of thehysteresis study, in which the detailed analysis technique and the theoretical backgroundare exhibited. The experimental setup is given in section 3, and the experimental resultsappear in section 4. As an interpretation of the results, a theoretical model involving
the direct impact of the heat source modulation on turbulence is examined in section 5.
At last, the paper is summarized in section 6.

2. A brief review of transport hysteresis

For describing the thermal transport property in plasma, a number of theoretical models
have been developed so far. One of the most commonly used models is the local
diﬀusion–convection model [10]. An advantage of this model is that the transport
can be expressed only by two scalar coeﬃcients, i.e., the diﬀusivity and the convective

5
velocity. However, if the assumed model is improper in accounting for the actual plasmatransport, obtained results immediately mislead us in interpreting the plasma thermal
confinement [28, 29, 30]. To prevent overlooking phenomena outside the assumed model,
we prefer to directly observe the flux–gradient relation.
Spatiotemporal evolution of the electron heat flux perturbation q̃e (t, r) inducedby the heating source modulation P̃ (r, t) can be obtained by the energy conservation
equation as
[

]

1 ∫r
3
∂ T̃e (r, t)P̃ (r, t) − ne (r, t)
V ′ (r)dr,q̃e (t, r) = ′V (r) 02∂t(1)

where V ′ (r) is the radial derivative of the plasma volume profile [18, 19]. Data in diﬀerent
modulation periods are regarded as independent realizations, which are subject to theconditional ensemble averaging for reducing the statistical noise. By drawing obtainedq̃e (t, r) as a function of the local electron temperature gradient, the flux–gradient relation
is obtained.
By performing the flux–gradient relation analysis, the transport hysteresis wasfound [18, 19]. The typical transport hysteresis is illustrated in Fig. 1 [27, 34, 35].
There are two diﬀerent dynamics in the heat flux evolution having fast and slow time
constants. When the ECH is turned on, the heat flux increases with a fast time scale
and a slight change in the electron temperature gradient. It is followed by the heat flux
evolution with a slow time constant, which is well approximated by the local diﬀusion
model. When the ECH is turned oﬀ, a fast drop of the heat flux occurs. Consequentslow decreases in the heat flux and the local electron temperature gradient finally close6
the trajectory as a parallelogram loop. Here, the peak-to-peak variations in the heat
flux and in the electron temperature gradient at a single modulation of the heat source
are denoted as δqECH and −δ∇Te , respectively. The magnitude of the heat flux “jump”
at the fast time scale immediately after the ECH turn-on or turn-oﬀ is expressed asδqjump . The entire heat flux is therefore modeled as
qe = −ne χSlow∇Te + δqjump ,e(2)

where χSlowis the slow time scale diﬀusivity.
e

Since the variation in the electronistemperature gradient at the fast time scale dynamics is negligibly small, χSloweapproximated as
χSlow∼ −(δqECH − δqjump )/ne δ∇Te .
e(3)Here, the electron density is treated to be constant in time during the MECH according
to the experimental observation.

In this diagram, the heat pulse diﬀusivity χHPecorresponds to the slope of a diagonal connecting the left bottom and the right top.
When δqjump is absent, χSlow
is equivalent to χHP
and the local diﬀusion model holds.
eeAt the moment of the ECH turn-on or turn-oﬀ, the heat flux drastically changes
with a tiny change in the local electron temperature gradient. This is the typical featureof the nonlocal transport, i.e., flux variation not driven by the local gradient. Here, thecontribution of the oﬀ-diagonal terms in the transport matrix is also excluded since any
local parameter cannot vary in such a fast time scale. Theoretically, this fast nonlocal
response is modeled to be an enhanced turbulent fluctuation directly driven by theapplied heat source. In other words, the applied heat source is regarded as a “hidden

7parameter”, which induces the bifurcation in the flux–gradient relation. The direct
impact of the heat source on the turbulence is also considered to be strongly related
to the power degradation of the thermal transport [36, 37]. As a diﬀerent exampleof the “hidden parameter” in the flux–gradient relation, the electron density gradientis claimed to be responsible for the nonlocal cold pulse propagation by only using an
oﬀ-diagonal local transport model [38, 39, 40].

3. Experimental setup

The set of MECH experiments was performed in the 20th experimental campaign of
the Large Helical Device (LHD). The magnetic axis and the toroidal magnetic field in
the vacuum configuration are Rax = 3.6 m and Bt = 2.75 T, respectively. The plasma
minor radius is defined by the eﬀective minor radius in which 99 % of the plasma kinetic
energy is confined, to be a99 ∼ 0.6 m. The plasma is sustained by two tangential neutral
beams (NBs) injected in the balanced manner to prevent the NB driven plasma current.
The MECH focused on the core is superposed on it to study the heat pulse electron
thermal transport. The electron temperature perturbation is measured by the electron
cyclotron emission (ECE) radiometer [41], whose intensity is calibrated by the electron
temperature data measured by the Thomson scattering [42]. The ECH deposition profile
is calculated by the ray-tracing code LHDGauss [43].
It was demonstrated that the hysteresis width strongly depends on the line averaged
electron density [19]. We refrain to make a one-by-one comparison of plasmas with

8
Table 1. List of dataset used in the transient transport analysis

Date of experiment

Shot numbers

Gas puﬀ

Beam source

November 28, 2018

146808–146824

D

D

December 7, 2018147880–147883

H

D

February 8, 2019152210–152237

HH

diﬀerent isotope contents to avoid an imperfect match of the density, which could
provide an ambiguity to the results. Instead, the line averaged density dependencesof the hysteresis width in D, H and D-H mixed plasmas are compared.
Table 1 summarizes the date of experiment, the shot number, and the plasma fuelgases. Because the target plasmas are NB produced, not only the gas puﬀ but also thebeam fueling impacts the plasma ion purity. The experiments on November 28, 2018
were performed in the D experiment period, therefore both the gas puﬀ and the beam
were D. Similarly, data from the H plasmas were obtained in the H experiment periodof February 8, 2019, thus H-puﬀ and H-beam were used. On those experiment dates,
the plasma facing components (PFCs) were conditioned by each fuel gas. In addition
to this database, the mixed ion plasma data were obtained using the H puﬀ in the Dexperiment period of December 7, 2018. Since the PFCs were maintained by the Dgas, the recycling D from the walls were the dominant particle source in particular in
the low electron density plasma conditions. In order to maintain the desired mixture
rate, intensive discharge cleanings with H puﬀ were performed between the shots. The
shot-to-shot density scan was performed by controlling the gas puﬀ rate with a fixed ion

9purity.
Figure 2 shows the experimental condition in the database plotted in the line
averaged density–D/H ratio space. Here, the D/H ratio is evaluated as IDα /(IDα + IHα ),where IDα and IHα are the intensity of the Dα emission and the Hα emission measured by
the passive spectroscopy, respectively. Each point corresponds to one discharge, where
the time-evolving data are averaged in the time period subject to the transient transport
analysis of ∼ 2 s. Temporal variations of the line averaged density and the D/H ratio
in that time period are small, as shown by the error bars for each point. Data from
diﬀerent experiment dates are characterized by approximately constant D/H purities,
at 89 %, 60 %, and 4 %, which we call the D plasmas, the mixed plasmas, and the H
plasmas, respectively. The line averaged density is continuously scanned both in D and
H plasmas in a wide range, which is suﬃcient to observe the density dependence in thehysteresis width [19]. In addition, four data points in low density regime are obtained
from the mixed plasmas. As a representative case comparison among the D, H, andmixed plasmas, data at the line averaged density of ∼ 1.3 × 1019 m−3 are chosen. Theirshot numbers are #146822, #152229, and #147882, respectively.

4. Experimental results

4.1. Target discharge
Figure 3 shows the typical time evolution of the plasmas parameters in this experiment.
The injected power of the balanced NBs is approximately 3.6 MW. Short pulse

10
injection of a perpendicular NB is performed as the probe beam of the charge exchange
recombination spectroscopy measurement (data are not shown here). Modulation ECH(MECH) with the frequency of 23 Hz and the amplitude of ∼ 1 MW launched by a single
gyrotron is applied. The energy flux from electrons to ions by collision is calculated tobe typically less than 10 kW, which is negligibly small. The MECH power is depositednearly on-axis, reﬀ < 0.1 m, where reﬀ is the eﬀective minor radius [44]. The transienttransport analysis is performed in the time period of the density flat-top, i.e., 3.8 s to
5.6 s in this discharge. The ECE measurement displays a periodic electron temperature
response synchronizing the MECH pulses.
Variation of the long-time averaged mean plasma profiles in the line averaged
density scan is compared in plasmas with diﬀerent ion species. Figure 4 shows theelectron temperature profile, the electron density profile, and the ECH deposition profile
as a function of the line averaged density and the eﬀective minor radius. When the line
averaged density is decreased, the density profile changes from the hollowed profile tothe peaked profile. The electron temperature profile tends to sharply peak in the lowline averaged density case. In the high density cases, the ECH deposition radius moves
slightly outward because the ECH ray is subject to a flection. Nevertheless, the power isstill deposited within reﬀ < 0.15 m even in the highest density condition in this database.

11
4.2. Electron heat pulse transport
Radial profiles of the electron density and the electron temperature for the representative
discharges for the D, H, and mixed plasmas at the line averaged density of ∼ 1.3 ×
1019 m−3 are shown in Figs. 5 (a) and (b). The mean profiles diﬀer only slightly
regardless of the D/H ratio, in particular where the ECH deposition is absent. Only the
D plasma shows a large electron temperature gradient in the ECH deposition region of
reﬀ < 0.15 m, which is ascribed by the electron internal transport barrier (ITB). We willshow that the ITB transition condition is more tight in lighter isotope mass plasmas
below.
Figures 5 (c) and (d) show the fluctuation power of the electron temperature
perturbation being proportional to the square of the fluctuation amplitude and its
phase diﬀerence with respect to the MECH pulse at the fundamental frequency of themodulation, 23 Hz. At the outer radii with respect to the ECH deposition location,
reﬀ > 0.15 m, the radial derivatives of both the fluctuation power in the logarithmic
scale and the phase diﬀerence are almost identical among the D, H, and mixed plasmas.
Note that the vertical oﬀset in the fluctuation power profile is likely due to imperfectmatching of the density profile and ECH power absorption, and is unrelated to thetransport property. As discussed in Refs. [9, 31], the heat pulse diﬀusion coeﬃcient is afunction of the radial gradients of the fluctuation power and the phase diﬀerence whenthe electron thermal transport can be approximated by the local model. Diﬀerences inthe electron thermal transport property in the D, H, and mixed plasmas are invisible

12
where the ECH deposition is absent in the conventional local point of view. Note thatthe local thermal transport coeﬃcients are shown to be insuﬃcient to fully express theelectron heat pulse propagation in LHD [28, 30].
In order to compare the electron thermal transport properties in D, H, and mixed
plasmas more in detail, the heat flux evolution is derived using Eq. (1) with the measured
electron temperature response and the calculated ECH deposition profile. The obtained
heat flux is plotted as a function of the local electron temperature gradient as shownin the flux–gradient diagram in Fig. 6. The trajectories in the flux–gradient relation
when the MECH is on and oﬀ clearly diﬀer thus demonstrating the apparent input
power dependence of the heat flux and making the hysteresis loop. The finite hysteresis
widths in the D, H, and mixed plasmas seem to be identical. While, there are noticeable
diﬀerence in the modulation amplitude in the electron temperature gradient, which will
be discussed below.
Figures 7 (a)-(c) show the line averaged density dependence of the radial profile ofthe hysteresis width in the D, H, and mixed plasmas. The hysteresis width monotonicallydecreases as the measurement radius is apart from the ECH deposition radius. In
addition, the hysteresis width decreases as the line averaged density increases, asreported in [19]. For the quantitative comparison of the hysteresis width, the line
averaged density dependence of the hysteresis widths at reﬀ = 0.14 m, 0.20 m, and0.26 m are plotted in Figs. 7 (d)-(f). All three plasmas with diﬀerent isotope mass
show a similar decreasing trend of the hysteresis width with the increasing line averaged

13
density at diﬀerent radii. There is no significant diﬀerence in hysteresis widths exceeding
the scatter of the points due to experimental errors in the D, H, and mixed plasmas.
On the contrary to the hysteresis width, there is a noticeable isotope massdependence in the modulation amplitude in the electron temperature gradient −δ∇Te as
pointed out in Fig. 6. The line averaged density dependence of −δ∇Te is shown in Fig. 8(a). In the higher density range, −δ∇Te is mostly insensitive to the line averaged density.
However, when the line averaged density is decreased below a threshold level, −δ∇Tedrastically and monotonically raises. Deducing from the clear discontinuous nature of−δ∇Te evolution, it is considered that the electron temperature ITB is formed in thelower line averaged density discharges. The threshold line averaged density is clearlyhigher for the D plasma case at n̄e ∼ 1.6 × 1019 m−3 compared to the H plasma case atn̄e ∼ 1.2 × 1019 m−3 . A similar isotope mass dependence in the ITB threshold density
is also seen in the ion temperature ITB dynamics as shown in [33].
As discussed above, the hysteresis widths do not depend on the isotope mass of theplasma. Therefore, the isotope eﬀect in the ITB threshold density should be accounted
for by the slow time scale transport dynamics according to Eq. (2) and Fig. 1. We derive
the line averaged density dependence of the slow time scale diﬀusivity. Figure 8 (b)shows the line averaged density dependences of the peak-to-peak heat flux modulation
amplitude normalized by the local electron density δqECH /ne and the hysteresis width
δqECH /ne . Their diﬀerence, i.e., the heat flux driven by the local electron temperature
gradient at a slow time scale, is shown in Fig. 8 (c). It is shown that the heat flux driven

14by the local gradient gradually increases as the line averaged density decreases, and no
discontinuity is seen. The slow time scale diﬀusivity χSlow
defined by Eq. (3) is exhibitedein Fig. 8 (d). When the plasma is in the L-mode state in high density discharges, bothχSlowin D and H plasmas are scaled by ∝ n̄−1.2. The negative exponent on the lineeeaveraged density is suggestive of the density stability eﬀect in the confinement scaling[37]. As the density decreases, χSlow
drops oﬀ from the n̄e−1.2 trend, which triggersethe ITB formation. This transition in the χSlow
trend in D plasmas occurs at theehigher density level than that in H plasmas. The ITB transition in stellarator devices is
primarily ascribed to be the neoclassical radial electric field transition [32]. It is deduced
that the neoclassical root transition occurs in a higher density range in D plasmas, whichplausibly explains the isotope mass dependence in the transition density threshold.

5. Discussion

According to Refs. [25, 26, 27], the transport hysteresis is considered to be due to theimmediate response of turbulence amplitude to the increased heat input. In that model,
the fluctuation amplitude at the saturation level is predicted as
I=

I0
−2 ,
1 − γh χ−1
0 k⊥

(4)

where I0 is the fluctuation amplitude without considering the direct heating eﬀect, χ0
is the turbulent diﬀusion coeﬃcient in the L-mode, k⊥ is the wavenumber of fluctuationthat is of interest, and
γh ≡

∂PECH
∂pe

(5)

15
is the magnitude of the direct influence of the heating source on the fluctuation
amplitude. The turbulence fluctuation is amplified when the denominator of the termin the r.h.s. in Eq. (4) is smaller than unity. The time scale of the amplification canbe the ECH power absorption time, which is much faster than that of the fluctuation
growth by the local gradient increase.
If one takes the transport hysteresis into account, the inverse trend of theconfinement isotope eﬀect with respect to the Bohm/gyro-Bohm prediction can be
explained as follows. Bohm or gyro-Bohm scaling gives χ0 being proportional to the ion
mass. Since larger χ0 provides a larger denominator in Eq. (4), a smaller hysteresis
is expected in the heavier isotope mass.

A jump in the flux–gradient relation in

the hysteresis trajectory behaves to reduce the achievable temperature gradient at a
fixed heat input. Therefore, a smaller hysteresis with heavier hydrogen isotope mass isfavorable for obtaining a better confinement, which is an explanation of the transport
isotope eﬀect.
However, the present observation in LHD shows no isotope mass dependence of thehysteresis width in the D, H, and mixed plasmas. This observation implies that the
turbulent diﬀusion coeﬃcient χ0 does not have an isotope mass dependence. According
to Ref. [5], global confinement times of D and H plasmas scale similarly, which supports
this implication. The isotope eﬀect in the ITB formation is therefore considered to be
not due to the turbulence property itself, but due to the ambient radial electric field
condition.

16
Note that Eq. (4) is one of the possible models for explaining the isotope eﬀect in thehysteresis response of the transient electron thermal transport. For steady state plasmas,
other possible mechanisms were discussed, including the zonal flow eﬀects, [45, 46, 47],
the electromagnetic turbulence eﬀect [47], the trapped electron mode eﬀect [46], theenergetic ion eﬀect [48], and others. Application of these models for the transient
plasma response with some modifications is one of the interesting direction for future
study.

6. Summary

In this study, we performed a comprehensive comparison of the transport hysteresis
width in deuterium (D) plasmas, hydrogen (H) plasmas, and D-H mixed plasmas. The
core focused modulation ECH was applied as the heat source perturbation, and the heat
flux was evaluated using the energy conservation equation with the measured electron
temperature response and the ECH deposition profile calculated by the ray-tracing
scheme. Systematic density scan in plasmas with diﬀerent ion mass revealed that there
was no significant isotope eﬀect in their hysteresis width. It was found that plasmas
with heavier isotope mass can easily form electron ITBs. As the hysteresis width wasinsensitive to the isotope mass, the classical part of the diﬀusivity was considered to be
essential for the isotope eﬀect in the ITB formation.

17
Acknowledgments

The authors acknowledge all the members of the LHD Experiment Group for theirassistance. The authors also thank Professor S. Sakakibara for strong support and
S. Satake for useful discussions. This work is partly supported by the National Institutefor Fusion Science grants (17KLPH031 and ULHH033) and by the Grant-in-Aid for
Scientific Research of JSPS (17K14898).

18
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22'$*+,-.%/012/&$.%45(/&$

%$
&$
ECH
off

ECH
on
'$()
−.∇#$

−∇#$

Figure 1. Schematic of the flux-gradient relation when the transport hysteresis is present.

D#146822
Mixed#147882#152229
H

Figure 2. Experimental parameter map in the line averaged density–D/H ratio space for D,
Mixed, and H plasmas. The D/H ratio is given as IDα /(IDα + IHα ), where IDα and IHα are
the intensity of the Dα emission and the Hα emission measured by a passive spectroscopy,
respectively.

23#146822

Density flat top

(a)

PNB,p
PECH

PNB,co
PNB,ctr(b)(c)

reff = 0.07 m
0.15 m 0.23 m 0.30 m

0.38 m(d)ne [1019 m-3](e)Power density [MW/m3]

Figure 3. Time evolutions of (a) heating power, (b) line averaged density and diamagnetic
plasma stored energy, (c) electron temperature, (d) electron density profile, and (e) ECH
absorption profile.

24

D

(a-1)

(a-2)

(a-3)

Mixed

(b-1)

(b-2)

(b-3)

H

(c-1)

(c-2)

(c-3)

Figure 4. Line averaged density dependence of radial profiles of electron temperature (firstcolumn), electron density (second column), ECH absorption (third column) averaged in theoverall analysis time period for (a) D, (b) Mixed, and (c) H plasmas.

25
(a)

(
Power density[MW/m3]
H; #152229

Mixed; #147882(b)

D; #146822(c)

23 Hz MECH(d)Figure 5. Radial profiles of (a) electron temperature profile and ECH power density, (b) electron
density profile, and (c,d) fluctuation power being proportional to the square of the fluctuation
amplitude and phase of electron temperature modulation at 23 Hz.

26
reff = 0.17 m
Mixed; #147882

ECH
off

ECH
on

H; #152229

D; #146822

Figure 6. Trajectory of time evolution during the MECH in the flux–gradient diagram.

27

D

(a)

(d) reff = 0.14 m

Mixed

(b)

(e) reff = 0.20 m

H(c)(f) reff = 0.26 m

Figure 7. (Left column) Radial profile of the hysteresis width as a function of the line averaged
density for (a) D, (b) Mixed, and (c) H plasmas, and (Right column) radial profile of the hysteresis
width at (d) reﬀ = 0.14 m, (e) 0.20 m, and (f) 0.26 m.

28
(a)

(b)
!"*+, /()!"#$%& /()(c)(!"*+, − !"#$%& )/()(d)∝ (. )/0.2

Figure 8. Line averaged density dependence of (a) the amplitude in electron temperature
gradient modulation, (b) the hysteresis width δqjump and peak-to-peak heat flux modulation
amplitude δqECH normalized by the electron density ne , (c) (δqECH − δqjump )/ne , and (d) theslow time scale diﬀusivity.