J. Plasma Fusion Res. SERIES, YoL.4 (20O1) 3G42

Structure of the Radial Electric Field and Toroidal/Poloidal
Flow in High Temperature Toroidal Plasma
IDA Katsumi*, CHS Group, LHD Group and JFT-2M Group-'1)

National Institute for Fusion Science, Toki 509-5292, Japan
Japa, Atomic Energy Research Institute, Naka-machi, Naka-gun, Ibaragi,319-ll, Japan(Received: 5 December 2000 / Accepted: 18 August 2001)

Abstract
The structure of the radial electric field and toroidal/poloidal flow is discussed for the hightemperature plasma in torodidal systems, tokamak and Heliotron type magnetic configurations. The
spontaneous toroidal and poloidal flows are observed in the plasma with improved confinement. The
radial electric field is mainly determined by the poloidal flow, because the contribution of toroidal flow
to the radial electric field is small. The jump of radial electric field and poloidal flow are commonly
observed near the plasma edge in the so-called high confinement mode (H-mode) plasmas in tokamaks
and electron root plasma in stellarators including Heliotrons. In general the toroidal flow is driven by the

momentum input from neutral beam injected toroidally. There is toroidal flow not driven by neutral beamin the plasma and it will be more significant in the plasma with large electric field. The direction of these
spontaneous toroidal flows depends on the symmetry of magnetic field. The spontaneous toroidal flow
driven by the ion temperature gradient is in the direction to increase the negative radial electric field in
tokamak. The direction of spontaneous toroidal flow in Heliotron plasmas is opposite to that in tokamak
plasmas because of the helicity of symmetry of the magnetic field configuration.

Keywords:
radial electric field, toroidal plasmachanges at the plasma periphery (few cm), was observed

1. lntroduction
A radial electric field has been considered topossibly reduce the ripple loss and to prevent thedegradation of confinement in stellarators and helicalin DIII-D [8], JFT-2M t9,l0l, ASDEX [11]' The
importance of the radial electric field for the H-mode is
now widely recognized.

There are two important mechanisms in thedevices [1]. This is because the neoclassical transport
t2,31 is expected to become more important at higher
temperature and low collisionality plasmas [a]. In
tokamaks. after the transition from low confinement

formation of the radial electric field, one is the damping
term, which is viscosity in plasma rotations, and theother is a driving force to rotate the plasmas toroidallyor poloidally. In the damping term, both the neoclassicalmode (L-mode) to high confinement mode (H-mode [5])(L/H transition) was found in ASDEX, a spontaneous

parallel viscosity and perpendicular viscosity are
discussed. There are external and internal driving forces;
the external forces are momentum input or jxB and thebifurcation of the radial electric field was theoretically
proposed to cause it and thus refreshed the motivation ofinternal forces are ion and electron nonambipolar flux

research t6,?1. The phenomenon, that, associated with
the L/H transition, the radial electric field suddenly

02001 by The Japan Society of Plasma*

Science and Nuclear Fusion Research

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

36

IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal plasma(ion and electron loss induced radial current) due totransition of L- to H-mode is observed. The size of thepoloidal flow in H-mode has no dependence on potoidal
gyro-radius. The poloidal rotation velocity profiles andion temperature profiles at ohmic, L-mode and H-mode
phase are shown in Figure 1(a). The plasma always
rotates in the ion diamagnetic direction outside theseparatrix and in the electron diamagnetic direction
inside the separatrix. The position, where the plasma
does not rotate poloidally, moves outward as the plasmachanges from ohmic to L- to H-mode. The poloidal

density and/or temperature gradient or orbit loss.

2. Spontaneous Poloidal Flow
A spontaneous poloidal flow has been recognized
to be important in the confinement of toroidal plasmas,

since poloidal flow velocity and radial electric field
shear were found to contribute an improvement ofplasma confinement in H-mode plasmas t8-101. The
turbulence in the plasma is predicted to be suppressedby a E x B velocity shear through the mechanism of aflows outside and inside the separatrix are in the

nonlinear de-correlation [12,131. It has been confirmed
experimentally that the E x B shearing rate exceeds the

opposite direction to each other.

growth rate of the turbulence at the transport barrier

2.2 Spontaneous Poloidal Flow in Helical
System
In the Large Helical Device (LHD) the transitionu4,lsl.
2.1 Spontaneous Poloidal Flow in Tokamaks
The poloidal flow is in the electron diamagnetic

from negative electric field (ion root) to positive electricfield (electron root) is observed for the first time inplasmas with neutral beam injection (NBI) heating alone
at a low density of 0.4 - 1.0 x l0re m 3 1t61, regardlessthe direction of beam (in co, counter and balanced
injections). This is because the beam ion loss due to thedirection and appears suddenly near the plasma edge atthe H-mode transition. The poloidal rotation velocity
profile in H-mode has a peak at the separatrix. No

critical normalized ion collisionality, v*;, for the15

l0

t-modeoH\

a0I--rrr-iqn 1961

\ r\tr r.Tr\'n+-elcchon root-o- elestron rootu.+'\,--

,lri
l}

-.\

.

-10

-3

v8

,/+ H+node-l0tls {cur}

0.2

0.4

0.s
0.8
p

1.0

t.2

(c)

L-rnode

u'T

B

Er*0
H-modev+

v+

Fig. l Radial profilesof poloidal rotationvelocityatthetransitionof (a) LmodetoH_modeinJFT-2Mtokamak[10]and(b) ion rootto electron root in LHD Heliotron plasmas
t161. (c), (d) Flow patterns in tokamak H_mode plasmas andHelical electron root plasmas

37

IdaK. et al.. Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma

drift orbit is small enough compared with thewhere the direction of neutral beam injection is changed
from parallel to the plasma current to antiparallel' Non-

experiments [17-21], the transition from ion root toelectron root was observed only in plasmas with ECH'

diffusive momentum transport is found to be inneoclassical non am-bipolar loss. In previous

proportion to VTi. Figure 2 displays time evolution andradial profiles for discharges when the direction of the
NBI is revers ed at t = 750 ms with a plasma current of
243 kA. The co-injection is activated from 550 ms to
750 ms and the counter-injection from 750 ms to 950
ms in Figs. 2(a) and 2(c) and the counter-NBl istherefore it has been also open to question as to whether
the non-thermal electrons driven by ECH are required toachieve the transition. The transition of the radial
electric field from ion root to electron root clearly
demonstrates that non-thermal electrons are notactivated from 600 ms to 750 ms and the co-NBI fromnecessary for the transition, because there are no nonthermal electrons in NBI heated plasma. The edge radial

750 ms to 950 ms in Figs. 2(b), 2(d)' The toroidal
rotation velocity changes its sign depending on the
direction of the beam. The rapid changes in toroidal
rotation velocity after t = 750 ms are due to theelectric field sharply increases up to 15 kV/m in theelectron root as the electron density is decreased while
the absolute values increase gradually up to -5 kV/m inthe ion root over a wide range of electron density of 1.0- 3.0 x 101e m-3. The transition of poloidal flow in theelectron diamagnetic direction (negative E.) to flow inswitching of beam direction from co-injection (driving
positive toroidal rotation) to counter-injection (driving
negative toroidal rotation) or from counter-injection toco-injection. Gradual changes in toroidal rotation
velocity afterwards (800 ms -) are due to thethe ion diamagnetic direction (positive E) is observed at
p > 0.85 and there is no large poloidal flow observed indetermined by the radial transport of momentum driven
by neutral beam injection (NBI) with anomalous shear
viscosity. Although the E x B velocity shear due to theimprovement of momentum confinement associatedwith density peaking. Although the absorbed momentaof the beam are adjusted to be almost identical (injected
power of ctr-NBI is larger than that of co-NBI)' thetoroidal rotation velocity near the plasma center (R =1.35 m) in counter-injection is almost twice of that in
co-injection. The gradient of toroidal rotation velocity
estimated from the difference of toroidal rotation
velocity between R = 1.4 m and R = 1.5 m (indicatedtoroidal flow can be important in the plasma core, therewith arrows in Figs. 2(a) and 2(b)) in counter-injection

the plasma core. The absolute values of poloidal flow
measured in the electron or ion root are the levels
predicted by neoclassical theory [3].

3. Spontaneous Toroidal Flow
The toroidal flow has been considered to beis 2-3 times larger than that in co-injection. Figure 2 (c)'(d) displays profiles of toroidal momentum (mlnivQ) for
discharges when the direction of the injected neutralbeam changes from co- to counter and from counter toco at the flat top of the plasma current (/ = 750 ms)'have been few experiments that demonstrate aspontaneous toroidal flow not driven by NBI in
tokamaks 122-251. It is generally the case in tokamaks
that the plasma rotates parallel (anti-parallel) to theplasma current for the co-injected (counter-injected)
NBI, which corresponds to a positive (negative) radial
electric field (Er) in L-mode plasmas. However, when anegative Er is produced at the transport barrier, bothHere, mi is the ion mass and n; is the ion density ofdeutrons. As shown in Fig. 3(a), the differences of
toroidal rotation velocity between co-injection andcounter-injection becomes small, when the plasma
current, /o, is increased (poloidal field is also increased).
Figure 3(b) shows the off-diagonal coefficient given by
the slope in Fig. 3(a) as a function of plasma current'

localized toroidal flow in the counter-direction andlocalized poloidal flow in the electron diamagnetic
direction are observed even for plasmas with co-injected
NBI t26,271. These results show the need for detailed

The off-diagonal coefficients derived at p = 0.46 using
the transport analysis are also plotted for comparison.
This agreement suggests the validity of assumption off(co-nbi) = -f(ctr-nbi) and that the differences in themagnitude and profile of momentum input between coinjection and counter-injection can be ignored. The offdiagonal coefficient decreases as the plasma current, 10,
is increased. It is not clear whether the off-diagonal term
will disappear or simply decrease as proportional to lllemeasurements of both toroidal and poloidal flow at thetransport barrier, where the toroidal flow profile is notdetermined by the transport of momentum driven by

NBI alone.
3.1 Spontaneous Toroidal Flow in Tokamaks

A non-diffusive term in the toroidal-momentumtransport equation is evaluated by the analysis of thetransport of toroidal rotation in the transient phase,38

IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal plasma
100

(*)

' ++- 1.35 --i-rn:243kA 4lxg

50

€o

100

t.5o

=1ail

5n

(b)
p

Til

=243kA ---'-;i.4
I

+0

E

-u

----f-

-t
scn

J=to

> -JU

- 100

- 100

- l{A
LJV

-150f.'..,,

550 600 650 700 ?50 800 850 900 950
time (ms)80

550 600 650 700 ?50 800 850 900 950

80

co to ck

40

40

nme

ctr to co

0

-q 40
e

F -go
-120
-160

d

0.2

0.4

.
'
+
r
o
+
0.6

pp

-40

_51

?40.6ms?57.3ms
773.9ms?90.dms!'

807.3ms
823.9ms

+

-80
-120

840.6ms- 160

0.8" J40. ms---4-'757
msoms---f- 7'13.
790. m5ms*---+- 807.
823. ms- 840. ms

Fig.2(a),(b) Timeevolutionof toroidal rotationvelocityatR=1.!g, 140, 1.45,1.S0, 1.55, 1.60mand(c),(d) radial
profiles of toroidal momentum during the transient phase for discharges when the direction of the NBI isreversed. (a), (c) The co-injection is activated from 550 ms to 750 ms and the counter-injection from 750 ms to g50
ms' (b), (d) The counter-NBl is activated from 550 ms to 750 ms and the co-NBl from 750 ms to 950 ms [24].

when the plasma current is increased above 350 kA. The
range of plasma current available in the JFT-2M is notwide enough to conclude the Ip dependence of the offdiagonal coefficients. If this current dependence is dueto the drift orbit physics, the off-diagonal term should
disappear in the plasma with large minor radius andincreases as the plasma current is decreased.

3.2 Spontaneous Toroidal Flow in Helicallarge plasma current, where the drift orbit loss is

SystemA toroidal flow anti-parallel to the <E. x Be > drift
direction is observed in the hot electron mode plasmas
when a large positive electric field and a sharp electron

negligible. However, the off-diagonal term of toroidal
momentum is observed in the large tokamak with alarge plasma current [28]. Therefore the off-diagonaltemperature gradient are sustained inside the internaltransport barrier in the Compact Helical System (CHS)[29]. This toroidal flow reaches up to 5 x 104 m/s at theterm is considered to be not due to the orbit physics andit is general characteristic in tokamaks regardless thesize of plasma or plasma current. The plasma current

plasma center and it is large enough to reverse thedependence of the off-diagonal coefficient observed infavors flow in the minimum VB direction at thetransport barrier.
The reversal of toroidal flow is observed when the
2 nd ECH pulse (r = 60-140 ms, Pur, = 0.11 MW) is
applied to the NBI plasma (t = 40-l2O0 ms E167 = 36 kV

toroidal flow driven by tangentially injected neutral
beam. These observations clearly show that the plasma

JFT-2M at least supports the hypothesis that the offdiagonal coefficient is proportional to lllo or llBo. The
ratio of non-diffusive viscosity coefficient to diffusive
viscosity coefficient is evaluated to be 0.1 to 0.3, which39ldaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma--r.-II]-JUf=l+JKfI
50
40

*t
\E

tr

0.3

Kfl

:242kA - E-ri:155 kA:243kA .d- Ip:258k4

(b)

tt
0.2

a*

\-{

E

= e

a

t0

0.1

_+- off-diagonall0

tr off-diagonal trans-4 -3 -2-l

50

100 r50 200 250 300

35u

rP (kA)dT,/dr (lreV/m)

(c)

{d)

Spantaneou$ flow. --"2-.t'--"

large Ipp0

Fig. 3 (a) The difference of gradient of toroidal rotation velocity between co-injection and counter injection as a functionof the gradient of ion temperature at R = 1.45 m (p = 0.46) for discharges with the various plasma current. (b) Offdiagonal coefficient a function of plasma current with a simple formula and with a transport analysis [2a] (c), (d)relation of plasma flow respect to the direction of magnetic field for large and small plasma current (lo).
large electric field of 10-20 kV/m and the large poloidal
flow of 10-20 km/s are produced near the plasma center

PNil = O.7 MW) with low electron density below 0.7 x

lgte .-3. Hete p is the normalized averaged minor
radius (p = rla).The electron temperature increases up
to 2 keV (hot electron mode), while it is only 0.2 keV(p = 0.3) [Fig. a(a)].

when there is no 2nd ECH pulse, which indicates asignificant improvement in electron confinement during
the 2nd ECH pulse, the electron collisionality is low
enough to make the plasma to be in the electron root
(positive electric field). The positive radial electric field

tangentially in the co-direction. Here the "co" direction(positive flow velocity) is defined as parallel to theis mainly contributed by the poloidal flow in theflow velocity) is defined as anti-parallel to thedirection parallel to the <E, x Bo> drift. The Lorenz
forces due to the toroidal flow and the force due to theion pressure are negligible in the radial force balance[30]. The Lorenz force due to the poloidal flow isalmost balanced with the force due to the radial electricfield and therefor the magnitude of Er is roughly equal
to vsB6 in CHS plasmas. The radial electric field
derived from plasma flow with the radial force balance
agrees well with that measured with HIBP [31]. The

equivalent toroidal plasma current. As seen in Fig. 4(b),the plasma rotates parallel to the NBI when there is no

The neutral beam is injected to the plasma

equivalent toroidal plasma current, which would
produce the average transform actually produced by theexternal coil current. The "counter" direction (negative

2nd ECH. This is simply because the toroidal
momentum from the NBI causes the plasma toroidal
flow. However, when the 2nd ECH is turned on, thetoroidal flow velocity decreases and finally the plasma
rotates anti-parallel to the NBI. These measurements
clearly show the driven toroidal flow associated with alarge poloidal flow (and large positive radial electric40

IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma

20
15
10

trn
F-J

{B}

-10

+rarith 2ndECH

1{-o- no 2nd ECH

-20
0.0

0.2

40
30

L mode

=
-.9-

20

€'

x

110ms

-*o -J

10r
Y*r+__

En

&

>alo
-20
-30

Co-NBIt el?ctron mode+-rarith 2ndECH

40
0

0.2

0.4

0.6

0.8

1.0

D

Fig. 4 Radial profiles of poloidal flow velocity at t = 110 ms and (b) toroidal flow velocity at t = 110 ms for the discharges
with and without 2nd ECH pulse [29]. (c) Mod-B contour and flow pattern at p = 0.3 in CHS. The arrows stand forthe flows in plasmas for NBI and NBI + ECH discharges.

field) during the 2nd ECH pulse. The driven toroidal
flow reaches 5 x 104 m/s at the plasma center and it islarge enough to overcome the toroidal flow driven bytangentially injected neutral beam. It should beemphasized that the direction of the toroidal flow isanti-parallel to the direction of <E. x Be> drift. Thispoloidal flow observed in the H-mode in tokamaks is
the jump of poloidal flow to the electron diamagnetic
direction associated with the sudden increase of negative
radial electric field shear. The turbulence levels in theplasma are also reduced as predicted by the anomaloustransport models. On the other hand, the transition ofpoloidal flow observed in helical plasma is the change

fact has not been predicted before, because a simple
analogy from the experiments in tokamaks implies thatthe direction of the toroidal flow associated with a large
radial electric field is parallel to the direction of <Er xfrom electron diamagnetic direction to the ion
diamagnetic direction, which is due to the reduction ofripple loss by large radial electric fields as predicted by

Be > drift. This is because the toroidal viscosity is nearly

the neoclassical theory.

zero due to the toroidal symmetry and the direction of
the toroidal flow is simply determined by the directionof the <E. x 86 > drift in most discharges in tokamaks.

The spontaneous toroidal flows are observed intokamak and helical plasmas. They become moresignificant at the transport barrier where the ion orelectron pressure gradients become large. The

4, Discussion

spontaneous toroidal flow in tokamaks is parallel to thedirection of <C, x Be> drift, while the spontaneous
toroidal flow in helical plasmas is anti-parallel to thedirection of <E, x Be ) drift. This difference in the
direction of spontaneous toroidal flow is due to the

Although the transition of radial electric field andpoloidal flow and spontaneous toroidal flow areobserved both in tokamak and helical plasmas, there aredifferences in the direction of flows. The transition of

4l

IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma

tl2l H. Biglari, P.H. Diamond and P.W. Terry, Phys.
Fluids B 2. (1990) l.

difference of symmetry of magnetic field configuration.
Since the plasma tends to flow along the minimum VB
direction, where the parallel viscosity becomesminimum, the spontaneous toroidal flow in tokamak is

t13l K.C. Shaing, E.C. Crume Jr. and W.A. Houlberg,
Phys. Fluids B 2, (1990) 1492.
ll4l K.H. Burrell, Phys Plasmas 4, (1997) 1499.
ll5lE.J. Synakowski et al.,Phy. Rev. Lett. 78, (1997)

always parallel to the <E. x Be> drift direction. In
helical plasmas, the spontaneous flow has spiralstructure due to the helical symmetry and the toroidal
flow can be antiparallel to the <E,x Be > drift direction
depending on the direction of pitch of spiral structure.
In conclusion, the spontaneous poloidal andtoroidal flow are observed in tokamak and helicalplasmas associated with the large positive or negative
radial electric field near the transport barrier. The
understanding of the mechanism to drive thespontaneous poloidal and toroidal flow will be the key
issue in the research of confinement improvement of

2972.

tl6l K. Ida, H. Funaba, S. Kado et al.,Phys. Rev. Lett.
86, (200r) s297.

[17] H. Idei, K. Ida, H. Sanuki et al.,Phys. Rev. Lett.
7r, {1993) 2220.
tl8l A. Fujisawa, H. Iguchi, T. Minami et al., Phys.
Rev. Lett. 81, (1998) 2256.
[19] J. Baldzuhm et al., Plasma Phys. Control. Fusion
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t20l A. Fujisawa, H. Iguchi, T. Minami et al., Phys.
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t22lK. Nagashima, Y. Koida and H. Shirai, Nucl.

high temperature toroidal plasmas.

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A1