Plasma and Fusion Research: Regular Articles

Volume 4, 051 (2009)

Rotational Stabilization of Resistive Wall Mode on JT-60U∗)
Go MATSUNAGA, Manabu TAKECHI, Nobuyuki AIBA, Genichi KURITA,
Yoshiteru SAKAMOTO, Yoshihiko KOIDE, Akihiko ISAYAMA, Takahiro SUZUKI,
Takaaki FUJITA, Naoyuki OYAMA, Takahisa OZEKI, Yutaka KAMADA and JT-60 TeamJapan Atomic Energy Agency, Naka 311-0193, Japan(Received 24 July 2009 / Accepted 14 August 2009)
We have carried out experiments to clarify the stabilizing eﬀect of a plasma rotation on the resistive wallmode (RWM) that could limit the achievable-βN in high-βN plasmas above the no-wall ideal βN -limit. On JT-60U
plasma rotations are controlled using neutral beams with varying combinations of net torque input while keeping
βN constant. The RWM is destabilized as the plasma rotation is being reduced. Detailed measurements of themode structure revealed that the RWM has a global structure that rotates with the order of the resistive wall time.
In these experiments, it is found that the critical toroidal rotation speed for the RWM stabilization is less than
1% of the Alfvén speed. Moreover, the critical rotation does not strongly depend on βN . The results suggest thathigh-βN operation up to the ideal wall βN -limit could be possible by suppressing the RWM with a slow plasma
rotation in fusion reactors.
c 2009 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: resistive wall mode, plasma rotation, JT-60U
DOI: 10.1585/pfr.4.051

1. Introduction

istic devices the conducting wall has finite resistivity thestabilizing eﬀect is lost due to the wall resistivity [2]. This
results in additional instability originating from the wall
resistivity, that is, the resistive wall mode (RWM). The
ideal
with
RWM is destabilized in the region βfree
N ≤ βN ≤ βN
a characteristic growth time that corresponds to the skintime of the resistive wall τw (resistive wall time). Namely,
the growth rate and the mode rotation frequency slow down
to the order of τ−1
w . The RWM is predicted to have a global
eigen-function similar to that of the ideal mode. The factthat the RWM could limit achievable-βN in realistic devices makes RWM stabilization a critical issue in achieving
steady-state high-βN operations in ITER and fusion reactors.
Bondeson and Ward predicted that the plasma rotation
could stabilize the RWM [3]. In their numerical results theplasma dissipation could couple with the RWM stability
via the plasma rotation, and the rotation larger than several percent of the Alfvén speed is required for the RWM
stabilization. Several models have been proposed for therotational stabilization of the RWM [4–7]. If the plasma
rotation is to be eﬀective in stabilizing the RWM the required plasma rotation, hereafter referred to as the criticalrotation, should be quantitatively validated and experimentally identified because the plasma rotation in ITER and fusion reactors is predicted to be less than 1% of the Alfvénspeed [8].
For this reason we have carried out the high-βN experiments on JT-60U in order to investigate the critical rotation required for the RWM stabilization [11, 12]. Previously, the RWMs were observed in the reversed shear plas-

For a future fusion reactor, a steady-state high-β
plasma is necessary for it to be economical because thehigh-β means the high fusion output Pfus , which is definedas [1] Pfus ∝ p2 ∝ β2N Ip2 B2t ; where βN is the plasmapressure normalized by the device parameters of Ip and
Bt ; βN = βt /(Ip /aBt ) ∝ p /(Ip Bt ). Here, p, βt , Ip , Bt
and a are the volume-averaged plasma pressure, toroidal-β,
plasma current, toroidal magnetic field and plasma minor
radius, respectively. From the definition of βN operation in
the high-βN region means high fusion output even with acompact device, that is, the device could be said to be economically eﬃcient. However, the achievable-βN is limited
by ideal MHD instabilities. In such high-βN plasmas ideal
kink-ballooning modes that are driven by both the pressure
gradient ∇p(r) and the plasma current j(r) can limit theachievable-βN . The ideal MHD theory provides for two
limits that are determined by the boundary conditions in
the vacuum region surrounded the plasma. The lower limit
is the no-wall ideal β-limit (βfreeN ) that corresponds to thecase with a free boundary. The upper limit is the ideal-wallideal β-limit (βideal
N ) that corresponds to the case with theconducting wall close to the plasma, and the conducting
is larger thanwall has perfect conductivity. In general βideal
N
,
and
hence
the
ideal-wallcanimprovethe
MHD staβfree
N
ideal
and
β
becomesbility. Namely, the region between βfreeNNavailable with an ideal-wall, which can be called the “wallstabilized high-βN region.” Meanwhile, because on realauthor’s e-mail: matsunaga.go@jaea.go.jp∗) This article is based on the invited talk at the 24th JSPF Annual Meeting(2007, Himeji).

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c 2009 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 4, 051 (2009)mas where βfree
N was lower than that in the positive shear
plasmas on JT-60U [9]. The resistive wall location eﬀect
has also been investigated in the ohmic discharges where
the current-driven RWMs are destabilized by decreasing
the surface-q below a low integer value [10]. In studying
the plasma rotation eﬀect JT-60U has the advantage thatthe plasma toroidal rotation can be widely controlled using neutral beams (NBs) with varying combination of net
torque input. The NBs in JT-60U are composed of coand counter-tangential and perpendicular injections (SeeSec. 2.1). Utilizing the NB system the plasma rotation waschanged at a constant βN in order to evaluate the plasma
rotation eﬀect only. Hereafter plasma rotation will be used
to denote “toroidal” plasma rotation. This paper provides
detailed results of high-βN experiments that focused on therotational stabilization of RWM.

N-NBs is less than that from the P-NBs because the N-NB
beam current is less instead of the high beam energy. These
NBs enables both the direction and profile of a plasma rotation to be controlled while keeping βN by stored energy
feedback control.

2.2 Ferritic steel tiles and resistive wall
Before the 2006 experimental campaign, ferritic steel
tiles were installed inside the JT-60U vacuum vessel to reduce a toroidal magnetic field ripple that could enhance
fast ion ripple loss [15]. For example, the toroidal magnetic field ripple can be reduced from 1.5% to 1.0% at
Bt = 1.6 T. That reduction improves the absorbed NB
power by about 35% with large volume plasmas close to
the wall. High-βN experiments can take place with theplasma close to the wall for wall stabilization with suﬃcient heating power. Figure 2 gives the poloidal cross section of JT-60U with a plasma and the ferritic steel tiles.
The ferritic steel tiles cover the inside of the outboard vacuum vessel where the toroidal ripple is large. In the experiments the plasma was moved close to the outer wallby up to d/a 1.2, where d is the wall radius. As mentioned above, a RWM is characterized by the resistive walltime τw defined as τw = μ0 dδ/ηw , where ηw and δ are thewall resistivity and thickness of the resistive wall. The JT60U vacuum vessel consists of double layers of Inconel
625 whose thickness is 6.1 mm [16]. The resistivity of Inconel is about 1 × 10−6 Ωm, which corresponds to a resistive wall time of τw ∼ 10 ms. The eddy current on the ferritic steel tiles is thought to be negligible compared with

2. High-βN Experiments on JT-60U
2.1

Neutral beam injection system

In order to investigate the critical rotation needed for
RWM stabilization the plasma rotation was controlled using neutral beam (NB) injections in JT-60U. As shown in
Fig. 1, the JT-60U has various types of NBs [13,14]. There
are 11 positive ion based NBs (P-NBs) with an energyof ∼85 keV. The P-NBs consist of 4 tangential (TANGNBs) and 7 perpendicular NBs (PERP-NBs). The TANGNBs contain 2 co-tangential (in the direction of Ip ) and 2
counter-tangential (in the opposite direction of Ip ) injections. The power of all the P-NBs is ∼2 MW. In addition,
there are 2 negative ion based NBs (N-NBs) with an energy of ∼350 keV. Note that the momentum input from theFig. 2 Poloidal cross section of JT-60U with a plasma and theferritic steel tiles. The ferritic steel tiles cover the insideof the outboard vacuum vessel. The red line indicates theseparatrix.

Fig. 1 Top view of the JT-60U torus with NB heating system.
PERP and TANG stand for perpendicular and tangentialNBs; N-NB is negative ion based NB.

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Inconel vessel because the clearance between the tiles isabout 1 cm and each tile has several 2 mm slits to avoid
any large eddy currents, and hence with regard to low-n
MHD stability it is reasonable to expect that the Inconel
vessel only determines the wall eﬀect.

2.3

spectroscopy (CXRS) [17], described here as the angularfrequency fφ , were larger than 2 kHz at both the q = 2
and q = 3 surfaces (Fig. 3 (d)). Continuous NB injection
was used to achieve βN reaching about 2.8 (Fig. 3 (e)). At
t = 6.0 s one of the counter-NBs was switched to co-NB
in order to change only the plasma rotation but not βN(Figs. 3 (b) and (c)). In addition, in order to keep βN constant, a stored energy feedback control, which is used tocontrol a number of the PERP-NBs, was applied after t =5.9 s. The plasma rotation then slowly decelerated, and finally a strong β-collapse occurred at t = 6.23 s (Fig. 3 (e)).
Before the NB switching took place at t = 6.0 s, the plasma
rotation already began to decelerate. The deceleration isdue to the reduced number of PERP-NBs by the stored energy feedback control because the PERP-NBs can drive acontour plasma rotation due to fast ion ripple loss. Ideal
MHD stability analysis using MARG2D [18] revealed βfreeNto be estimated to be 2.3, that is, ∼ 3 li [19]. The achievedfree
2.8 exceeded βfree
βN
N (Fig. 3 (e)). High-βN above βN
was therefore achieved for the time duration of 0.5 s. At
t = 6.21 s the n = 1 instability was growing (Fig. 3 (f)).
That instability then finally induced a strong β-collapse.
Figure 4 shows enlarged waveforms in Fig. 3. Just be-Experimental results

For the purpose of identifying of the critical rotation needed for RWM stabilization high-βN experiments
were carried out with the plasma close to the outer wallat d/a 1.2. As mentioned above, since the ferritic steel
tiles improve the NB absorption power, it is possible toaccess the high-βN region above βfree
N where the wall stabilization is expected. Figure 3 gives the waveforms ofa high-βN discharge where Ip and Bt were 0.9 MA and1.57 T, respectively. In this discharge, in order to accessthe high-βN above βfree
N , suﬃcient momentum input fromthe TANG-NBs was used to rotate the plasma. The plasma
rotations measured using charge exchange recombination

Fig. 4 Expanded waveforms of high-βN (Fig. 3) and high-βp discharges just before collapse (disruption): (a) time evolution of βN and Dα emission, (b) n = 1 integrated magnetic
perturbation with the poloidal cross section. cf. (c) and(d) give the high-βp discharge with d/a 1.7.

Fig. 3 Waveforms of high-βN experiment: (a) Plasma current,
PERP-NB and N-NB injection power, (b) counter- and(c) co-TANG-NB power, (d) plasma rotation frequency
at q = 2 and 3, (e) βN with 3 li ∼ βfree
N , (f) n = 1 integrated
magnetic perturbation.

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fore the β-collapse an n = 1 magnetic perturbation was
gradually growing. The growth time of the instability was
about 10 ms, which is comparable with the resistive walltime τw of JT-60U. During that growth phase the confinement degraded with the same time scale as the instability shown in Fig. 4 (a). Since this instability directly affects the energy confinement it suggests that the instability
has a global mode structure. The results indicate that theobserved instability is an n = 1 RWM. For the sake ofcomparison, the instability observed in the high poloidal-β(βp ) discharge with Ip /Bt = 1.5 MA/3.57 T is provided in
Figs. 4 (c) and (d). The time ranges with both the plots is
150 ms. Note that a high-βp discharge is associated witha large internal transport barrier (ITB), and thus a fairly
steep pressure gradient exits. In this discharge the plasma
was positioned far from the wall with d/a 1.7. The discharge was terminated by a disruption that occurred due toan n = 1 instability. The growth time of the observed instability was less than 1 ms, which is much shorter than the
RWM growth time. It is considered that wall stabilization
with d/a 1.7 is less eﬀective than with d/a 1.2. The
instability is thought to be an ideal kink-ballooning modethat becomes unstable as βN reaches βfree
N [20]. However,
it is diﬃcult to clearly identify the instability with a large
plasma-wall separation because a RWM root continuously
connects to the ideal kink-ballooning mode [6].
In the βN constant phase, ion temperature T i aroundthe q = 2 and q = 3 surfaces basically remained un-changed within an accuracy of |ΔT i /T i | < 5%. Internal
inductance li slightly increased with Δ li / li ≤ 5%, whichis due to j(r) penetration. These measurements indicatethat ∇p(r) and j(r) basically remained unchanged. It isconsidered therefore that the RWM became unstable dueto the deceleration of the plasma rotation only. As shownin Fig. 4, edge localized modes (ELMs) were continuously
observed. While the RWM was growing a final ELM wasobserved at t = 6.22 s without any change in ELM frequency. This then means that the RWM did not seem tohave aﬀected the pedestal structure at first. Namely, theRWM began to grow from the core region, thus suggesting
the eigen-function to be a large structure inside the plasma.

2.4 Mode structure of RWM
Figures 5 (a) and (b) give the contour plots of the perturbed magnetic field with the high-βN discharge where
the RWM was observed. These were measured using thetoroidally-distributed eight saddle loops and poloidallydistributed magnetic probes. The upper plots provide thetoroidal distribution of the radial magnetic components
δBr . The lower plots provide the poloidal distributionof the poloidal magnetic components δBθ . Both signals
are integrated, and the toroidal axisymmetric component(n = 0) is removed from the upper one.
As seen in Fig. 5 (a) the RWM has a clear n = 1
toroidal mode structure. Meanwhile, Fig. 5 (b) reveals thatthe poloidal structure is not uniform. Namely, the ampli-

Fig. 5 Comparison of poloidal and toroidal mode structures between n = 1 RWM (left) and m/n = 3/1 tearing mode (right). Upper
plots give the toroidal distributions of perturbed radial magnetic fields δBr ; lower plots give the poloidal distribution of perturbed
poloidal magnetic fields δBθ . Arrows indicates the direction of the mode rotation. Toroidal angle is defined as the same direction
as Ip ; poloidal angle is defined from the midplane at the LFS.

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RWM grew, T i inside the q = 2 surface was gradually
dropping, and finally the T i profile globally lost. This
then means that the RWM has a radially extended eigenfunction that is also consistent with the MARG2D results(See Sec. 2.5).

tude at the low field side (LFS: bad curvature) is larger
than that at the high field side (HFS: good curvature).
Here, the poloidal angle is defined from the midplane at
the LFS; the divertor region corresponds to around −π/2.
In Fig. 5 (b), although the poloidal structure seems to have
two periods (m = 2), the wave length (angle) is not π, andis rather shorter. The dominant poloidal mode number istherefore considered to be m ≥ 3, and the poloidally nonuniform structure is attributed to the multi poloidal components. This is consistent with the result calculated using MARG2D (See Sec. 2.5). In addition, the RWM was
slowly rotating in the co-direction with a mode frequencyof ∼20 Hz. Since the RWM is a wall-trapped mode, a frequency of zero could be predicted if there was no plasma
rotation. With a plasma rotation, the RWM is theoretically predicted to have a slow rotation comparable to anorder of τ−1
w [3]. Actually, the observed RWM rotated in
the co-direction to Ip . The direction was thought to be followed by the direction of the plasma rotation at the q = 2
surface. For comparison, the magnetic structures of an
m/n = 3/1 tearing mode observed in the ohmic discharge
are provided on the right-hand side of Fig. 5. In this discharge the m/n = 3/1 tearing mode was destabilized onlyby the plasma current. Since the tearing mode was composed of a single poloidal component the poloidal structureis almost uniform. The mode frequency was about 300 Hz
in the counter-direction of Ip . In this discharge, since no
NB was injected, the mode frequency was considered to
be followed by a spontaneous plasma rotation at the q = 3
surface that was determined by the transport.
Figure 6 gives the time evolution of the ion temperature T i profiles during the growth of the RWM. As the

2.5 MHD stability analysis
MARG2D code [18], which is the liner MHD stability
analysis code, was used to estimate the MHD stability withand without a conducting wall near the plasma. Note that
MARG2D is based on ideal MHD analysis, not including
the eﬀect of the resistive wall and the plasma rotation. Figure 7 (a) provides a stability diagram of critical-βN versus
the wall location d/a. Here, d/a = ∞ corresponds to thecase of no-wall. Decreasing d/a improves the ideal-wall
ideal
limit, thus, expanding the region between βfree
N and βN .
ideal
the ideal kink-ballooning
In the region βfree
N ≤ βN ≤ βN
mode is stabilized by an ideal-wall, and thus is a wall-Fig. 7 MARG2D results: (a) Stability diagram of βN vs wall
location d/a, (b) eigen-function of ideal kink-ballooning
mode with an ideal-wall.

Fig. 6 Time evolution of ion temperature profiles during n = 1
RWM growth measured using CXRS.

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stabilized high-βN region. The open circle in Fig. 7 (a) describes the corresponding point in this experiment where
the RWM was observed. In the experiment the plasma wasstable with an ideal-wall but unstable without a wall. As
mentioned above, since RWM was predicted to be unstable
ideal
in the region βfree
N ≤ βN ≤ βN , that observation is consistent with the prediction. The eigen-function of the ideal
mode with an ideal-wall is provided in Fig. 7 (b) as the radial displacement. Note that the eigen-function is shownas rξr , allowing the 2D eﬀect to be understood, thus, themode expanse in the poloidal direction. From the calculated eigen-function, it is predicted that the driving at theq = 2 surface is dominant. In such a high-βN plasma, both∇p(r) and j(r) determine the MHD stability. The internal
components m = 1, 2, 3 are driven by ∇p(r) and the external components m ≥ 4 are driven by j(r). Since the overall
structure is localized at the low field side (LFS), this mode
can induce an eddy current at the outer wall, suggestingthat the stabilizing eﬀect of the outer wall is larger than the
inner one. At the moment, it is thought that the estimatedeigen-function qualitatively agrees with that of the resistive
wall, except near the wall region, and although the analysis
does not take into account wall resistivity.

2.6

Plasma rotation profiles

In this experiment the RWM was observed as theplasma rotation was being reduced while keeping βN constant by the stored energy feedback control. This meansthat the plasma rotation is considered to be capable ofchanging the stability of RWM from stable to unstable.
Figure 8 gives the time evolution of the plasma rotation
profiles measured using CXRS and with the q-profile measured using motional stark eﬀect (MSE) spectroscopy [21].
After switching from counter-NB to co-NB the rotation
profiles decelerated around the q = 2 surface. In particular, since the eigen-function estimated using MARG2D
has a dominant component for m = 2 compared with theother poloidal components, the plasma rotation at q = 2
surface was thought to be eﬀective in the stabilizing of the
RWM. At the RWM onset the plasma rotation at q = 2 wasaround 0.5 kHz. This plasma rotation is considered to be
the critical plasma rotation for RWM stabilization.

Fig. 8 (a) Time evolution of plasma rotation profiles afterswitching counter- to co-TANG-NBs until RWM onsetand (b) q-profile at t = 6.2 s.

2.7 Cβ vs plasma rotation diagram
It is found that the critical plasma rotation for RWM
stabilization is much less than 1% of the Alfvén speed at
the q = 2 surface. To clarify the dependence of the criticalrotation on βN , the target value used in the stored energy
feedback control was systematically changed from shot toshot. Figure 9 provides the results obtained from the βN target scan as a Cβ versus fφ diagram, where Cβ is deideal− βfreefined as Cβ = (βN − βfree
N )/(βN
N ). Namely C β = 0
and 1 correspond to the no-wall (βN = βfreeN ) and ideal)
limits,respectively.
Theaxes gives thewall (βN = βidealN
plasma rotation frequency fφ and its corresponding nor-

Fig. 9 Dependence of critical plasma rotation with RWM stabilization on Cβ . Circles indicate the RWM onsets. The
axes plot plasma rotation frequency fφ and that normalized using the Alfvén time fφ τA at the q = 2 surface. The
red curve corresponds to the discharge in Fig. 3.

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malized value over the Alfvén time τA defined as 2πR/VA ,where R and VA are the major radius and the Alfvén speed,
respectively.
Each trajectory corresponds to the time evolution of asingle discharge, with the open circles revealing the onsetof the RWM. In these discharges the plasma rotation was
first accelerated in order to raise βN . When βN reached
the target value of βN the plasma rotation was reducedby switching the TANG-NBs as mentioned above. The
RWMs were triggered when the plasma rotation became
the critical value. The boundary in the diagram reveals thedependence of the critical rotation. The dependence on Cβ
is not strong, indicating that accessing βideal
could be posN
sible even with the slow plasma rotation ∼ 0.3% of VA .
will
The results indicate that high-βN operation up to βidealNbe possible in ITER and a fusion reactor where the plasma
rotation is predicted to be slower than 1% of the Alfvénspeed.

at the q = 2 surface was less than 1 kHz, corresponding
to about 0.3% of the Alfvén speed. Moreover, the dependence of the critical rotation on βN was investigated bychanging the target value of the stored energy feedback
control. This resulted in the obtained dependence not being
strong against Cβ , which then means that a high-βN operis possible in ITER and fusion reactors
ation up to βidealN
where a fast rotation can no longer be expected. It should
be noted that experimental results obtained on DIII-D alsosuggest the slow critical rotation for the RWM stabilization [22–24]. On DIII-D high-βN experiments took placeby using balanced-NB injections based on a co-plasma rotation. Theoretically the kinetic eﬀect would be considered
to play an important role in a slow critical rotation [25,26].
Based on the experimental results, the further research on
the rotational stabilization of the RWM is required fromboth the theoretical and experimental points of view.

Acknowledgments
3. Summary

This work was supported in part by a Grant-in-Aid
for Young Scientists (B) from the Ministry of Education, Culture, Sports, Science and Technology of Japan,
No. 17760672 and No. 21760702.

We have carried out the experiments in order to investigate the rotational stabilization of the RWM in the JT60U tokamak. The plasma rotation was controlled using
a combination of TANG-NBs while keeping βN constantusing the stored energy feedback control. During the βN
constant phase the plasma rotation was only decelerated,
and then an instability whose growth time was about 10 ms
appeared. The slow growth time was equivalent to the resistive wall time of JT-60U. Compared with the instability
observed in a high-βp plasma with d/a 1.7 the growth
1.2 was clearlytime in a high-βN plasma with d/a
slower. MARG2D analysis revealed that the achievedβN where the instability was observed would exceed βfree
N .
From these results, the instability is identified as the RWM.
Detailed measurement of the mode structure revealed that
the RWM to have a clear n = 1 toroidal mode structure.
Meanwhile, the poloidal mode structure was non-uniform,
and thus the amplitude at the LFS was much larger thanthat at HFS. Namely, the RWM has a ballooning structure poloidally. This point completely diﬀers from that ofan instability such as the tearing mode, which only has asingle poloidal component. The T i -profiles measured using CXRS during the growth of the RWM reveal that the
RWM to have a radially global mode structure. In addition, the RWM was slowly rotating with about τ−1
w . Thedirection of the mode rotation was found to follow the direction of the plasma rotation at the q = 2 surface, which isalso consistent with the MARG2D analysis and theoreticalpredictions. At the onset of the RWM the plasma rotation[1] ITER Physics Basis, Nucl. Fusion 47, S285 (2007).
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