J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)51–59
000–000

Recent Results from LHD Experiment with Emphasis on
Relation to Theory from Experimentalist’s View
YAMADA Hiroshi, IDA Katsumi, WATANABE Kiyomasa, SAKAKIBARA Satoru, INAGAKI Shigeru,
MURAKAMI Sadayoshi1, NARUSHIMA Yoshiro, OHYABU Nobuyoshi, YOKOYAMA Masayuki,
YOSHINUMA Mikiro, COOPER W.A.2, KOBUCHI Takashi, OSAKABE Masaki, TOI Kazuo, SUZUKI Yasuhiro3,
AKIYAMA Takeshi, ASAKURA Nobuyuki4, ASHIKAWA Naoko, EMOTO Masahiko, FUJITA Takaaki4,
FUJIWARA Masami, FUNABA Hisamitsu, GONCHAROV Pavel, GOTO Motoshi, HAMADA Yasuji,
HIGASHIJIMA Satoru4, HINO Tomoaki5, HOSHINO Mitsuyasu6, ICHIMURA Makoto7, IDEI Hiroshi8,
IDO Takeshi, IKEDA Katsunori, ISAYAMA Akihiko4, ISOBE Mitsutaka, ITOH Takafumi6, ITOH Kimitaka,
KADO Shinichiro9, KALININA Diana10, KANEBA Takahiro10, KANEKO Osamu, KAWAHATA Kazuo,
KAWAZOME Hayato3, KONDO Katsumi3, LYON J.F.11, MASE Atsushi8, MASUZAKI Suguru,
MATSUOKA Keisuke, MIURA Yukitoshi4, MIYAZAWA Junichi, MORISAKI Tomohiro, MORITA Shigeru,
MUTO Sadatsugu, MUTOH Takashi, NAGAOKA Kenichi, NAGASAKI Kazunobu3, NAGAYAMA Yoshio,
NAKAMURA Yukio, NAKANISHI Hideya, NARIHARA Kazumichi, NISHIMURA Kiyohiko, NISHIURA Masaki,
NISHIZAWA Akimitsu, NODA Nobuaki, NOTAKE Takashi6, NOZATO Hideaki9, OHDACHI Satoshi,
OHKUBO Kunizo, OYAMA Naoyuki4, OKA Yoshihide, OKADA Hiroyuki3, OZAKI Tetsuo, PETERSON Byron J.,
SAGARA Akio, SAIDA Tomoya12, SAITO Kenji, SAKAMOTO Mizuki8, SAKAMOTO Ryuichi,
SASAO Mamiko12, SATO Kuninori, SEKI Tetsuo, SHIMOZUMA Takashi, SHOJI Mamoru, SUDO Shigeru,
TAKAGI Shoji, TAKAHASHI Yoshiyuki, TAKASE Yuichi9, TAKEIRI Yasuhiko, TAKENAGA Hidenobu4,
TAKEUCHI Norio6, TAMURA Naoki, TANAKA Kenji, TANAKA Masayoshi, TOKUZAWA Tokihiko,
TORII Yuki6, TSUMORI Katsuyoshi, WATANABE Fumitake6, WATANABE Tsuguhiro, WATARI Tetsuo,
YAMADA Ichihiro, YAMAGUCHI Taiki10, YAMAMOTO Satoshi3, YAMAZAKI Kozo, YOSHIDA Naoaki8,
YOSHIMURA Shinji, YOSHIMURA Yasuo, KOMORI Akio and MOTOJIMA Osamu
National Institute for Fusion Science, Toki, 509-5292, Japan1
Kyoto University, Kyoto, 606-8501, Japan
2
CRPP, Ecole Polytechnique Federale de Lausanne, Switzerland
3
Kyoto University, Uji, 611-0011, Japan
4
Japan Atomic Energy Research Institute, Naka Fusion Research Establishment, Ibaraki, 311-0193, Japan
5
Hokkaido University, Sapporo, 060-8628, Japan
6
Nagoya University, Nagoya, 464-8603, Japan
7
Tsukuba University, Tsukuba, 305-8577, Japan
8
Kyushu University, Kasuga, 816-8580, Japan
9
The University of Tokyo, Tokyo, 113-8658, Japan
10
Graduate University for Advanced Studies, Kanagawa, 240-0193, Japan
11
Oak Ridge National Laboratory, Oak Ridge, TN, USA
12
Tohoku University, Sendai, 980-8579, Japan(Received: 6 January 2004 / Accepted: 11 March 2004)

Abstract
The Large Helical Device (LHD) has been extending an operational regime of net-current free plasmas towards
the fusion relevant condition with taking advantage of a net current-free heliotron concept and employing a
superconducting coil system. Heating capability has exceeded 10 MW and the central ion and electron temperatures
have reached 7 and 10 keV, respectively. The maximum value of β and pulse length have been extended to 3.2% and
150 s, respectively. Many encouraging physical findings have been obtained. Topics from recent experiments, whichshould be emphasized from the aspect of theoretical approaches, are reviewed. Those are (1) Prominent features in
the inward shifted configuration, i.e., mitigation of an ideal interchange mode in the configuration with magnetic hill,
and confinement improvement due to suppression of both anomalous and neoclassical transport, (2) Demonstration of©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: hyamada@lhd.nifs.ac.jp
151

Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

bifurcation of radial electric field and associated formation of an internal transport barrier, and (3) Dynamics ofmagnetic islands and clarification of the role of separatrix.
Keywords:
Large Helical Device, energy confinement, MHD stability, radial electric field, magnetic island,internal transport barrier, magnetic configuration

1. Introduction

magnetic islands.
More detailed reports related to LHD experiment can befound in several articles in the current issue.

Experiments in the Large Helical Device (LHD) havebeen progressing steadily since the first plasma in 1998 [1].
LHD has a helical heliotron magnetic configuration [2] andemploys a fully superconducting magnet system, which
provides capability of steady state operation. During 6
experimental campaigns in these 5 years, many encouraging
physical observations have emerged in conjunction withengineering demonstration of superconducting and heating
technologies [3-6]. Intensive theoretical works have been
devoted to the LHD project. Some theoretical predictions havebeen successfully demonstrated in the experiment and some
unexpected but favorable experimental findings have beenrequiring further progress in theory. Major highlights fromrecent experiments which attract theoretical interests arereviewed in this article.
The nominal major and minor radii of LHD are 3.9 m
and 0.6 m, respectively, which leads to the plasma volume of
30 m3. The superconducting coil system including thecryogenic and the power supply systems has provided steadystate magnetic field around 3 T routinely. A pair of helicalcoils consists of 3 layers with independent power supply. The
aspect ratio of the plasma and rotational transform can becontrolled by coordinating coil currents in each layer. Threesets of poloidal coils can change the position and the shapeof the plasma column. In particular, the position of themagnetic axis has distinguished effect on both transport andMHD (magneto-hydro-dynamics) stability. In addition tothese main superconducting coils, LHD has ten pairs of
perturbation coils which can generate low-order magnetic
islands in the plasma. This experimental set-up provides large
flexibility of magnetic configuration. The available heating
source has been extended to 10.3 MW of NBI (Neutral Beam
Injection), 2.1 MW of ECH (Electron Cyclotron Heating) and2.7 MW of ICH (Ion Cyclotron Heating). The NBI system isequipped with three tangential negative-ion-based neutralbeam injectors and the nominal injection energy is as high as
180 keV [7]. The microwave sources used for ECH are two
84 GHz gyrotrons, two 82.7 GHz gyrotrons and three
168 GHz gyrotrons [8]. Six ICRF (Ion Cyclotron Resonant
Frequency) antennas of a single center strap have been
installed at the three toroidal sections [9].
In the following sections, first the outline of recent
progresses is described briefly. Then, three major topics arepresented, i.e., (1) prominent feature in the configuration with
the inward shifted magnetic axis, (2) observation ofbifurcation of radial electric field and associated formation ofinternal transport barrier, and (3) effect and dynamics of

2. Outline of progress
Along with growth of heating capability, plasma
parameters have been progressing steadily. The plasma stored
energy has reached 1.25 MJ, which is catching up leadinglarge tokamaks. Also central electron and ion temperatures
have reached 10 keV and 7 keV, respectively and the
maximum pulse length has been beyond 2 min. The maximum
values of β and density to date are 3.2% and 1.6×1020 m–3,
respectively [6]. In particular, high β discharges have been
demonstrated in the region where a linear MHD stability
theory predicts growth of an interchange mode. Density limit
is determined by the power balance and no hard limit like theGreenwald limit in tokamaks has not been recognized [10].
The LHD enables exploration of physics of net-current freeplasmas towards fusion relevant regime represented in above
mentioned typical plasma parameters. In addition, nondimensional parameters are of importance as well to getcomprehensive physical understanding. Figure 1 shows theachieved regime in the primarily important non-dimensional

Fig. 1

2
52

Operational regime of net-current free plasmas inhelical experiments (LHD, W7-AS, ATF, CHS andHeliotron E) on the plane of normalized gyro radius ρ*and collisionality νb*. Here collisionality is normalized
by the bounce frequency in a banana orbit.

Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

parameters, i.e., normalized gyro radius ρ* and collisionality
νb*. Data from medium sized helical experiments are alsoplotted. It can be pointed out that the LHD has largely
extended the envelope of the operational regime of netcurrent-free plasmas. Two major approaches to the reactor
regime poses two major subjects. In the direction to low ρ*,
the understanding anomalous transport is a key. Also in the
direction to the deep collisionless regime, controlling
neoclassical transport is, in particular, important in helicalsystems.
A database for energy confinement time τE in helicalsystems has advanced with compilation of data from LHD.
Figure 2 shows the comparison of experimental data with theprediction from the ISS95 scaling [11],τE

ISS 95= 0.079a2.21

β∝ τB ρ *–0.71

0.65

R

ν

–0.16

P

–0.59

–0.04
*

0.51

ne B

ι

0.83 0.4
2/3

the core [14]. The former factor seems to be robust
characteristics in LHD since the edge pressure at ρ = 0.9 canbe described by a unique scaling independent of the positionof the magnetic axis [12]. Here ρ is the normalized minor
radius. In addition to the former factor, the latter factor
distinguishes the advantage of the geometry with the inward
shift of the magnetic axis from the outward shifted
configuration. The upper envelope of data from LHD as wellas W7-AS is comparable to tokamak H-mode.

3. Effect of tailoring magnetic
configuration
3.1 Confinement and thermal transport
In the following discussions including MHD nature, theposition of the magnetic axis is a key. When the magnetic
axis is shifted inward in LHD, the orbit of helically trapped
particles fits to the magnetic flux surfaces well. In contrast,
deviation between the orbit and flux surface becomes large
in the case with outward shift of the magnetic axis. Alongwith the same direction, a good neoclassical transport can be
anticipated in the inward shifted configuration. The scenario
to get good confinement in terms of neoclassical transport
can be summarized as follows. In the 1/ν regime, a heat flux
q is a very strong function of temperature T like.

Here, a, R, P, n–e, B and –ι 2/3 are minor and major radii in theunit of m, heating power in the unit of MW, line averaged
electron density in the unit of 1019 m–3, and magnetic field in
the unit of T, and rotational transform at two thirds radius.
Non-dimensional expression of the energy confinement timenormalized by Bohm time τB indicates that ISS95 ischaracterized by gyro-Bohm nature and no definitive
dependence on β and collisionality. Data from tokamak Lmode and H-mode are also plotted in Fig. 2 and ISS95 gives
tolerable fits to both data set. Performance of LHD plasmas
has shown improvement upon ISS95 up to a factor of two[12]. This improvement is proved to be due to (1) noenhancement of heat diffusivity in the edge and consequent
high edge pressure [13] (2) reduction of heat diffusivity in

q ≈–

εt
erB

2

helical ripples, LT is the scale length of the temperature
gradient, e is the unit electrical charge, and r is the minor
radius. In this regime, super-banana motion of helicallytrapped particles degrades confinement. This is so called
helical ripple transport. By optimizing geometry, an effective
helical ripple can be reduced, consequently heat flux can besuppressed [15]. One of the real approaches is the inward shiftof the magnetic axis. This scenario is not, however, sufficient
to realize good confinement in the deep collisionless regime.
Another scenario relies on favorable effect of radial electricfield Er. In the non-axisymmetric system, the radial electricfield is determined by the neoclassical ambipolar relation.
When the radial electric field is present, the 1/ ν regime⎯changes into the collisional detrapping (√ν ) regime where⎯D √⎯ν ∝ √ν /Er1.5 and then the collisionless detrapping (ν)
regime where Dν ∝ ν /Er2. The heat flux in the ν regime isexpressed by q ≈ –Fig. 29/2

ε h1.5 T , where εt and εh are toroidal andLTεt n 23/2

ε h0.5 T . When large positive Er is
2
LTErobtained in the electron root, the heat flux can be reduced
significantly. It is pointed out that negative Er causes
degradation of confinement under some circumstances due tohelical and/or toroidal resonance [16]. Therefore the electronroot is also favorable to avoid this unfavorable resonance.
Figure 3 shows the confinement enhancement factor on
ISS95 for the configurations with a different position of themagnetic axis. A distinct confinement improvement by the
inward shift (the major radius of the magnetic axis: Rax =3.6 m) can be seen. Hereafter, this configuration is represented
by ISC (Inward Shifted Configuration). Figure 4 shows theconfinement enhancement factor as a function of collisionality

Comparison of energy confinement in experimentswith prediction from the ISS95 scaling.

3
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Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

Fig. 3

Confinement enhancement factor on ISS95 for thecases with different magnetic axes (Rax = 3.6 m, 3.75 m,
and 3.9 m).

Fig. 5

Fig. 4(a) Electron temperature profiles and (b) Effective
thermal diffusivity profiles for 3 cases with different
magnetic axes (Rax = 3.6 m, 3.75 m, and 3.9 m). Lineaveraged density (3.1×1019 m–3) and heating power(6.3 MW) are the same for all cases.

(Ion Temperature Gradient mode)/TEM (Trapped ElectronMode) by the FULL code has been investigated [17], butcoherent results have not obtained yet. If a crude argument isallowed, ITG/TEM are more stable in LHD than in tokamak
because of shorter connection length between bad and good
curvatures [18] and that ITG/TEM are more unstable in the
inward shifted configuration because of bad curvature due tomagnetic hill.
Figure 5 shows the profiles of electron temperature andeffective thermal diffusibity in the discharges with different
magnetic axis. Besides the position of magnetic axis, major
parameters are fixed on the same condition. Line averaged
density is the same at 3.1×1019 m–3 although there is somestructural difference in the profile. The deposited power isalso the same at 6.3 MW and the deposition profiles are quite
similar to each other. Nonetheless, pronounced difference inelectron temperature can be seen (see Fig. 5(a)). The central
temperature is doubled when the axis is shifted inward from
3.9 m to 3.6 m. This confinement enhancement isdistinguished in the core region within ρ of 0.7 while theperipheral region does not show any significant difference.

Confinement enhancement factor is plotted as afunction of collisionality (νb*) for the cases withdifferent magnetic axes (Rax = 3.6 m, 3.75 m, and3.9 m).

for 3 cases with different positions of the magnetic axis. It
should be noted that improvement in ISC can be seen in wide
collisionality and remains in the collisional regime where theneoclassical transport does not play an essential role.
Therefore this geometrical property in ISC causes reductionof anomalous transport [12]. Neoclassical optimization also
contributes improvement, which is indeed seen more clearlyin the deep collisionless regime in Fig. 4. Confinement
degradation dependent on collisionality is observed in theconfiguration with outward shifted magnetic axis which is not
optimized in terms of neoclassical transport in the 1/ν regime.
In other words, no distinct dependence of confinement in ISC
even in the deep collisionless regime is a demonstration ofgeometrical optimization for neoclassical transport theory.
With regard to anomalous transport, a linear stability of ITG
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Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

Improvement of thermal transport in ISC is clear in the coreregion although all cases are located at the same level in the
peripheral region (see Fig. 5(b)). In the second section,
confinement enhancement in LHD is compared with medium
sized heliotrons (ATF, CHS and Heliotron E). Compared withthe medium sized experiments, the scale merit beyond the size
scaling in LHD has been found. It is due to high edgepressure. The thermal diffusivity is not deteriorated even close
to the boundary. This leads to confinement enhancement offactor of 1.8 in LHD on medium sized heliotrons. In addition,
further improvement in the core region by ISC results in theconfinement enhancement factor of up to 2.6.

3.2 MHD stability
In LHD, it has been mentioned that ISC, i.e., Rax =3.6 m has better confinement properties when the confinement
performance is evaluated based on the ISS95 global energy
confinement scaling [11]. From a viewpoint of high-energy
particle confinement properties, the configuration with themagnetic axis shifted inward is considered to be a better
configuration. Also, from a viewpoint of the MHD
equilibrium limit, ISC provides room for the Sharanov shift
and consequently yields the higher equilibrium β limit. On
the contrary, in heliotron devices, ISC has been considered to
be unfavorable from a viewpoint of MHD stability becauseof enhanced magnetic hill. However, the MHD instability of
ISC is found to be much mitigated from the prediction of alinear stability theory in the experiment. Volume average β ’sof 3.2% with pellet and of 3% by gas puffing have beenachieved without any disruptive phenomena. Magnetic axis
shift with ∆R/ap ~ 50% are observed in 〈β〉 ~ 2.5%. Abrupt
declination of global energy confinement time against β has
not been observed below 〈β〉 ~ 3.2%.
LHD has a strong magnetic shear, and there are many
low order rational surfaces from –ι = 2/5 to 3/2. Nonetheless,–ι = 1/2 and –ι = 1/1 rational surfaces are considered as typicalrational surfaces at the core and the edge, respectively, where–ι = 1/2 and –ι = 1/1 rational surfaces are located at ρ ~ 0.5
and ρ ~ 0.9, respectively. Figure 6 (a) shows the experimentally observed pressure gradients at ρ = 0.5 in Rax = 3.6 m
configuration with 〈β〉-dβ/dρ diagram. Solid and dashed lines
denote the stability boundaries for low-n ideal mode andMercier mode, respectively [19]. The low-n ideal MHD
unstable region is calculated by a 3-D MHD stability
analyzing code (TERPSICHORE [20]). Here, the growth rateof a low-n ideal MHD mode, γ low-n = 10–2 ωA is defined as
the stability boundary, which corresponds to Mercier
parameter [21], DI ~ 0.25. Here ωA is the Alfvén frequency.
It should be noted that the stability boundary based on the
low-n mode analysis is considered as that for global modes,
and that the Mercier condition, DI = 0, corresponds to thestability boundary for localized modes [22]. When plasmas
approach the high β regime, the achieved pressure gradientslook to avoid the low-n linear ideal MHD mode unstableregion in the core. Although most of the experimentallyobserved pressure gradients do not enter the low-n unstable

Fig. 6

Evolution of pressure gradient at core ((a) ρ = 0.5) andat periphery ((b) ρ = 0.9) with the increase of β. The
dotted line is the boundary of Mercier criterion andhatched regionis low-n ideal MHD unstable region
predicted from the calculation by TERPSCICHORE[18].

region, they do not seem to be limited by the Mercier
condition. In particular, low-n unstable region disappears at〈β〉 = 1.8% due to spontaneous formation of magnetic well,
the pressure gradient evolves more than twice larger thanthose below 〈β〉 = 1.8%. The amplitude of the resonant
magnetic fluctuation (m/n = 2/1) increases as dβ/dρ increases.
Then the increment of the amplitude becomes smaller in 〈β〉= 1 ~ 1.8% once, where the β-gradients are saturated against
β, than in other β region. The resonant fluctuation in the core
has not been observed in the β region of 〈β〉 < 0.3% and 〈β〉> 2.3%, where corresponds to Mercier stable region [23].
Figure 6(b) shows the experimentally observed pressure
gradients at ρ = 0.9 in Rax = 3.6 m configuration with〈β〉-d β/dρ diagram [19]. The upper limit of the achievedpressure gradients at ρ = 0.9 in the profile data analyzed here
is located at the beginning of the unstable region. At the edge
region, it is still unclear whether the low-n ideal mode limits
the pressure gradients because the experimentally achieved β
555

Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

4. Observation of bifurcation of radial
electric field and associated formationof internal transport barrier

is not still enough high to make clear it. On the contrary, theβ-gradients does not seem to care the Mercier condition in
the edge as well as in the core.
There exists an experimental observation suggestinga sign of effect of low-n modes on a plasma discharge.
Figure 7 is a waveform of a typical high-β discharge [24]. In
this case the m/n = 2/1 mode which has the resonance in thecore is pretty quiet. However, the burst of modes localized in
the periphery and the edge start over β of 2.3%, and the stored
energy and confinement seem to hesitate about further
evolution. Also it should be noted that m/n = 2/3 mode has
no resonant surface at least in the vacuum calculation.
Possibility of healing of the ergodic region in the edge or
excitation of external mode should be considered [25].

Importance of radial electric field, in particular, in nonaxisymmetric configuration, has been recognized widely.
Understanding of bifurcation mechanism of Er is progressingin the LHD experiment. A highlighted event attracting bothexperimental and theoretical interest is the transition from theion root to the electron root in collisionless plasmas. This
event is predicted by the neoclassical ambipolar condition,i.e., balance between the electron flux Γe and the ion flux Γi[26]. A theoretical calculation for the radial electric field in
the edge region is shown in Fig. 8 (a) [27]. In this calculation,
the temperature is fixed and the density is scanned. Therefore
the horizontal axis can be rephrased into collisionality. Herethree configurations with different magnetic axis position areplotted. In the high density regime, only one ion root exists.
As the density decreases, namely, collisionality decreases,
multi-roots come up and transition to the electron root
becomes possible. The threshold density, which is equivalent
to collisionality, depends on configuration. In ISC, transition
density is quite low since asymmetric flux is suppressed.
Figure 8 (b) is the corresponding experimental observationon the same diagram [27]. In ISC, the plasma remains in theion root. In contrast, the electron root is formed in the caseof outward shifted configuration. In the case between them,
the plasma wanders in the halfway. It is also pointed out that
improvement of heat transport is clarified experimentally inthe case with large neoclassical transport [28].
High electron temperature has been achieved throughformation of an internal transport barrier (ITB) [29] associatedwith the transition from the ion root to the electron root [26].
When the central ECH is applied to NBI target plasmas,
abrupt formation of ITB by tiny increase of ECH power has
been observed. Figure 9 (a) shows the electron temperature

Fig. 7

Waveforms of a high β discharge. A solid curve is β, adotted curve is a confinement enhancement factor on
ISS95, and a thin solid curve is an amplitude ofmagnetic fluctuation of m = 2/n = 3 mode [23].

Fig. 8

Radial electric field is plotted as a function of density for the cases with different magnetic axes (Rax = 3.5 m, 3.75 m, and3.9 m). (a) Calculation based on neoclassical transport. (b) Experimental observation [26].

656

Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

Fig. 9Fig. 10 Plasma response to externally generated magnetic
island of m = 1/n = 1. (a) Field line calculation of
vacuum magnetic field. (b) Parameter space (Teisland, ne)for island suppression. Open circles are the cases withno detectable island. Solid circles are the cases with avisible island in electron temperature profile [30].

Formation of internal transport barrier. (a) Electron
temperature profiles for different heating conditions. (b)Normalized heat conductions of inside ITB (ρ = 0.15)
and outside ITB (ρ = 0.4) is plotted as function of thetemperature gradient [29].

are discussed. Reduction in heat diffusivity by a factor of
5–10 inside the ITB has been confirmed by a power scan anda heat/cold pulse propagation scheme. The transport analysis
shows that the χeinc in the plasma with ITB is 1 m2/s, which
is much lower than that without ITB by more than an orderof magnitude. Because of χeinc < χe, the χe decreases as theheat flux is increased inside the ITB (confinement
enhancement). It should be noted that the heat transport in
ITB is still anomalous and it is reasonable that anomaloustransport is suppressed by Er or its shear.

profiles. NBI target plasma is shown in a dotted curve [30].
A broken curve is the case of ECH power of 0.58 MW.
Increase of only 200 kW of ECH power pushes the central
electron temperature by more than 50% and a large
temperature gradients appears near the plasma center at ρ <0.3. The radial profiles of Er are derived from poloidal flow
velocity vθ measured with charge exchange spectroscopy(CXS) using fully ionized Neon (0.5–1%) impurity [28]. The
transition of Er from small positive value to the large positive
value is observed at ρ < 0.4 when the ECH power exceeds
the threshold. In the case with the collisionality νb* (ρ = 0.27)> 0.3, there has not been observed transition of Er andincrease of temperature gradient.
The formation of the electron internal transport barrier
is due to the bifurcation phenomena of the electron heattransport, which is clearly demonstrated in the relation
between the electron heat flux normalized by density andtemperature gradient as seen in Fig. 9 (b) [30]. Here, therelation between the temperature gradient and heat flux,
especially incremental χeinc [= (1/n)dq/d(∇T )] in the plasma
with ITB at significant low collisionality regime νb* < 0.2

5. Magnetic island
The final topic is related to effect of magnetic topology.
As mentioned in introduction, LHD has a capability togenerate a resonant island externally as seen in Fig. 10 (a).
The response of plasma to this island is attracting interests,
in particular, in comparison with a neoclassical tearing modein tokamaks. Usually, local flattening in temperature profile
corresponding to this island is observed. In specific condition,
however, this island becomes invisible. In Fig. 10 (b) [31],the existence of magnetic island is summarized in theparameter space on the temperature and density where theisland should be located. Solid circles indicate that the island
is visible in the temperature measurement. In contrast, open
7
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Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

circles are invisible cases where the island is suppressed. If a
crude experimentalist’s insight is allowed, the parameter spaceis divided by two curves, which leads to the idea that theisland is healed in the high-β and collisionless regime.
Figure 11 shows another aspect of a function of magnetic
islands. Electric potential profiles are derived from thepoloidal rotation of the plasma [32]. The resonance of theexternal perturbation (m/n = 1/1) is located at 4.05 m. The
magnetic island width is enlarged by increasing currents inthe perturbation coil from the top to the bottom. When theisland is small, flattening of potential in the island is observed.
When the island width is increased further, a clear poloidal
flow in the island is generated and specific potential structureappears (the bottom case). This dynamics indicates that
topological interface (separtrix of the magnetic island) has apotential to generate large Er shear, eventually linking topossibility of confinement improvement.
Since the temperature profile in the magnetic island isusually flat, heat transport in the island cannot be evaluatedin a steady state manner of power balance analysis. Therefore
transient transport analysis is prerequisite. LHD provides an
excellent experimental platform of this study since a large
static island which does not rotate can be generated. By
controlling the phase of the island, cold pulse propagation
inside and outside the island is investigated. Figure 12 (a)shows the cold pulse propagation in the island [33]. In thiscase, the tracer encapsulated solid pellet [34] is injected
through the X point of the island to induce a cold pulse.
Temperature evolution after that is measured along the chordcrossing the O point by ECE (Electron Cyclotron Emission)
diagnostics. In contrast, Fig. 12 (b) is the case with the pellet
deposited in the island and ECE measurement passing throughthe X point [33]. A simulation result based on simple diffusive

Fig. 11 Effect of externally generated magnetic island on radial
electric field profile. Island width is gradually enlarged
from the top to the bottom by increasing the current of
the perturbation coil [31].

Fig. 12 Cold pulse propagation (a) inside the magnetic island and (b) outside the magnetic island [32].

858

Yamada H. et al., Recent Results from LHD Experiment with Emphasis on Relation to Theory from Experimentalist’s View

Referencesmodel is also illustrated in Fig. 12. From this analysis, theheat transport in the magnetic island is found to besignificantly reduced by a factor of more than 10.

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6. Summary
The LHD has been extending an operational regime
towards fusion relevant condition with taking advantage of anet current-free heliotron concept and employing a
superconducting coil system. Heating system has been
upgraded and available power has exceeded 10 MW, which
has enhanced plasma parameters. Many encouraging physicalfindings have been obtained, ex., simultaneous achievementsof mitigation of MHD instability criteria and good
confinement, and formation of internal transport barrier. Somehighlight data should be emphasized in terms of theoretical
approaches. Mitigation of an ideal interchange mode in theconfiguration with magnetic hill remains a challenging issue.
Nonlinear process of growth of instability or stabilization
effect [35] which has not been incorporated in the presently
available model should be explored. Confinement
improvement due to suppression of both neoclassical andanomalous transport has been realized simultaneously by ISC.
The former (neoclassical) achievement is a successful
demonstration of the theory but a coherent theoreticalunderstanding for the latter (anomalous) achievement has notbeen available yet. Regarding bifurcation of the radial electricfield, a qualitative agreement with neoclassical theory has
been obtained and quantitative argument is being available.
ITB formation has a close relation to this mechanism.
Confinement of high energy particles can be alsocharacterized by an available theory (3-D simulation [36])well and a quantitative argument with the experiment is in
scope although it is not described in this paper. LHD provides
an experimental platform to verify innovative attempts withregard to the effect of magnetic topology, ex. dynamics ofmagnetic island, role of sepratrix, etc. with taking advantageof large flexibility of magnetic configuration.

Acknowledgements
A number of national and international collaborations ina wide spectrum for the LHD project are acknowledged. The
authors wish to thank all technical stuff of the LHD groupfor their helpful support during this work.

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