J. Plasma Fusion Res. SERIES. Vol.5 (2002) 88-93

Role of Radial Electric Field Shear at the Magnetic
lsland in the Transport of Plasmas
IDA K., OHYABU N., MORISAKI T., NAGAYAMA Y., INAGAKI S., YOKOYAMA M., ITOH K.,
YOSHIMURA M., LIANG Y., NARIHARA K., KOSTRIOUKOV A. Yu., PETERSON B.J',
TANAKA K., TOKUZAWA T., KAWAHATA K., SUZUKI H., KOMORI A.
and LHD Experimental Group
National Institute for Fusion Science, Toki 509-5292, Japan(Received: 21 December 2001 / Accepted: 2 May 2002)

Abstract
The structures of radial electric field and transport at the magnetic island are investigated using

nlm=lll external perturbation coils in the Large Helical Device (LHD). The radial profiles of plasma
potential, as well as the electron temperature and density, shows flattening inside the magnetic island andthe large shear of the radial electric field is observed at the boundary of the magnetic island. When thecurrent of nlm=lll external perturbation coils becomes large enough, the finite radial electric fieldappears inside the magnetic island. The abrupt appearance of plasma flow inside the magnetic island
suggests the non-linearity of the viscous force at the boundary of the magnetic island. The thermal
diffusivity perpendicular to the magnetic filed inside the magnetic island is estimated with the cold pulse
propagation, which is produced by a tracer-encapsulated solid pellet (TESPEL). The time delay andamplitude of the electron temperature of the cold pulse show much lower thermal diffusivity inside themagnetic island (0.16 m2ls; than that outside the magnetic island (2 m2ls;, which is a clear evidence forthe significant reduction of heat transport inside the magnetic island.

Keywords:
radial electric field, magnetic island, spontaneous poloidal flow, flow shear, transport

1. Introduction
The transport at the magnetic island has beencandidates to explain the correlation. However, there arefew experiments in studying the radial structure ofradialrecognized to be important, since the phenomena imply
a significant change of transport at a rational surface.
The recent observations of the internal transport barriers

electric field at the magnetic island [3,4], because therotations of magnetic island itself makes themeasurements of radial electric field difficult.

at or near the rational magnetic surface in tokamak

There have been the observations that demonstrateplasmas imply the importance of magnetic islands in thethe low particle and heat diffusivity inside the magnetic

plasma confinement [1]. The position of transportbarrier is often correlated to the location of low orderrational magnetic surface [2]. Since the radial electricisland. The low particle diffusivity inside the magnetic
island was observed when the particle is fueled into themagnetic island by fueling pellet , which was called as"snake" modulation, in JET [5]. More recently thepossible role of magnetic island on the local variation offield shear is considered to cause or trigger theformation of the transport barrier, the radial electric field
shear at the boundary of magnetic island is one of the@2002by The Japan Society of Plasma
Science and Nuclear Fusion Research

C orre sponding author' s e - mail : ida @ nifs. ac.j p

88ldaK. et al., Role of Radial Electric Field Shear at the Magnetic Island in the Transport of Plasmas

thermal diffusivity has been reported by RTP

along the line of sight within the beam width of theneutral beam. The spatial resolution becomes poor near
the plasma center and relatively good near the plasmaedge and it is +1.5 cm at the R=4.05 m.

experiment [6]. In spite of the importance of transport at
the magnetic island, there is no direct measurement ofthermal diffusivity inside the magnetic island. This isbecause, the transport analysis based on the temperature

Figure I shows the poloidal cross section of the last

gradient and radial heat flux in the steady state is invalid

closed magnetic flux surface and magnetic island

due to the flatlening of electron temperature inside thecalculated (without zero beta) for the discharge with themagnetic island [7]. The localized flattening of theelectron temperature profile is due to a modification of
the magnetic topology resulting from the magnetic
island produced by the perturbation field and not due tothe increase of energy transport. When there is no local
heating inside the magnetic island, the electron
temperature profile shows flattening even though themagnitude of the thermal diffusivity is small inside themagnetic islancl. In order to evaluate the transport inside
the magnetic island, the transient transport analysis is

nlm=lll external perturbation coil current, 1n7.=171, of-1200 A and electron temperature and density profiles.
The magnetic island is located near the plasma edge at p

= 0.85. As seen in Fig. l(b), the flattening of both of

1.0

0.5

necessary.

Although the structure of radial electric field andradial electric field shear is a crucial parameter tounderstand the good confinement (low diffusivity)

9ooN

inside the magnetic island, there have been no clear
measurements of poloidal flow or radial electric field
and transport inside the magnetic island except forplasma edge. The structure of radial electric field andheat transport inside the magnetic island are discussed in-0.5

this paper.

-1.0
3.0

2. Magnetic lsland Produced by the n/m=
1/1 Perturbation Coil

3.5

4.0

5.0

4.5

R(m)

3

The Large Helical Device (LHD) t8l is a Heliotron(b)device (poloidal period number L = 2, and toroidal
period number M = 10) with a major radius of R"* = l.J- 4.1 m, an average minor radius of 0.6 m, magnetic
field up to 3 T. The radial electric field (E ) is derived
from the poloidal and toroidal rotation velocity andpressure gradient of Neon impurity measured withcharge exchange spectroscopy [9] at the mid plane inwithout isl

co
I

a!
O\)

ofr
o

t-l trF

I

et1

LHD (vertically elongated cross section) using a radial-lforce balance. 'the radial force balance equation can be

J

c-)

F

expressed as 4 - @ntZt)r(dptldr) - (v&o- vaB6), whereC),B4 and Bs are toroidal and poloidal

magnetic field and 21,
ny p1 a;ta ion charge, density and pressure of impurity
measured, respectively.The Large Helical Device (LHD)0-1.0

has nlm=lll external perturbation coils. The size ofmagnetic island can be controlled up to 10cm bychanging the current of the perturbation coils. The
spatial resolution of the measurements of the radial---r-Te 19803--"-'Te 19814
l.7s--'-- 19803
19814 l.7s-

with island

ffr
',i
r'lc

I
I
r

rq
ll

-0.s 0.0p 0.5 1.0

Fig. 1 (a) Poloidal cross section of the last closed mag-netic flux surface (LCS) and nlm=l/1 magnetic
island and (b) radial profiles of electron density
and temperature for the plasma with and withoutmagnetic island, where p is a normalized minor

electric field using the charge exchange spectroscopy isdetermined by the length of integration of the signal

radius.
89

IdaK. et al., Role of Radial Electric Field Shear at the Magnetic Island in the Transport of Plasmas

electron density and temperature is observed for theplasma with magnetic island (/n7-=171 = -1200 A), while
there is no flattening observed for the plasma withoutmagnetic island. The flattening width of electron
temperature is considered to represent the width ofmagnetic island in the plasma, which would not be
identical to the width of vacuum magnetic island due to0-60

the healing effect [7]. Since there is no pressure gradientinside the magnetic island, one can expect the flat space-6

potential and zero radial electric field inside thee;0Jmagnetic island.

3. Radial Electric Field Profiles Near the
Magnetic lsland

rrl

--6

When the current of n/m=1/1 external perturbationcoils is small (see 260 A in Fig. 2), no island structureappears in the profile of radial electric field as well as

ion temperature. As the perturbation coil current
increases, clear structure of magnetic island appears in-6

the radial electric field. Widths of island, !/11 and !/ss,
are estimated from the radial profiles of ion temperatureand radial electric field measured.

0

The widths are given by a least-squares fit of themeasured profiles to the model profiles, where the ion
temperature gradient is zero for R1 - Qlz)Wri < R < Ri
+ (ll2)Wl and the radial electric field is zero for Ri - (l/Z)Wn < R < Ri + (,12)WE. Here R1 is the major radius-6
3.8

for the center of the magnetic island. Although thosewidths are not identical because of the difference ofradial diffusion of energy and momentum, both widths
increase as the current of r/m=1/1 external perturbationcoils 1n7.=171 is increased. When the size of magnetic
island is large (e.g. lntm=yt = -1200 A) enough to drive
the convective flow inside the magnetic island, only thewidth W11, rot Ws,, can be experimentally determined.
As the perturbation coil current increases, the widthof magnetic island estimated from the radial profiles ofradial electric field also increases up to 9 cm, whichcorresponds to 17 Vo of the averaged minor radius. Here
we assume the zero radial electric field inside themagnetic island to estimate the width of island. In thecalculation of model profiles, the smoothing due to thespatial resolution of the measurements is taken into
account. Because of this smoothing, the apparent radial
electric field inside the magnetic island can be finite
even the radial electric field is zero as assumed in themodel when the width of the island is smaller than the

3.9

4.0
R(m)

4.r

Fig. 2 Radial profiles of radial electric field, measured

with charge exchange spectroscopy for various
current of n/m=111 external perturbation coils,
In1^=11 , for the plasma with magnetic field of 1.5 T,
vacuum magnetic axis of 3.5 m. The last closed
surface are at F=3.28 m and R-4j0 m at thecross section vertically elongated. The major radius for the center of island, R,, is indicated withline as a reference. The dashed lines are calculated profiles of radial electric field using simple
model, where the radial electric field is zero inside
the island. The width of magnetic island, W.,, estimated from radial electric field profiles are also

indicated.
the magnetic island and zero radial electric field inside
the island. Due to the shear viscosity, the boundary

itself should have finite width 4. This width isdetermined by the viscous coefficient p and the ratioof radial electric field to radial current and given by the
A= {tteoe**E,/j,, where fre"* is dielectric constantspatial resolution.

and E,, j, are radial electric field and neoclassical radialcurrent to sustain the E, outside of the magnetic island,

In the model, radial electric field jumps at theboundary of magnetic island, i.e. finite values outside90

ldaK. et al., Role of Radial Electric Field Shear at the Magnetic Island in the Transport of Plasmas

respectively [10]. The values of shear width .4 can beisland is linearly proportional to the flow shear andconstant in space, the plasma flow inside the magnetic
island is proportional to the square of island width, W,
as v - (WU5)(dveldr), where dis the shear width at theestimated to be 1.2 cm using the experimental values of
eo%",pEfi,= 70 ps

I l] and p = 2 mzls [l2] and it is too

small to be measured with the charge exchange
spectroscopy which has the spatial resolution ofboundary of magnetic island. Therefore non-linearity ofviscous force is required to cause the sudden appearanceof plasma flow inside the magnetic island.
When the normalized collisionality of the plasma ishigh (v" > 0.1 ), the plasma is in the ion root, where the+1.5 cm.

4. Plasma Space Potential in the Electron
and lon Root
If the space potential is not flat inside the magnetic

radial electric field is negative and more negativeisland, both the radial electric field and the poloidal flow
should be finite inside the magnetic island. Because of

towards the plasma edge [3]. On the other hand, when
the normalized collisionality of the plasma is below thecritical values of 0.1 (v" < 0.1 ), the plasma is in thethe conservation of particle flux inside the magnetic
island, the poloidal flow should be convective, if itexists inside the magnetic island. When the poloidal

flow is convective, the sign of radial electric field

0.0,(a)r^rshould be reversed across the center of magnetic island

and radial electric field shear appears inside the

I

dcm

I

l1------;lmagnetic island.

9-0.
J4

Because of the plasma flow damps (when the island

width is below the critical value, 9 cm for theexperimental conditions shown in Fig. 2), the radial-()nelectric field becomes zero and space potential becomesPflat zero inside the magnetic island. Figure 3(a) shows

g

LHD

-tt

the space potential profiles for the plasma with different

lcm

magnitude of nlm=l/l perturbation coil current. In
LHD, the flattening width of space potential can beextended up to 8 cm, without the appearance of plasma-%1hj

4.UU 4.U)R(m)flow along the magnetic flux surface inside the magnetic
island. However, when the width of magnetic island
exceeds 9 cm (e.g. in the plasma for /,v.=vr = -1200 A

4.IU

4.1

in Fig. 2), the plasma flow along the magnetic flux
surface inside the island appears as seen in Fig. 3(b).
th islaThe convective poloidal flow inside the magnetic islandis driven by the unbalance of viscous force between
inside and outside the magnetic island. If there is nodifference of poloidal flow velocity between the twoIIboundaries of magnetic island, the force due to theviscosity at the boundary cancels each other and there
should be no net torque to drive the flow inside themagnetic island. When the difference in poloidal torqueat the boundaries overcomes the damping of flow inside
the magnetic island, the flow along the magnetic flux
surface appears inside the magnetic island and the
direction of the flow is considered to be determined by
the sign of velocity shear at the x-point of magnetic
island. The existence of the critical width for theappearance of plasma flow is due to the non-linearity ofthe viscous force at the boundary of the magnetic island.
If the viscous force at the boundary of the magnetic

I#xi"".

-.t\
'E <
-|F:
\r
d2anl > oIIIlis landsl

R(m)Fig. 3 (a) Radial profiles of space potential for different
size of magnetic island. The island width is below

the critical values for the sudden apperance ofplasma flow inside the magnetic island. (b) Radial
profiles of space potential with and without magnetic island for the plasma in the ion root {v*" >0.1, negative F.) and electron root (v+" < 0,1 positive E).

9l

ldaK. et al., Role of Radial Electric Field Shear at the Magnetic Island in the Transport of Plasmas

electron root, where the radial electric field is positiveand more positive towards the plasma edge. Therefore

measured with ECE.

the direction of convective poloidal flow should bereversed depending on the sign of edge radial electricfield. The change of sign of poloidal flow and thepulse inside the magnetic island is much longer than thatAs shown in Fig. 4, the response time of the cold
observed outside of the magnetic island. The amplitudeof the cold pulse is also smaller inside the magnetic
island than outside of the island. The time delay andresulting change ofcurvature of space potential @2aDlde> 0 or d2@/df < 0) are clearly observed as seen in Fig.
3. The convective poloidal flow inside the magnetic

amplitude of the electron temperature of the cold pulse
inside the magnetic island is reproduced by simulationof the cold pulse propagation in a slab model with a low
thermal diffusivity of 0.16 m2ls, which is smaller thanthat (2 m2ls) outside the magnetic island by more than
one order of magnitude. Because the structure of themagnetic island (the effect of poloidal asymmetry) is notisland is in the direction to decrease of the gap ofpoloidal flow or radial electric field at the boundary ofmagnetic island.

5. Transport Inside the Magnetic lsland
It is an interesting issue whether the transport isincluded in the analysis, the estimate of the absolutevalue of the thermal diffusivity is rather crude.
However, the differences in pulse propagation insideand outside the magnetic island clearly demonstrate thereduction of energy transport inside the magnetic island.

improved or not inside the magnetic island due to theradial electric field. Unless there is a localized fueling or
heating at the center of O-point of the magnetic islandby pellet injection or ECH, significant peaking of
density of temperature is not expected, because
magnetic field in the both side of center of magnetic

6. Gonclusions
The radial profiles of plasma potential, as well as
the electron temperature and density, show flattening
inside the magnetic island and the large shear of theradial electric field is observed at the boundary of themagnetic island. When the current of nlm=lll external
perturbation coils becomes large enough, the finite
radial electric field appears inside the magnetic island.
The plasma flow inside the magnetic island abruptly
appears by the non-linearity of the viscous force at theboundary of the magnetic island. The thermal diffusivity

island is connected. The flat profile does not represent

the large diffusion or large diffusivity inside themagnetic island. The alternative approach to study thetransport is pulse propagation experiment. The transportcoefficients such as thermal diffusivity can be estimatedfrom the amplitude and time delay of the heat or cold
pulse. The tracer-encapsulated solid pellet (TESPEL) is
injected to the X-points of the magnetic island and thecold pulse propagation in the electron temperature is

o.t2
0.08

j

s, 0.04
F-Exp.
-----Simulation

2.r9

R = 3.00m(ourside)

evidence for the significant reduction of heat transport
inside the magnetic island.
This work is partly supported by grant-in-Aid forscientific research of MEXT Japan. The authors would
like to thank Dr. A. Fujisawa and Dr. M. Tanaka for
useful discussions and the technical support on LHD forthe experiments. One of the authors (KI) acknowledged
discussion with Prof S-I. Itoh and Dr. M. Yaei.

X=2.0mzlst:;-'

R=2.90 m(Inside0-0.04

perpendicular to the magnetic filed inside the magnetic
island is estimated with the cold pulse propagation. The
thermal diffusivity inside the magnetic island is O.16 m2l
s, which is much smaller than that outside the magnetic
island (2 m2ls;. The experimental results show a clear

LHD #029555

Radiometer= 0.16 m2ls

2.21

2.23

2.25

Time (s)References

Fig. 4 The response of electron temperature to the cold

tll Y. Kamada, Plasma Phys. Control. Fusion 42,465

pulse produced by the tracer-encapsulated solid
pellet (TESPEL) inside (F=2.9 m) the out side
(R=3.0 m) the magnetic island. The calculated
time traces reproducing the measurements withthe heat diffusivity of )(=016 and 2.0 m2ls are alsoplotted in dashed lines.

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93