J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Numerical analysis of a toroidal rotation eﬀect
on the type-I ELM in JT-60U
N. Aiba, N. Oyama, A. Kojima, S. Tokuda1)
1)

Japan Atomic Energy Agency, Naka 311-0193, Japan
Research Organization for Information Science and Technology, Tokai 319-1106, Japan(Received: 26 October 2009 / Accepted: 23 February 2010)

Eﬀect of a toroidal rotation on the type-I edge localized mode in JT-60U is investigated numerically. As
the result of the numerical analysis, it is conﬁrmed that the plasma rotating experimentally in the co-direction
to the plasma current is approximately on the stability boundary of the MHD mode even when the rotationis neglected. However, the plasma rotating in the counter-direction is far from the stability boundary under thestatic assumption. Since both plasmas have the type-I ELM, the edge MHD stability is reassessed with the toroidal
rotation eﬀect. This stability analysis clariﬁes that the rotation of this counter rotating plasma can destabilize theedge localized MHD mode, and can resolve the discrepancy that the type-I ELM is observed in the plasma that is
MHD-stable under the static assumption.
Keywords: ELM, ideal MHD stability, toroidal rotation, Frieman-Rotenberg equation

1. Introduction

In Ref. [7], furthermore, we have clariﬁed that this destabilization is mainly caused by the diﬀerence between thefrequency of the eigenmode and the toroidal rotation frequency, and this eﬀect becomes eﬀective only when therotation proﬁle has large shear in the radial direction.
Based on these results, in this paper, we investigate
numerically the eﬀect of the toroidal rotation on the type-I
ELM in JT-60U. Fortunately, in the last campaign of JT60U, several diagnostics were installed so as to obtain highspatial resolution proﬁles near the pedestal, and realize toanalyze the edge MHD stability with high accuracy.
This paper is organized as follows. Section 2 introduces the proﬁles of the toroidally rotating equilibria reconstructed with the experimental data of the JT-60U typeI ELMy H-mode plasmas. Section 3 shows the numerical results of the stability analysis in not only the rotating
but also the static cases. By comparing the results in bothcases, we discuss the toroidal rotation eﬀect on the typeI ELM in JT-60U. Section 4 presents a summary of thiswork.

In tokamak plasmas, a transport barrier sometimes appears near the plasma surface, and makes a pedestal structure in the plasma density and the temperature proﬁles.
The plasma with such pedestal structures, called H-mode,is favorable to improve a energy conﬁnement, which isenough to reach burning plasma conditions. In such Hmode plasmas, edge localized modes (ELMs) are usuallyobserved, and constrain the maximum pressure gradient in
the pedestal [1].
The recent experimental results in JT-60U show thatthe plasma toroidal rotation at the pedestal has an impact
on the ELM phenomena [2, 3]. However, this dependenceof the ELM phenomena on the toroidal rotation is complicated to understand only with the experimental results.
In fact, the toroidal rotation can change not only the ELM
phenomena but also the equilibrium pressure (density, temperature) proﬁle near the pedestal, and it is diﬃcult to identify whether the transport property or the stability property
is responsible for this change of the pedestal proﬁle. For
comprehending such a complicated dependence between
the ELM phenomena and the plasma rotation, it is necessary to understand the physics with the theoretical andnumerical analyses.
Previous numerical and experimental works have reported that the ideal MHD modes destabilized near theplasma surface, called the peeling-ballooning mode, isthought to be responsible for the type-I ELM [1, 4]. On
the basis of this result, we investigated the toroidal rotationeﬀect on the ideal MHD modes at tokamak edge pedestal,and reported that the edge localized MHD mode can bedestabilized by the toroidal rotation with shear though theballooning mode stability changes little [5]; an other paper
also reported that the toroidal rotation shear increase thegrowth rate of intermediate wave length MHD modes [6].

2. Equilibrium proﬁles

The equilibria analyzed numerically are obtainedby the reconstruction with the experimental data of theE49228 and the E49229 plasmas in JT-60U; the detailsof these plasmas are shown in Ref. [8]. As discussed inRef. [8], these plasmas have the same toroidal magnetic
ﬁeld Bt0 = 4.0[T] and plasma current I p = 1.6[MA], but
the plasma rotation proﬁles are diﬀerent between E49228
and E49229, whose toroidal rotation are in the co-(CO.)
and ctr-(CTR.)directions to the plasma current, respectively. Such a diﬀerence of the rotation proﬁles are due
to changing the combination of the momentum input withneutral beam injection (NBI). By changing the rotation
proﬁle from CO. to CTR., the type-I ELM frequency increases from ∼ 37[Hz] to ∼ 45[Hz], and the ELM energy

author’s e-mail: aiba.nobuyuki@jaea.go.jp

74©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

6

(a)

3

/m ]

8

T i , T e [keV]

2

2

4

50

ne [x10

6

p [kPa]'D'LY>DX@

ne (E49228)
ne (E49229)
p (E49228)
p (E49229)

100



:GLD>0-@




(b)

T i (E49228)
T i (E49229)
T e (E49228)
T e (E49229)

4



−19

(&R

10

N. Aiba et al., Numerical Analysis of a Toroidal Rotation Effect on the Type-I ELM in JT-60U

(c)





0

Fig. 1 Waveforms of the E49228 (CO.) and the E49229 (CTR.)
plasmas, which are rotating in the co- and the ctrdirections, respectively. The red line and the blue line
show the divertor Dα intensity and the diamagnetic stored
energy Wdia . The type-I ELM frequency is ∼ 37[Hz]and ∼ 45[Hz], and the ELM energy loss is ∼ 89[kJ]and ∼ 46[kJ] in the E49228 and E49229 plasmas, respectively.

2<j.B>/<B >2−10

7LPH>V@0<j.B>/<B > [a.u.]

0.5

1

ρvol.

1

D

'



red: E49228, blue: E49229

q

0

2





1

ρvol.

q

E49229 (CTR.)



0.5

4



0

(d)
E49228 (CO.)

GLD



1

ρvol.

0



0.5

2

0



: >0-@

>DX@

05(&WU



'LY





0


7LPH>V@Ω [kHz]



0



−5



0.5

ρvol.

1

Fig. 2 Proﬁles of (a) T i and T e , (b) ne and p, (c) Ω, (d)� j · B�/�B2 � and q, in the E49228 (CO.) and the E49229(CTR.) plasmas, respectively.

3. Stability analysis
3.1 Stability analysis without a toroidal rotation

In this subsection, we investigate and compare theideal MHD stability properties of the E49228 (CO.) andthe E49229 (CTR.) plasmas without a toroidal rotationeﬀect. This stability analysis is performed with the
MARG2D code [10, 11] for the ﬁnite-n MHD mode analysis and the BETA code [12] for the inﬁnite-n ballooning
mode analysis, where n is the toroidal mode number. In
this paper, the range of n of the analyzed MHD modes isfrom 1 to 30, and ∞.
The main object of the edge MHD stability analysis is
to clarify the achievable pedestal pressure without instability. As the pedestal pressure becomes larger, the edge bootstrap current density also increases, and the edge MHD stability property is mainly determined by these equilibrium
proﬁles. From this viewpoint, as mentioned in previous
works [4, 11], the edge pedestal pressure gradient and theedge current density are the main parameters for the edge
MHD stability analysis. In this paper, for varying these parameters, the pressure proﬁle and the current proﬁle near
the pedestal are changed asloss becomes about half from ∼ 89[kJ] to ∼ 46[kJ]; thewaveforms of these plasmas are shown in Fig.1.
Figure 2 shows the proﬁles of (a) the temperatures of
the ion T i and the electron T e , (b) the electron number density ne and the pressure p, (c) the rotation frequency Ω,and (d) the parallel current density � j · B�/�B2 � and thesafety factor q, respectively; these are the proﬁles just before the ELM crash.
� Here ρvol. is the radial coordinate
deﬁned as ρvol. ≡ V(ψ)/Vtot. , V is the volume in eachﬂux surface, ψ is the poloidal ﬂux normalized as ψ = 0(= 1) at the axis (surface), Vtot. is the plasma total volume, j is the plasma current density, and B is the magnetic
ﬁeld. The � j · B�/�B2 � proﬁle is obtained by estimating thebootstrap current, the neutral beam driven current, and theohmic current with the ACCOME code [9]. The eﬀective
charge Ze f f values and the poloidal beta β p values are (2.6,0.85) and (2.8, 0.81) in the E49228 (CO.) and the E49229(CTR.) plasmas, respectively. Hereafter, the E49228 andthe E49229 plasmas are called as the CO. and CTR. plasmas. The proﬁles of T i and ne near the pedestal are measured with high spatial resolution by CXRS and LiBP [8].
Note that the T i proﬁles outside the top of the T i pedestal(ρvol. > 0.93) are similar to each other but the ne proﬁle of
the CTR. plasma is diﬀerent from that of the CO. plasma;
the ne pedestal top and foot changes from ρvol. = 0.93 and0.99 (CO.) to 0.91 and 0.96 (CTR.). Such a diﬀerence ofthe ne pedestal proﬁle changes the position where the pressure gradient becomes maximum and the bootstrap current
proﬁle as shown in Figs.2 (b) and (d).

p0 (ψ) ∝p0−org (ψ)... (0 ≤ ψ < 2ψ ped − 1.0),(1)p0 (ψ) ∝p0−org (ψ) · (1.0 + C ped · Ψ)and... (2ψ ped − 1.0 ≤ ψ ≤ 1.0), (2)
⎛
�2 ⎞2
��
⎜⎜⎜
�� ψ − ψ ped ��� ⎟⎟⎟⎟⎜(3)Ψ ≡ ⎜⎝1.0 − �⎟ ,� 1.0 − ψ ped �� ⎠

� j · B�/�B2 � ∝� j · B�/�B2 �org

+ C BS � j · B�/�B2 �BS ,

75

(4)

0.7

where p0 is the ﬂux function part of the plasma pressure,p0−org is the original p0 value of the reconstructed experimental data shown in Fig.2 (b), ψ ped is the ψ value at the
top of the pressure pedestal, � j · B�/�B2 �org (� j · B�/�B2 �BS )is the original (bootstrap) � j· B�/�B2 � value calculated with
the ACCOME code shown in Fig.2 (d), and C ped (C BS )is the parameter for changing the pressure (current) proﬁle near the pedestal. Note that since we ﬁx the poloidal
beta β p and the plasma current I p , the proﬁles of p0 and� j · B�/�B2 � are no longer same as the original proﬁles everywhere when C ped , C BS � 0. Also note that the plasmapressure is no longer the ﬂux function in case that theplasma is rotating [13], and when the rotation is purely
toroidal, the pressure can be written as⎡ ⎛ 2⎞⎤⎢⎢⎢ 2 ⎜⎜⎜ R⎟⎟⎥⎥⎜⎢
p = p0 (ψ) exp ⎣ M ⎝ 2 − 1⎟⎟⎠⎥⎥⎦ ,
(5)
R0

(a)

stability boundary E49229

0.5

0.5

jped

jped

0.6

0.6

(b)

α94

3

(c)

1

2

α94

3

(d)

−2

−2

0

0

s94

s94

2

2

stability boundary

0.4

2

4

1

4

0.4

stability boundary

stability boundary E49229

E492281

under the isothermal condition on each magnetic surface(T = T (ψ)). Here M is the Mach number that is the ratio of
the toroidal rotation velocity vφ = R0 Ω to the ion thermal√velocity vth = 2T i /mi as� �2
mi R20 Ω2
vφ
=
,
(6)
M 2 (ψ) ≡
vth
2T i

2

α94

3

1

2

α94

3

Fig. 3 Stability diagrams without the toroidal rotation eﬀect onthe ( j ped , α94 ) plane of (a) the E49228 (CO.) and (b)the E49229 (CTR.) plasmas, and those on the (s94 , α94 )plane of (c) the CO. and (d) the CTR. plasmas, respectively. The (green) circle and (red) triangle mean stableand unstable for the ﬁnite-n MHD modes, the solid line
shows the stability boundary determined by the ﬁnite-n
MHD modes and the inﬁnite-n ballooning mode, and thetarget expresses the equilibrium values observed experimentally. As shown in these ﬁgures, the CO. plasma isapproximately on the stability boundary of the edge localized MHD mode, but the CTR. plasma is far from thisstability boundary.

mi is the ion mass, R is the coordinate of the cylindricalcoordinate system (R, Z, φ), and R0 is the major radius of
the equilibrium.
Figure 3 shows the stability diagrams on the ( j ped ,α94 ) and (s94 , α94 ) planes, where j ped is the current
density averaged over (2ψ ped − 1.0) ≤ ψ ≤ 1.0, αis the normalized pressure gradient deﬁned as α ≡−(μ0 /2π2 )(d p0 /dψ)(dV/dψ)(VR/2π)0.5 , μ0 is the permeability in the vacuum, s is the magnetic shear deﬁned ass ≡ 2V/q(dq/dV), and the subscript 94 expresses the valueat ψ = 0.94. Figures 3 (a) and (c) indicate that the CO.
plasma is approximately on the stability boundary of theedge localized MHD mode without a toroidal rotation effect. In fact, the n = 12 peeling-ballooning mode becomes
marginally unstable by increasing C ped to 0.1; this increment is thought to be within the error of the edge proﬁlemeasurements.
On the other hand, as shown in Figs.3 (b) and (d), theCTR. plasma is far from the stability boundary without atoroidal rotation, and to make the plasma unstable, it isnecessary to increase C ped > 0.25. Since such a large increment in pressure is no longer within the margin of theerror, this CTR. plasma without a toroidal rotation is stableagainst ideal MHD modes.

3.2

E492280.7

N. Aiba et al., Numerical Analysis of a Toroidal Rotation Effect on the Type-I ELM in JT-60U

in these plasmas. The numerical analysis including a rotation eﬀect is performed with the MINERVA code [14],which solves the Frieman-Rotenberg equation [15], thelinear ideal MHD equation with ﬂow. As mentioned in
the previous subsection, since the CO. plasma becomes
marginally unstable by increasing C ped to 0.1, we investigate the toroidal rotation eﬀect on the edge MHD stability under the condition C ped = 0.1 in both CO. and CTR.
plasmas. Note that MARG2D solves the eigenvalue problem associated with the two-dimensional Newcomb equation [10]NY = −λ0 RY,(7)

and realizes to calculate the eigenvalue numerically evenwhen the plasma is stable (λ0 > 0), where N is the Newcomb operator, Y ≡ rξ, r is the radial coordinate, ξ is theplasma displacement, λ0 is the eigenvalue, and R is theweight function deﬁned in Ref. [10]. This advantage realizes to identify the stability boundary of the MHD mode as
the contour of λ0 = 0 in the static equilibrium case.
However, since the MINERVA code solves the initial

Stability analysis with a toroidal rotation

As mentioned in the previous subsection, the CTR.
plasma without a toroidal rotation is stable against ideal
MHD modes. However, as already mentioned, the typeI ELM was observed experimentally in this plasma. To
understand this discrepancy, in this subsection, we investigate the toroidal rotation eﬀect on the edge MHD stability

76

n

20

0.85

30

value problem of the Frieman-Rotenberg equation,
∂2 ξ
∂t2

+
=

Fs
Fd

≡
≡

∂ξ
+ ρ(u · ∇)(u · ∇)ξ∂tF(ξ) = F s (ξ) + Fd (ξ),
��∇ ξ · ∇p + Γp∇ · ξ
2ρ(u · ∇)+(∇ × Q) × B + j × Q,��∇ · ρξ(u · ∇)u − ρu(u · ∇)ξ+ρ(u · ∇)(u · ∇)ξ,0

−λ0 , γ/ωA0

γ / ωA0= 0.005

0.95

1

0

stable−λ0 (w/o rot.)γ/ωA0 (rot.1)
γ/ωA0 (rot.2)
γ/ωA0 (rot.3)

10

n

20

30

(8)
and 1.2 times larger than rot.1, respectively. Figure 5 (b)shows the n dependence of −λ0 and γ/ωA0 in the CTR.
plasma. As shown in this ﬁgure, though the CTR. plasma
without rotation is stable against ideal MHD modes, thetoroidal rotation of CTR. plasma (rot.1) destabilizes the
MHD mode, and the n = 20 mode becomes marginallyunstable. Moreover, by increasing the rotation frequency,
not only the growth rate but also the n number of the most
unstable mode become larger; for example, when the rotation proﬁle is rot.3, the n = 26 mode is the most unstablemode, whose γ/ωA0 approaches to 0.02.
Based on these numerical results, we investigate thestability boundary of both the CTR. plasmas with thetoroidal rotation shown in Fig.2 (c). Figure 6 shows thestability diagram on the ( j ped , α94 ) and the (s94 , α94 ) planesin the CTR. plasma with and without the toroidal rotation.
As shown in these ﬁgures, by adding the toroidal rotation, the stability boundary moves to the smaller α94 side,
and as the result, the threshold pressure gradient becomes
smaller from α94−max � 2.77 to � 2.28 under the same
� j · B�/�B2 � � 0.5 condition. Moreover, the n number ofthe MHD modes, which determines the stability boundary, becomes larger as the rotation frequency increases,
and the destabilizing eﬀect of the toroidal rotation becomesstronger as the n number of the MHD mode increases. For
example, on the stability boundary at � j · B�/�B2 � � 0.5,
the n number of the MHD mode changes from 16 to 20
by adding the toroidal rotation. This result is consistent
with the results of the qualitative and quantitative analysesof the rotation and the rotation shear eﬀects on the edge
MHD stability in Refs. [5, 7, 14], and resolves the discrepancy mentioned at the front of this subsection.

(9)
(10)

this code cannot identify strictly the marginal condition(γ/ωA0 = 0). Here ρ is the plasma mass density, u is theequilibrium rotation velocity, F is the force operator, F s
is the force operator that has the same vector form as thatin static equilibrium case, Fd is the sum of the remaining
force terms that express the rotation eﬀect on the force operator F, Q is the ﬂuctuation of the magnetic ﬁeld givenbyQ ≡ ∇ × (ξ × B) ,ρvol.

unstableFig. 5 (a) Enlarged view of Ω of the CTR. plasma. To investigate the rotation eﬀect on the MHD stability in the CTR.
plasma, three kinds of the rotation proﬁle (rot.1, rot.2,
rot.3) are used for the stability analysis. (b) Dependencesof −λ0 and γ/ωA0 on n in the CTR. plasma, whose rotation proﬁle is Ω = 0, rot.1, rot.2, and rot.3, respectively. The toroidal rotation of CTR. plasma (rot.1) destabilizes the MHD mode, and the n = 20 mode becomes
marginally unstable.

Fig. 4 Dependences of −λ0 and γ/ωA0 on n in the CO. plasma
with and without the toroidal rotation when C ped = 0.1.
The toroidal rotation has little impact on this CO. plasma,
and the n = 12 mode is marginally unstable.

ρ

0.9−0.06 −0.04 −0.02−2−λ0 (w/o rot.)γ/ωA0 (w/o rot.)γ/ωA0 (with rot.)

10

0.02

0

Ω [kHz]stablew/o rot.
rot.1
rot.2
rot.3

−4

−0.06 −0.04 −0.02

0

(b)

(a)

unstableγ / ωA0= 0.0050−λ0 , γ/ωA0

0.02

N. Aiba et al., Numerical Analysis of a Toroidal Rotation Effect on the Type-I ELM in JT-60U(11)and ωA0 is the toroidal Alfvén frequency at the axis. Accordingly, the stability boundary is determined by extrapolating γ into 0 from computable (positive) γ values in casethat the equilibrium rotates. Note that one of γ/ωA0 used
for extrapolating is enough small (∼ 5.0 × 10−3 ) to identify
the stability boundary with high accuracy. In this paper,
since we assume that the plasma rotation is purely in thetoroidal direction, u can be written as u = R2 Ω∇φ.
Figure 4 shows the n dependences of −λ0 and γ/ωA0
in the CO. plasmas with and without the toroidal rotation
whose proﬁle is shown in Fig.2 (c). As shown in this ﬁgure, the rotation proﬁle of the CO. plasma has little impact on the edge MHD stability, and the n = 12 mode ismarginally unstable as in the static case.
Next, we investigate the rotation eﬀect on the edge
MHD stability in the CTR. plasma. In this analysis, weinvestigate not only the n dependence but also the rotation
dependence of γ/ωA0 by changing the rotation proﬁle fromrot.1 (original proﬁle shown in Fig.2 (c)) to rot.2 and rot.3
shown in Fig.5 (a). These rot.2 and rot.3 proﬁles are determined by increasing the Ω value at ρvol. = 0.92 as 1.1

4. Summary

We analyze numerically the toroidal rotation eﬀect on
the type-I ELM property by comparing the stability prop-77

ply that the destabilizing eﬀect by the toroidal rotation withshear is more eﬀective in the E49229 plasma than that in
the E49228 plasma. Actually, at the marginally unstable point near the operation point on the ( j ped , α94 ) diagram, the δWrot.−n2 /δWK value at ( j ped , α94 ) = (0.50, 2.28)
is −4.95 × 10−4 in the E49229 plasma, and this is about
twice as large as that (= −2.52 × 10−4 ) at ( j ped , α94 ) =(0.55, 2.75) in the E49228 plasma, where δWK ≡ �ξ |ρ| ξ�
is the kinetic energy. The more detailed discussion about
the destabilizing mechanism is reported in Ref. [7].
In this paper, since the measurements with high spatial
resolution is necessary for the edge MHD stability analysis of the experimental results, and the physics of thetype-I ELM is relatively well-understood qualitatively andquantitatively, we select the E49228 and the E49229 typeI ELMy H-mode plasmas as the objects of the numericalanalysis. To understand the toroidal rotation eﬀect on the
ELM phenomena in more detail, it is important to understand this eﬀect on not only the type-I ELM but also theother ELMs. Particularly, as discussed in Ref. [2], thegrassy ELM strongly depends on the toroidal rotation frequency, and since the ELM energy loss of the grassy ELM
is much smaller than that of the type-I ELM, this grassy
ELM is thought to be more favorable than the type-I ELM
for ITER and future devices. From this viewpoint, we will
investigate the toroidal rotation eﬀect on the grassy ELM
and will report in near future.

4

0.7

N. Aiba et al., Numerical Analysis of a Toroidal Rotation Effect on the Type-I ELM in JT-60U(a)

E49229(b)boundary
w/o rot.

0.4

boundary
w/o rot.

1

2

α94

3

−2

0.5

0

s94

jped

0.6

2

boundary
with rot.

boundary
with rot.

1

2

α94

E492293

Fig. 6 Stability diagrams on (a) the ( j ped , α94 ) and (b) the (s94 ,α94 ) plane of the CTR. plasma, respectively. The (blue)
circle and (orange) triangle means stable and unstable forthe ﬁnite-n MHD modes, the solid line shows the stability boundary of the ﬁnite-n MHD modes and the inﬁniten ballooning mode in the CTR. plasma with the rotation
proﬁle rot.1., the broken line shows the stability boundary of the ﬁnite-n MHD modes in the CTR. plasma without the rotation., and the target expresses the equilibrium
values observed experimentally. By adding the toroidal
rotation, the stability boundary moves to the smaller α94
side, and as the result, the threshold pressure gradient becomes smaller from α94−max � 2.77 to � 2.28 under thesame � j · B�/�B2 � � 0.5 condition.

erties between the E49228 and the E49229 type-I ELMy
H-mode plasmas in JT-60U, which are rotating in theco- and ctr- directions to the plasma current, respectively.
As the result of the stability analysis, we clarify that thetoroidal rotation has little impact on the MHD stability inthe E49228 co-rotating plasma, and this plasma just before
the ELM is approximately on the stability boundary of theedge localized MHD mode in each static and rotating case.
On the other hand, the E49229 ctr-rotating plasma is far
from the stability boundary under the static assumption. In
this ctr-rotating plasma, the toroidal rotation destabilizes
the edge MHD mode, and reduces the stability limit of thepressure gradient near the pedestal. As the result of thisdestabilization, this ctr-rotating plasma just before ELM
is also considered as the marginally unstable against edge
MHD mode.
As mentioned in the introduction, we have reported
that the destabilization of edge localized MHD mode by
the toroidal rotation with shear is mainly caused by thediﬀerence between the frequency of the eigenmode and thetoroidal rotation frequency; this mechanism is identiﬁed by
deﬁning the energy in Ref. [7] as��(12)δWrot.−n2 ≡ n2 �ξ ��ρ(ω2 − Ω2 )�� ξ�.

Acknowledgments

The authors are grateful to Dr. M. Mori, Dr. T. Ozeki
for their support. This work was partially supported by the
Ministry of Education, Science, Sports and Culture, Grantin-Aid for Young Scientists (B), 2009, 21760698.

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This energy is proportional to n2 , and increases as the rotation shear becomes larger. By comparing the rotation
proﬁles between the E49228 and the E49229 plasmas, therotation shear near the pedestal in the E49229 plasma is locally more than twice that in the E49228 one. Moreover, as
mentioned in Subsec.3.2, the n number of the marginallyunstable mode is 20 in the E49229 plasma, which is larger
than that in the E49228 plasma (= 12). These results im-78