Proceedings of ITC/ISHW2007

Properties of internal diﬀusion barrier inhigh density plasmas on Large Helical Device
Ryuichi SAKAMOTO1) , Masahiro KOBAYASHI1) , Junichi MIYAZAWA1) , Satoshi OHDACHI1) ,Tomohiro MORISAKI1) , Suguru MASUZAKI1) , Ichihiro YAMADA1) , Motoshi GOTO1) ,Katsumi IDA1) , Shigeru MORITA1) , Satoru SAKAKIBARA1) , Kenji TANAKA1) ,Kazuo KAWAHATA1) , Kiyomasa WATANABE1) , Yasuhiro SUZUKI1) , Hisamichi FUNABA1) ,Sadayoshi MURAKAMI2) , Naoko ASHIKAWA1) , Yoshio NAGAYAMA1) , Yoshiro NARUSHIMA1) ,Byron J. PETERSON1) , Mamoru SHOJI1) , Chihiro SUZUKI1) , Masayuki TOKITANI1) ,Shinji YOSHIMURA1) , Nobuyoshi OHYABU1) , Hiroshi YAMADA1) , Akio KOMORI1) ,Osamu MOTOJIMA1) and LHD experimental group1)
1)

National Institute for Fusion Science, Japan
2)
Kyoto University, Japan

An experimental study is performed in order to extend the operational space of internal diﬀusion barrier(IDB) plasma, which was originally found in pellet fueled high density discharges with the local island divertor
conﬁguration, to an intrinsic helical divertor conﬁguration in large helical device (LHD). It is revealed that the
IDB can be reproducibly formed in intrinsic helical divertor conﬁgurations as in the local island divertor conﬁguration. The IDB is eﬃciently formed by central pellet fueling in the outer shifted magnetic conﬁguration(Rax > 3.7 m). Attainable core plasma density becomes higher as the magnetic axis shifts outward. Maximum
core density reaches 1 × 1021 m−3 . Central pressure exceeds 130 kPa, and therefore very large Shafranov shift(∆/aeﬀ ≥ 1/2) due to high central beta is observed even at high magnetic ﬁeld (Bt ∼ 2.54 T).
Keywords: stellarator, internal diﬀusion barrier, pellet fueling, divertor, magnetic conﬁguration

1

Introduction

Conﬁnement improvement is one of the most important issues of magnetic conﬁned fusion plasma research. The internal diﬀusion barrier (IDB) which enables core plasma toaccess high-density/high-pressure regime has been foundin multi pellets fueled high density discharges with an active pumped local island divertor (LID) conﬁguration inlarge helical device (LHD) [1]. A high density core plasma
with 5 × 1020 m−3 is maintained by the IDB located atρ = 0.5 and the IDB plasma exhibit the highest fusion
triple product on LHD, n0 T 0 τE = 4.4 × 1019 keV m−3 s.
The IDB is similar to pellet enhanced performance(PEP) mode, which is ﬁrst found in JET[2] then in the othertokamaks [3, 4], on the point that both lead to strongly
peaked pressure proﬁle. On the other hand, unlike the tokamak PEP mode, there is no clear indication of increasein the temperature gradient and inward particle convection in IDB. Although the LID conﬁguration has eﬃcientpumping due to the localized installation, heat removal isproblem for the same reason with the present LID design.
Therefore, IDB formation in intrinsic helical divertor conﬁguration which have larger heat receiving area than LID
conﬁguration is highly desired from a standpoint of comauthor’s e-mail: sakamoto@LHD.nifs.ac.jp

patibility with a fusion reactor.
An experimental study has been performed in order toexplore the operational space of the IDB discharge with the
intrinsic helical divertor conﬁguration in LHD.

2

Experimental Set-up

LHD is a heliotron type full superconducting stellarator
with a pair of continuously wound M = 10 helical coils
and three pairs of poloidal coils. The plasma major radius
at vacuum magnetic ﬁeld is variable in the range of 3.5 m
to 4.0 m, the averaged plasma minor radius is ∼ 0.6 m andthe magnetic ﬁeld strength is ≤ 3 T[5]. A helical divertor
is intrinsic divertor conﬁguration in heliotron type device.
The divertor has open structure with forced water-cooledcarbon target plate and there is no pumping capacity except wall pumping. The heat receiving area is about 50
times larger than LID conﬁguration and it arrow high heating power and long pulse experiments.
Three negative ion based high energy (up to 180
keV) neutral beam injector (NBI) are employed for plasma
heating. Typical NBI heating power is 12 MW in total. Solid hydrogen ice pellets are launched from outboard
side mid-plane by using 10 barrels in-situ pipe-gun pellet injector[6]. The typical pellet mass and velocity areProceedings of ITC/ISHW2007
1.5 − 2.0 × 1021 atoms per pellet and 1000-1200 m/s, respectively.

3Internal Diﬀusion Barrier Formationin Helical Divertor Conﬁguration

3.1

fueling

3.2 pre-set magnetic axis

Typical plasma proﬁles of the gas-puﬀ and pellet fueleddischarges at the same magnetic conﬁguration Rax = 3.75
m in the same line integrated density ne l = 3 × 1020 m−2
are shown in ﬁgure 1. The normalized minor√ radius ρ isexpressed as ﬂux coordinate, namely, ρ = Φ where Φ isthe toroidal ﬂux function, which is normalized by the valueof the last closed ﬂux surface. The negative and positive ρvalue indicate inboard and outboard side of the plasma, respectively. Since particle source is limited to peripheral forthe gas-puﬀ fueling, the density proﬁle typically becomesﬂat or slightly hollow. In the case of the pellet fueling, the
IDB which has a steep density gradient inside ρ = 0.55
is formed and the central density is remarkably increased
while peripheral density is reduced. A noteworthy ﬁndingis that the electron temperature of the pellet fueled plasma
is higher in spite of the fact that the central density is morethan double. The plasma pressure proﬁle calculated assuming the ion temperature proﬁle is the same as measured
electron temperature proﬁle, show an obvious increase of
the plasma energy density in the core region (ρ < 0.55).

ne 1020 [m-3]P [kPa]Pellet, #68996, 1.466 s
BT= 2.54 T, PNBI= 11 MW
Gas Puff, #63555, 1.603 s
BT= 2.64 T, PNBI= 9.5 MW

120
100
80
60
40
20
0
3

(a)

(b)

2
1
0
1.0

Te [keV]The attainable central pressure of the pellet fueled plasma
is about four times larger than that of the gas-puﬀ fueled
plasma, even exceeding atmospheric pressure. The plasma
β becomes high even though the magnetic ﬁeld is high(Bt > 2.54 T) and thus the plasma proﬁles suﬀer very large
Shafranov shift (∆/aeﬀ ∼ 1/2) .

(c)

0.5

0
-1.0

-0.5

0

0.5

1.0

ρ
Fig. 1 Comparison of (a) Plasma pressure, (b) electron densityand (c) electron temperature in the gas-puﬀ (blue open
circle) and pellet (red ﬁlled circle) fueled discharges atthe same magnetic conﬁguration Rax = 3.75 m.

The global energy conﬁnement time reaches a maximum ininward shifted magnetic conﬁgurations (Rax = 3.60 − 3.65
m which give a maximum plasma volume) by employing pellet fueling[7]. The IDB, on the other hand, iseasy to produce in outward shifted magnetic conﬁgurations (Rax > 3.7 m). One characteristic diﬀerence between conﬁgurations is magneto-hydrodynamic stability
properties, considered to be favorable as the magnetic axis
shifts outward[8] because the region with magnetic well iswide, especially at ﬁnite β. It is also important that thepoloidal distribution of a divertor ﬂux changes with magnetic conﬁgurations[9]. The divertor ﬂux tends to concentrate on the inboard side and this leads to a localized increase of neutral pressure due to recycling in the inward
shifted magnetic conﬁgurations. This situation is estimatedto cause a peripheral density rise which is incompatible
with the core fueling. Contrary to this, the divertor ﬂux
tends to spread uniformly poloidally in the outward shiftedmagnetic conﬁgurations and this behavior leads to suppression of peripheral particle source. This situation is
expected to compensate the lack of pumping capacity athelical divertor.
Figure 2 shows the temporal evolution of characteristic plasma parameters in several nine-pellet fueled discharges at magnetic axes Rax = 3.65 m, 3.75 m and 3.85
m. Let timing of the ﬁnal pellet injection be t = 0. In
each cases, NB heating power and magnetic strength are
11 MW and 2.54 T, respectively. The IDB formation period is denoted by ﬁlled symbol. It is diﬃcult to deﬁne onset and termination timing of the IDB regime because the
IDB proﬁle gradually changes in time. The IDB is temporarily deﬁned by existence of a clear bend in the density proﬁle. While the same number of pellets were injected, attainable central plasma density becomes higher
as the magnetic axis shifts outward and the maximum central density at Rax = 3.85 m is doubled compare to thedensity at Rax = 3.65 m. At the same time, the central temperature follows quite a similar course after pellet injection
although central density varies widely depending on magnetic conﬁguration. As the result, higher central pressure
is attainable in the outward shifted magnetic conﬁgurations
where the IDB is formed. The point to observe is that there
is a plateau of the pressure rise in the high density phaseas shown by two-headed arrows in ﬁgure 2(a). The plateau
begins to appear during the pellet injection phase, namely
density increase phase, and continues until the excess density drops to the onset level. This phenomenon indicatesProceedings of ITC/ISHW2007
PNBI= 11 MW, BT= 2.54 T

ne 1020 [m-3]P [kPa](b)

6

CDC event4
20Rax= 3.85 m (#69268)
Rax= 3.75 m (#68996)
Rax= 3.65 m (#68956)

2

-0.2

0.0

0.2

0.4

4

(b)

3
2
1
0
1.0

(c)

1

50
0

ne 1020 [m-3]500Te [keV](a)100

Te [keV]P [kPa]

100

0
-0.4

PNBI= 11 MW, BT= 2.54 T(a)

9 Pellet Injection

(c)

0.5
Rax= 3.75 m (#68996)
Rax= 3.65 m (#68956)

0
-1.0

0.6

-0.5

0

Time [s]Fig. 2 The temporal evolution of (a) Plasma pressure, (b) electron density and (c) electron temperature in nine-pellets
fueled discharges at magnetic axes Rax = 3.65 m (green
circle), 3.75 m (red triangle) and 3.85 m (blue square).
The magnetic ﬁeld strength and NB heating power are
2.54 T and 11 MW, respectively. Filled symbols denotethe formation of IDB.

1.0

Fig. 3 Comparison of (a) Plasma pressure, (b) electron densityand (c) electron temperature between Rax = 3.65 m (blueopen circle) and 3.75 m (red ﬁlled triangle) at the timing of T e (0) = 1 keV. The magnetic ﬁeld strength and
NB heating power are 2.54 T and 11 MW, respectively.
Hatching denotes IDB formation region.

ne(0)1020 [m-3]8BT= 2.539 T, PNBI= 11 MW(a)6ne(0) at max. P(0)
4
2
0
150

max. P(0) [kPa]

conﬁnement degradation in high density regime. As themagnetic axis shifts outward, the onset density level increase as indicated by broken line in ﬁgure 2(b), namely
2.7 × 1020 m−3 at Rax = 3.65 m and 5.0 × 1020 m−3 at
Rax = 3.75 m, and duration of the plateau becomes shorter.
Finally the plateau of the pressure rise is hardly observedat Rax = 3.85 m and the pressure is increase in a linear
fashion during and after pellet injection. After that, thepressure and density decrease suddenly at t = 0.18 s, while
any noticeable changes are not observed in the temperature. This unexpected event is referred to as core density
collapse (CDC) and will be discussed later. It must be also
noted that the ﬁnal density levels out after the disappearance of the IDB. The ﬁnal density becomes lower as themagnetic axis shifts outward, contrary to the IDB phase,and this observation supports a reduced recycling in theoutward shift conﬁgurations.
Figure 3 shows a comparison of plasma proﬁles between Rax = 3.65 m and 3.75 m at the timing of T e (0) = 1
keV. Density proﬁles of the two conﬁgurations are quite
diﬀerent even though the temperature proﬁles are identical. For Rax = 3.65 m, the density proﬁle has a parabolic
shape. On the other hand, the IDB with steep density gradient is formed on the inside of ρ = 0.55 and central density reached to almost double in the case of Rax = 3.75 m.
Thus magnetic conﬁguration is another factor of the IDB

0.5

ρ

(b)

100

50
IDB formation
0

3.6

3.7

3.8

3.9

Rax [m]Fig. 4 Conﬁguration dependence of (a) central electron density at the instant of maximum central pressure and(b)maximum central pressure.
The magnetic ﬁeld
strength and NB heating power are 2.54 T and 11 MW,
respectively.

Proceedings of ITC/ISHW2007
1.5
mantle: ρ= 0.8

IDB phase

D= 0.41 m2/s

1.0

Γe/ne

formation in addition to pellet core fueling.
The magnetic axis dependence of the IDB plasmas
is summarized in ﬁgure 4. Attainable central density becomes higher as the magnetic axis shifts outward and thecentral density exceeds 5 × 1020 m−3 . The point to observe is that there is a sharp increase in central densityand pressure around Rax = 3.7 m and central pressure
reach its greatest value, ∼ 130 kPa, at the neighborhoodof Rax = 3.85 m. The maximum central pressure is limitedby the CDC event as shown in ﬁgure 2.

IDB: ρ= 0.5
D= 0.042 m2/s

0.5

IDB:
ρ= 0.4

core: ρ= 0.2
0

0

1

2

3

4

-(dne/dρ)/ne

4 Properties of IDB Plasmas

15
mantle: ρ= 0.8
IDB phase

6.
4

m2
/s

10

≈

5

e

Figure 5 shows a change of IDB proﬁles from moment tomoment. The IDB structure, which has localized sharp
density gradient, namely box-like density proﬁle, is observed at 1.2 s. Then density gradient is gradually decreases and spread into core region during density decay
and temperature recover phase. Finally the IDB structure changes to linear proﬁle at 1.6 s with keeping central pressure. During the proﬁle change, a collisionalityνb∗ , which is normalized by a bounce frequency of banana
particles, decrease monotonically in the plateau regime(10 ≥ νb∗ ≥ 1). This IDB structure change, from boxlike proﬁle to linear proﬁle, is explained by lack of particle
source inside IDB for the following particle transport analysis.
The particle transport coeﬃcient of IDB plasma is calculated by using relationship between time evolution andgradient of density proﬁles after pellet injection. Figure

Fig. 6 Particle ﬂux normalized by electron density as a functionof density gradient after pellet injection in various minor
radius. Filled symbols denote the period of IDB formation.

χparticle transport

Pe/ne [keVm/s]

4.1

0
0

1

2

3

-(dTe/dρ)/a [keV/m]Fig. 7 Heat ﬂux normalized by electron density as a function oftemperature gradient after pellet injection in low density
mantle (ρ = 0.8). Filled symbols denote the period of
IDB formation.

ne [1020 m-3]

6
4#68996
Bt= 2.539 T
Rax=3.75 m

6 shows relationship between normalized particle ﬂux andnormalized density gradient. Gradient and y-intercept of
this plot indicate diﬀusivity (De ) and convection velocity(ve ) according to the following relational expression.

2

Pe [1020 keV/m-3]

Te [keV]

0
1.0

0.5

0
3

1.20 s1.36 s1.60 s

2
1
0

3.0

3.5

4.0

R [m]
Fig. 5 Change of IDB structure.

4.5

Γe
1 ∂ne
= −De
+ ve ,nene ∂ρ
∫ewhere Γe = − A1 ∂n∂t dV is particle ﬂux assuming no particle source inside the ﬂux surface. The ﬁlled symbols denote the period of IDB formation. Diﬀusivity of core region inside IDB (ρ ≥ 0.5) is kept at low level as D = 0.042
m3 s even high density gradient and inward convection velocity can not be observed. Therefore IDB core can be described with diﬀusive nature and the proﬁle change, boxlike to linear, is explained by lack of particle source inside
IDB. And also the core diﬀusivity is said to be not sensitive to collisionality in the range of plateau regime. On theother hand, the mantle plasma cannot keep the density gradient in high particle ﬂux IDB phase, namely, mantle diffusivity deteriorates during IDB phase. Notable characteristics of the IDB plasma is that the thermal transport coeﬃ-

Proceedings of ITC/ISHW2007#69286, Rax=3.85 m, Bt= 2.54 T

6

Before CDC

β(0) [%]

2

After CDC
t=1.500 s

0

Te (keV)

β(0)

4

0.15

0.05
vertical elongation

0.6
0
1.0

0.4

1.1

1.2

1.3

1.4

1.5

0

κeff

0

Fig. 9 Shafranov shift amount ∆shift and central beta β0 at the
maximum central pressure as a function of the eﬀective
ellipticity κeﬀ . The ﬁlled symbol in β0 denote the occurrence of CDC event.

6

β (%)

0.20

CDC free

0.10

0.2

4
2

tem.
-1.0

-0.5

0

0.5

1.0

ρ
Fig. 8 Change of plasma proﬁles before and after CDC event.

cient, which is relationship between heat ﬂux and temperature gradient remain unaﬀected by big change of the particle transport as shown in ﬁgure 7. These results lead to separation of conﬁnement region between the IDB core (highdensity gradient) and low density mantle (high temperature
gradient), and therefore high-density/high-pressure plasma
is attained in the IDB discharge. The IDB core is formedby the deep pellet fueling and intrinsic good particle conﬁnement property. The low density mantle have advantages to suppress radiation loss, and therefore density limitof IDB plasma is extremely extend to high-density regime.
In addition, low density mantle secure temperature gradient for high-density/high-pressure core plasma.

4.2

CDC

2

0.8

0

0.25

ΔShift6

t=1.485 s

4

0.30

8

ΔShift [m]ne (1020 m-3)

8core density collapse event

Figure 8 shows plasma proﬁles just before and after CDC
event. In the CDC event, the high density core plasma is
expelled on the sub millisecond time scale () without having any impact on the central temperature. CDC event istypically observed in the high performance discharges with
IDB. The mechanism of the CDC is not yet elucidated, but
it may be involved with MHD instability and/or equilibrium limit arising from very large Shafranov shift. Therefore, suppression of the Shafranov shift is potential solution to avoid CDC event. Pﬁrsch-Schlüter current control
by a vertical elongation, namely ellipticity κ control, is ameans of Shafranov shift suppression [10] in helical sys-

Figure 9 shows the Shafranov shift amount and central beta at the maximum central pressure as a functionof the eﬀective ellipticity κeﬀ , which is deﬁned by ratio of line densities between vertical elongated and horizontally elongated poloidal cross-section. As the κeﬀ become large, amount of Shafranov shift monotonically get
smaller. Attainable central pressure, which is restrictedby CDC event, is become large until κeﬀ = 1.2 and theattainable central pressure increase by 20 % compare to
standard conﬁguration κeﬀ = 1.0. Extreme vertical elongation beyond κeﬀ = 1.2 result in a degradation of central
beta although the CDC event is not observed. Under thecondition of κeﬀ ≥ 1.2, MHD instability which is diﬀerent
from CDC event is observed and conﬁnement degradation
is suggested.

4.3

impurity behavior

In helical system, neoclassical ambipolar diﬀusion predict
ion root (negative radial electric ﬁeld Er ) in high density
regime and the negative Er lead to impurity accumulation. In general, impurity behavior is one of the mostconcerned topics in high-density discharges, because radiation collapse due to loss of power balance tends to takeplace by less impurity contamination than a low density
discharges. Contrary to theoretical prediction, signiﬁcant
indication of impurity accumulation is not observed by Zeﬀ
and bolometric measurements although negative Er in the
IDB plasma is veriﬁed by a charge exchange recombination spectroscopy. Existence of impurity accumulation due
to negative radial electric ﬁeld has not been conﬁrmed,
nevertheless impurity contamination is not a signiﬁcant
problem in the IDB discharge. Divertor modeling study using EMC3-EIRENE code suggests impurity shielding po-

Proceedings of ITC/ISHW2007
tential in ergodic layer [11], namely, outward friction force
by plasma ﬂow dominate impurity behavior and impurity
tend to be expelled from LCFS in high-density regime.

5

Conclusion

An experimental study is performed to explore the operational space of a high density plasmas due to the IDB
which was originally found in pellet fueled high density
discharges with the active pumped LID conﬁguration in
LHD. The IDB with steep density gradient has been produced at an intrinsic helical divertor conﬁguration as in
LID conﬁguration by optimizing the pellet fueling andmagnetic conﬁguration. Core fueling by multiple pellet
injection is essential for the IDB formation and the IDB
easily appears in the outer shifted magnetic conﬁguration(Rax > 3.7 m). Conﬁnement region is separated into low
density mantle and high density core in IDB plasma. This
lead to high-density/high-pressure core plasma. The central density reaches 1 × 1021 m−3 at Rax ≥ 3.9 m and thecentral pressure has reached 1.3 times atmospheric pressure. Although negative Er is veriﬁed, harmful impurity
contamination has not been observed in IDB plasma. CDC
event, which arise from very large Shavranov shift, restrict
operational regime. Suppression of Shafranof shift withellipticity control can mitigate CDC event and the centralpressure increase by 20 % of standard conﬁguration. Investigation of long-duration sustainability of the pellet fueled
IDB is critically important from a perspective of extrapolation to fusion reactor scenario. Nonetheless, the IDB isan encouraging ﬁnding and it demonstrates the potential
for alternative path to high-density/low-temperature fusion
reactor in helical devices.
This work is supported by NIFS06ULPP521.
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