J. Plasma Fusion Res. SERIES, Vol. 5 (2002) 3-11

lnternal Transport Barrier Physics for Steady State Operationin Tokamaks
WAKATANI Masahiro, FUKUDA TaKeshii, CONNOR JacK W.2, GARBET Xavief,
GORMEZANO Claudea and MUKHOVATOV Vladimit'
Graduate School of Engineering, Kyoto Univ., Uji 611-0011, JapanI Naka Fusion Research Establishment, Japan Atomic Energy Research Institute, Ibaraki 311-0193, tapan
2 nUnefOM/UKAEA

Association, Culham Science Centre
EFDA-JET
CSU,
Culham Science Cente"
4
Associazone EURATOM-ENEA sulla Fusione C.R. Frascati) ITER Physics Unit, ITER Naka Joint Work Site
(Received: ll December 2001 I Accepted:25 June 2002)

Abstract
Experimental results for the ITB (Internal Transport Barrier) formation and sustainment arecompiled in a unified manner to find common features of ITBs in tokamaks. Global scaling laws forthreshold power to obtain the ITBs are discussed. Theoretical models for plasmas with ITBs are
summarized from stability and transport point of view. Finally possibility to obtain steady-state ITBs will
be discussed in addition to extrapolation to ITER.

Keywords:
tokamak plasma, confinement improvement, internal transport barrier, steady state operation, ITER

1. Introduction
According to recent experimental results on the
improved confinement in tokamaks with an ITB(Internal Transport Barrier), it is recognized that steadystate operation of tokamaks becomes realistic, since afraction ofbootstrap current can be sufficiently high [1].
Thus, it is important to understand physics of the ITB
from various point of views. So far all major tokamaks
presented experimental results on plasmas with ITBs.

However, understanding for the formation andsustainment mechanism of ITB is primitive compared to
the H-mode plasmas with ETB (edge transport barrier)[2]. Therefore, the aim of this review is to compile
experimental results for the ITB formation andsustainment in a unified manner, and find common
features of ITBs. Then global scaling laws for thethreshold power to obtain the ITBs will be discussed.

Next theoretical models for plasmas with ITBs fromstability and transport point of view are summarized.
Finally the possibility to obtain steady-state ITBs will be
discussed. Also the extrapolation to ITER will beshown.

2. ITB Database
ITBs were originally produced by intense central
heating of a low density target plasma with strong
positive magnetic shear. The increasing demand forsustained, highly integrated tokamak performance (withrespect to substantially enhanced confinement, improved

stability and a large bootstrap current fraction) in a
steady state, sees ITBs as one of the most efficient andattractive approaches. On the other hand, the edge
barrier produced at the H-mode transition also play a@2002 by The Japan Society of Plasma

Corresponding author's e-mail: wakatani@ energy.lcyoto-u.ac.jp

Science and Nuclear Fusion ResearchWakatani M. et al., Internal Transport Barrier Physics for Steady State Operation in Tokamaks

substantial role in further reducing transport andimproving stability by broadening the global pressure
profile. Already the requirements for edge transport

the ITB. However, the ratio of the Z; values at two
different radial locations is also used in order to define
ITB formation in ASDEX-Upgrade; this corresponds tobarrier formation have been carefully studied in various
tokamaks and integrated into an international database

Lr.> 1.4 x 102 [3] is also employed as a measure of

to derive a scaling law for the power threshold [].
However, the formation conditions for ITBs have notyet been extensively investigated, and apparent
inconsistencies between different devices are often
discussed.

Accordingly, the international ITB database
working group has been established to address
primarily: (i) the power threshold scaling for ITB
formation; (ii) the confinement scaling for plasmas with
ITBs for extrapolation to future devices; (iii) theunderlying physics of ITB formation by comparison
with theoretical models; as well as (iv) thecontrollability of ITB characteristics. At present, 37

a breakdown ofprofile stiffness. The criterion P*r.= P,/

ITB formation in JET. Here, p, = c"la"i is the ion
Larmor radius at the sound speed and L7" is acharacteristic length of electron temperature gradient.
This criterion scales as T05|BR. As to the location of
ITBs, the ITB foot or Proo, where the pressure profile
starts to increase is defined to be either at the local
maximum in the second derivative of the ?t profile or at
the local minimum of lLrr-t l, as depicted in Fig. I (c),where 27, is a characteristic length of ion temperature
gradient. The magnetic shear at the local maximum ofd2Tildr2 is close to zero or positive, even in negative
shear plasmas, whereas the ITB foot can be formed bothin negative and positive regions in reversed shear

scientists working on 13 different tokamaks have been
involved in the activity, and an international database,plasmas in JT-60U and DIII-D, possibly as a result of
the heating profile. In other words, even in plasmas withwhich is composed of a 0-D database with 126 variables
and 6 kinds of 2-D profile databases, is being
accumulated. This section first reviews thenegative central shear, the ITB can be formed at alocation with positive shear if the heating profile isbroad; a large gross heating power is required in thiscase. The ITB foot moves inward in a few 100 ms at thephenomenological conditions for ITB formation,comparing those for the 13 tokamaks, based on
published results and discussions at the ITB database
working group meetings. However, the ultimate aim of
this section is to extract common features to resolve theunderlying physics of ITB formation.
In addition to parameters similar to those included
in other international databases such as the one ref. [l]is based on, variables which reflect profile information

have been introduced into the 0-D ITB database.
Furthermore the profile database is composed ofmultiple time slices during ITB formation in order toallow modelling of the dynamics of ITB development.
However, it is expected that a scaling of critical power

JT-f0u I 803.16S3

(n) 7
6

*1

7a

:,
F'

2
I

I
D

f-0 l-5 4-0 4,5 5.0 5.5 6.0

or 7", respectively, at different locations from eachother.). Here, a bipolar change of the 4 profile between
the times just before and just after the formation of thebarrier is often observed in JT-60U as shown in Fig. I(a) and I (b). This indicates a reduction of the heat flux
across the barrier and a resulting reduction of T; outside

0.4 fl.6 0,$ 1.0

Dlll-D/$46$) rl !-6 s

rN'.'l\-*d!r,Idr:'''\ i !it"'consisting only of global engineering variables will not
suffice. Thus the condition on Z1 for barrier formation is
discussed here, except in the case of Tore Supra.
The standard approach employed for the definitionof ITB formation is the separation of the signals in two
neighbouring channels of either the CXRS or ECE
diagnostics (which are relevant to the measurement of Tt

0.0 1,1

Tinre Is]

.'

l

"

!,L ,'/'il''r'iiv

0.0

0.2

r:e

o,$ I.o

3

I

?E

o

J
lE
X

f,

-28
^c
-4

-:l -!

43
.5
-6
-7

Fig. 1 (a) Temporal evolution of f, at different locations

shown with normalized radii, which indicates the
ITB formation and (b) bipolar change of the I profile observed in JT-60U reversed shear discharge.
(c) The location of maxima of d2T/dr2 and 1/Ln in
the Dlll-D I profile, where r and Ln are measured
in [m]. Here p,"", where the pressure profile starts
to incerease is defined two ways; maximum of dd2Tldr2 and minimum of 11L".

Wakatani M. et al., Intemal Transport Barrier Physics for Steady State Operation in Tokamaks

time of ITB formation as the pressure profile changes.

Presently, ll4 JET,85 JT-60U, 27 ASDEXUpgrade, 22O DIII-D,23 Tore Supra and 24 FTU 0-D
database entries as well as 220 2-D DIII-D profile
database entrios are compiled in the International ITB
Database [4]. Figures 2. (a)-(c) show the B, dependenceof the critical heating power in JET, JT-60U, ASDEXUpgrade and FTU. The B, scan data for DIII-D and ToreSupra are included. The FTU database is from the ohmic
PEP mode and the others refer to barrier formation in

The significance of this result is that theoretical models
based on sheared E x B flows require rather a strong B,

dependence. For example, in refs. [5,6], threshold
powers of the forms n.Brm;tS and n,a3BrT"f (d/a, s/q),
respectively, are suggested for the case of Bohm-like
transport. Here, d is the beam deposition radius, S is theplasma surface area and f is a function of its arguments.
Therefore, the .E x B shear flow might well only be

the 7, profile. Elimination of the high density, high 's-

significant for the transport reduction but not for the
ITB formation itself. Figures 2 (d)-(0 show a distinctive
density dependence of the critical heating power in all

foot' data as u'ell as the low density, low 's-foot' data

the devices except Tore Supra, for which the span of theleads to a weak B, dependence. Here, s-foot is pd(lnq)ldensity scan is small. The density plays an importantrole in determining the heating power deposition profileand target 4 profile. Thus the reduction of heating power
demonstrated here is consistent with our experimental
experience that low density operation (where the target
density profile is peaked and the initial I" profile ishollow due to an increase of the resistive skin time) is
advantageous for ITB formation compared to the higher
density case. It should be noted here that both low shear
LHCD preheat pulses in JET and weak shear JT-60U
results achieve a reduced critical heating power. Figures
2 (g)-(i) show the s-foot dependence; a reduction of

dp at the ITB foot as defined above. The pulses with LH
preheat before the time of ITB formation are included in

the JET database, and these are examined
comprehensively in terms of the local magnetic shear at
the location of ITB formation. Then the B, dependence
disappears. Also in JT-60U, elimination of higher s-footpoints removes the B, dependence. In neither ASDEXUpgrade or Fl'U is a strong B, dependence observed.

. AtG!r*lt,:-ExlcreLn'J(cl l.

jq

-t

.F

i&1

2L

z'

critical heating power with reduced s-foot isdemonstrated. However, in the case of I" barrier
formation in Tore Supra, this dependence is notobservable or is slightly the opposite, possibly due to thefact that p-foot is fixed at rla = 0.4 in the database. As
can be seen in the JET data, the application of LHCD
does not automatically reduce the shear at the ITB footAl0

at higher density, indicating that the production ofnegative central shear does not necessarily produce an
ITB in the negative shear region. The 1o dependence is
not obvious in the presence of a large scatter, except for
it ,JH
{{t
'". t

:s

n{'lJ-!-4

E$

II!.D

low ,Io JT-60U data, in which P1e55, the loss-power,ln, $increases linearly with 10. Therefore, the heating profile*-3'

and magnetic shear at the location of an ITB seem toplay an important role in that centrally peaked heating

3,t
Aro

fT
F.o
&.

f,

&5

0

0.?0.40.60-$ l0 l.? t.4ls

0 t-;---i:'l0-0.! 0.0 0.5 1.0 l,J :.0-D. r 0^0 0. I o.? 0l 0.a o.J d6
sto, (uFper sle ftr
A UG ,fri Lower fdr TS)

Fig. 2 The dependence of critical heating power on Q in(a) JET, (b) JT-60U, Dlll-D and Tore Supra and (c)ASDEX-Upgrade and FTU. The density dependence of the critical heating power in (d) JET and
Dlll-D, (e) JT-60U and (f) ASDEX-Upgrade, ToreSupra and FTU. The dependence of critical heating power on s foot in (g) JET and Dlll-D, (h) JT60U and (i) ASDEX-Upgrade and Tore Supra. Heresroo, is a magnetic shear at proo,.

produces the ITB nearer the plasma centre.

Another intriguing feature observed in the multitokamak International ITB Database concerns theconfinement characteristics of ITB discharges. Thus thestored energy increases with plasma current and ITB
radius when 4,1n is fixed. In addition the heating power
dependence of the stored energy is stronger in thenegative shear case, indicating that the negative shear
plasmas exhibit superior confinement performance incomparison with the positive or weak shear plasmas.

Wakatani M. et al., Internal Transport Barrier Physics for Steady State Operation in Tokamaks

3. Theory of Internal Transport Barriers
Most theoretical models for ITB formation
ultimately rely on the suppression of microinstability
induced transport by sheared E x B flows, supported byexperimental observations of these near ITBs. (See thereviews by Staebler [7] and Wakatani [8]). Different
models emphasise the various contributions to E x B
arising from the radial ion force balance for the radial
electric field, E :E,=+# -r,tr+voBe(1)

simple, and useful, 'ru1e-of-thumb' deduced by Waltz et.
al. from numerical simulations of turbulence [15,16] is:(3)@n) Tr;,n(ah = O)

where the right hand side denotes the linear growth rate,of a drift wave instability (e.g. ion temperature gra-1;

dient (ITG) or trapped electron (TE) drift waves) in theabsence of the sheared rotation. This criterion is equivalent to a critical value of the parameter p*1 (= PilLn)[3]. It is encouraging that experimental values of ol" at

ITB formation are consistent with criterion (3) t2,17211. However it should be noted that this is too demand-

Thus transport equations forpl (ion pressure) and Vq (to-ing a criterion for the high values of the linear growthroidal flow velocity), with heating and momentum inputs, can determine contributions to E,; fluctuation in-

rates associated with short-wavelength electron temperature gradient (ETG) modes, which might explain the dif-

duced Reynolds stress, poloidal momentum inputs, say

ficulty in forming 7. barriers.

from ion Bernstein waves, or torques from non-An interesting study [22] has investigated the effectof reverse magnetic shear on quasilinear estimates of the
diffusion coefficient, D, = ynhl, where n is a toroidal
mode number and yn and l,o are the linear mode growthrate and wavelength, respectively; s = -0.5 is found to
be optimal (see Fig. 3). This can reduce the resultant
transport, allowing dpildr to build up; steeper gradients

ambipolar losses can drive Vs, where Vq is a poloidal
flow velocity (although Vs is often taken from neoclassi-

cal theory, using the NCLASS code [9]). However,
Staebler [10] has shown it is possible to have bifurcations in V6 when a poloidal momentum balance equation
with a turbulent viscosity is used. These 'jet-like' solutions resemble the spontaneous flows found in TFTR.
The E x B shear can lead to a reduction in theamplitude of turbulent fluctuations, even to theirsuppression, or to a decrease in the radial correlation
lengths, i.e. a breaking up of turbulent eddies. As wellas its effect in suppressing fluctuation amplitudes andcorrelation lengths, Teny [11] has emphasised the roleof E in reducing transport through its influence on theof E are created through eg. (1) and turbulence issuppressed further, this feedback mechanism leading toa possible bifurcation in the transport equations [22].

cross-phase of the fluctuations.

The suppression of microinstabilities by E x B
shear is characterised by the shearing frequency, ro6.
Hahm and Burrell [2] have defined this as,"=+*(^e)?

(2)

where R is the tokamak major radius. The factor containing the ratio of poloidal and radial wavenumbers, fts
and k, respectively, is normally taken to be unity, but
could be large for radially extended fluctuations. It isnoteworthy that arE is more effective on the low fieldside, consistent with some observations; it is also apparent that hollow current profiles with negative magnetic
shear are favourable. Criteria for the suppression of turbulent transport by o6 have been given by Biglari, Diamond and Terry [13] and Hassam [4]: a typical estimate is al'e> clR where c" is the sound velocity. In general, this is a complex issue. Fortunately, however, a-1.0 -0.s 0.0 0.5

1.0magnetic shear
Fig.3 Contours of quasilinear estimates of the
diffusivity, D" (in m2s-1), from linear modes, where
n is the toroidal mode number, are shown in the
n - s plane; s is the magnetic shear and the figure
shows s = -0.5 is optimal [22].

Wakatani M. et al., Internal Transport Barrier Physics for Steady State Operation in Tokamaks

Furthermore, roroidal gyrokinetic simulations of ITG
modes in the presence of a surface with s = 0 at q-1n
show that mode structures cannot cross this surface:independent modes exist on each side. Indeed, nonlinear

simulations show that this surface acts as a banier [23]with the 4 profile and questions of power (ormomentum) input confuse the issue and no simple
scaling is likely to obtain. Global turbulence simulations

show no obvious threshold, but the quality of the ITB
improves with increased power throughput. We have(see Fig. 4), alriough this is only partial as some modes(e.g., ETG modes) are not strongly affected 124).

The turbulence simulations described here areglobal, toroidal ones, driven by sources. This allows
interactions belween the prohles and the turbulence withpotentially complex feedback loops. The resulting
turbulent transport can exhibit avalanches and has a'bursty' charar:ter. Garbet et al. [25] have carried out

global, toroidal, three-dimensional simulations ofelectrostatic ITG turbulence and transport in a range off--;r\] t----F.t r--T,,Tt
J..., \l| *-1..!i\'. 025 0.5 0.t5 1 o 025 0.5 o?50 025 0.5 075 1 0=^eredGAJ:0.e
r6/a =0.5(b) r."/u

(a)

I

1

(c) r_/a =065

4 profiles. They find that in a monotonic 4 profile global

modes exist, leading to L-mode transport. However,when there is a minimum in 4(r) an ITB forms rr€itr {611
as a result of the disruption of the mode structure due tothe rarefaction of rational surfaces occurring there.
Specifically, a gap in the density of rational surfaces,with width L. - (2q^lnpilnr^rnd2qldr2)tt2, occurs at e^in.
This effect is exaggerated when 4-1n is near a rational
value, as seen in Fig. 5 for the resulting thermal

Fig. 4 Potential structures in the poloidal cross section
and corresponding radial profiles in the case of areversed (parabolic) q profile for three different
q-,n locations (solid lines in the figure), i.e. (a) r-,n/a = 0.5, (b) r.;"/a = 0.6 and lcl r^,^la = 0.65 [23]. The

location of the maximum pressure gradient, r(dashed line), is around r- = 0.6 and r, = r.rn incase (b). The profile of potential fluctuation istaken along the dotted line as shown in (a).

diffusivities.
These barriers are reminiscent of the results ofKishimoto et al. [23] who performed global, toroidal,
gyrokinetic particle simulations of ITG turbulence witha non-monotonic 4 profile and found that global mode
structures were broken up at qnin where a barrier
formed, as shown in Fig. 4. Garbet et al. found that
there was no power threshold, although an increasingheat flux rapidly increases the strength of the barrier
because of the resulting larger E x B flow shear. Indeed
the width of the ITB is controlled by the range of the Ex B shear flow. which has a dipole structure since E -.
-RS c6;p;1.35
RS clnin=l.5

dpjdr and the rnodel assumes a flat density profile andno input of mornentum. The turbulence itself evolves sothat large amplitude zonal flows result. The dipole
structure has the consequence that the barrier isstationary; inclusion of co-rotating toroidal flows, forinstance, leads to an outward propagation. Counterrotating, or balanced, flows are more favourable, withthe self-generated toroidal velocity (from the Reynolds
stress) playing an important role: neoclassical levels of
Zi result. In related work [26] it was found that transport'events' which occur as bursts. hardlv cross suchbarriers.
One key issue is whether there is a power thresholdfor ITB formation, as for H-mode. Clearly the interplay

0.4

0.6

0.8

Fig. 5 The radial profiles of the thermal diffusivity, 7n,from ITG simulations for three g profiles; thedashed line labels a monotonic. L-mode q profile;the dotted line labels a non-monotonic g profile
with a minimum q value, q*,. = 1.35; and the fullline labels one with a rational g-n = 1.5. The strongest ITB corresponds to gmin near a rational surface [25].

Wakatani M. et al., Internal Transport Barrier Physics for Steady State Opelation in Tokamaks

seen transport calculations are able to give a spatiotemporal evolution of ITBs in a range of situations; itwill be interesting to determine the range of variation
when they are used predictively for a next step device
like ITER. However, the transport simulations reflect, inpart at least, the need to satisfy criterion (3), which
typically translates into a condition on p*r - p;/11;. Thiscondition, well exhibited by JET ITBs [3], leads to a
threshold power scaling asr)tz,

Pn, n h"a RYtr 61 7(t-(4)

where we have assumed gyroBohm confinement, 7 *(pi2 vilLr) (R/1,1)/ with Vi the ion thermal speed and 7
an exponent lying in the range 0 < y < 1 . (Clearly different powers of pilL1 in 7 will lead to the same scalingfor P15 if pilL, is the critical parameter.) Expression (4)of course conceals important dependencies on heating

profiles and magnetic shear. A typical value for yis l/2,
implying(s)

Prr,n n"aR3t2Btn TY4This has some features of observed scalings but scales
unfavourably to next step devices.

4. Steady State Plasmas
The reactor relevance of ITBs relies mainly onachieving and controlling steady state regimes. A
tokamak plasma is characterised by several time scales
as shown in Fig. 6: the MHD instability growth time(from ps to ms), the confinement time (s), the current

diffusion time scale (100 s) and the plasma-wall
equilibrium time (> min). In principle, steady statemeans a discharge duration longer then the greatest ofthese time scales. In practice, the word 'steady state'covers various definitions in the literature. The mostcommon definitions refer to the confinement time (theseplasmas are sometimes called 'quasi steady state'), andto the resistive time scale.
A fully steady state ITB in a reactor ultimately

SecondMillisecond

tll

I

MHD

T.ansDort

MinuteCunrrttdiffusion

Hour

Wall nlrsma Ero'i,rnequilibrium

Physics
Activerv Radial
cooiia---PFC

Control

whoie srstem

Equilibiut

Fig. 6 Physical and technological time scales. Here PFC
denotes a plasma facing component.

requires the use of at least one (most probably several)current drive schemes. The current drive efficiency isusually expressed as 4co = nrRlrlPco, where n" is thedensity (in 1020 m-3), R the major radius (m), 1o thegenerated current (MA), PcD the additional power(MW). The efficiency is generally found to increaselinearly with the volume average electron temperature?". A fit to experimental results for Lower Hybrid
Current Drive is rlco = 1.2 T"/(5 + Z*) (7" in keV) [1].
A rough estimate of the power needed to fully sustain
the plasma current in a reactor leads to high values ofadditional power. Therefore, a large bootstrap current
fraction will be necessary to achieve a viable scenario.
In DIII-D, a half of 1o is supplied with the bootstrap
culrent IBs 121 l, and in JT-60U I Bsl I p - 0.7 2 is realized[28]. Fortunately, the natural profile of the bootstrap
current in a tokamak is hollow. This is favourable forthe achievement of magnetic shear reversal. However
the bootstrap current alone cannot sustain a steady state

ITB because the alignment with the required 4 profile
for an internal barrier is usually inadequate. It is notedthat a negative shear configuration is formed with therapid ramp up of plasma current but it is difficult tosustain the q profile. Several current drive schemes areavailable to provide naturally hollow current profiles in
hot plasmas. This is the case for Lower Hybrid Current
Drive (LHCD) because of the single pass absorption of
those waves on electrons for 7" 2 l0 keV. Neutral Beam

Injection (NBI) also allows some flexibility.
Nevertheless, in some cases the central current density
needs to be finely tuned. This requires an additional
scheme for central current drive. Electron Cyclotron

Current Drive (ECCD), Fast Wave Current Drive(FWCD) or high energy Neutral Beam Current Drive(NBCD) have already demonstrated their efficiency. In
the following we will separate the quasi steady state
discharges from those achieving a duration close to or
beyond the resistive time scale.

4.1 Ouasi-Steady lTBs
The first difficulty to overcome with ITBs concems
their MHD stability. Indeed the large pressure gradientat the barrier may locally exceed a stability limit. Thisissue is particularly critical if the magnetic shear is low

near the barrier. Theoretical calculations show that forpeaked pressure profiles, the p-limit is below the Troyon
value (normalised BN - 3). For a reversed shear plasma'
the Flimit decreases dramatically if the minimum valueof the safety factor, q.1n, is close to a simple rational.
Several recipes have been proposed so far to circumvent

Wakatani M. et al., Internal Transport Barrier Physics for Steady State Operation in Tokamaks

this problem.

zB). In ASDEX-Upgrade, it was possible to sustain an

A feedback control of B or an average ion pressure
more exactly based on the neutron rate production or on

the diamagnetic content has proved to be efficient in
TFTR, JET [18,29] and JT-60U [30]. Here the heating
power is controlled by observing a neutron production
rate. Unfortunately in JET, the feedback was not
optimised for DT plasmas [29]. In JT-60U, a similar
method avoids too large a pressure gradient whenrational values of 4 are encountered. In this way,
plasmas with Qot,"o - I (where Qor,"o is the equivalent
Q in a DT plasma) were achieved for a fraction of asecond, and Qp1,"q - 0.1 for ls (- rs). Control ofcurrent
and pressure profiles is needed to achieve longer pulses.
In spite of continuous progress, these feedback methods

barely maintain a stable plasma beyond a few
confinement times. The pressure profile has to be lesspeaked to achieve a longer pulse. This is why, in
general, the performance decreases with the plasma
duration.

4.2 Steady lTBs

A method commonly used to increase the pulse
length while improving performance consists ofcombining an ITB with an ELMy H-mode, i.e.
producing a double barrier. It has been possible tosustain a pulse with an ITB for several seconds in a
number of der.ices, namely JET [3,31], JT-60U [32],DIII-D [33,34]nd ASDEX-Upgrade [35]. In a few cases,
the duration was close to or longer than the resistive
time scale. Some examples are given in Table l. In JET,

ITB combined with an H-mode for 2.5 resistive times(- 40 til. In these plasmas, the 4 profile was clamped
because of the presence of fishbones.

5. Extrapolation to ITERInternal transport barriers may significantly
improve the plasma performance in future large devices.

In ITER [37], a20-30Vo increase in the transport energy
confinement time (26) relative to that expected for the
standard H-mode will allow ignition in a nominally p =10 regime, and a 50-60Vo increase in zu will be
sufficient for steady state operation with Q > 5. These
improvements in z6 are within the range achieved inmany experiments where ITBs have been created.
However, for reliable extrapolation of such regimes to
ITER conditions several critical questions need to beanswered. They include (i) the size scaling of theconditions for ITB formation, (ii) the possibility forsustaining ITBs at high plasma density (n.> 0.8 n6,
where n6 is the Greenwald density) and Ti = f", (iii) the
prevention of impurity accumulation inside the ITB, and(iv) the possibility of controlling ITBs.
There are two approaches to the prediction of theconditions for ITB formation in ITER. The first one ispurely empirical and based on analysis of theInternational ITB Database (see Sec. 2). A regression fitof the net heating power just before ITB formation infour major divertor tokamaks (JET, JT-60U, ASDEXUpgrade and DIII-D) with dominant ion heating gave
the following scaling for the ion ITB power thresholda DT discharge with Q = 0.4 lasted 0.5 s. In DD
plasmas, double barriers have been sustained for
durations up to l0 s (- 30rs) with By = 1.7 and H,ru*scp= 2.1 l3ll. Using a modified W-shaped divertor andt38lshaping, JT-60U was able to maintain discharges withan ITB up to 9 s (- 50zu) in the high-B'.1 ELMy Hmode [32]. In DIII-D, good performances have been

where re5 and 6e5 are, respectively, elongation and triangularity of the plasma cross section at 95Vo of thepoloidal magnetic flux, and units are MW, 101e fl-3, ffi
and T (the RMS error of this fit is IgEo). The ITB
threshold power predicted by this scaling for ITER at
low to moderate plasma density, n" < 3 x. 10re m-3, iswithin the capability of the ITER auxiliary heating system (100 MW). However, operation with an ITB at highobtained in the so-called Quiescent Double Barrier(QDB) regime with counter-NB injection. Plasmas with
Hrrnnasp = 3 and 6v = 3 lasted several seconds (i.e. 16

Table 1 Some results obtained with double barriers invarious devices.
tp,ru/?rH,rrr*,B.

ASDEX-Upgrade [35]

40

2.4

z

Dilr-D [34]

to

5

5

Devicetou* (s)pmr'r - 3.l4nlf a2t3 K[:4e.2 + 4, )-ott Bo " , (6)plasma density (n = 0.8 nc = 7 x l0re m-3 ) will requiresignificant power hysteresis. The scaling for the electron
ITB power threshold based on the small number of datain the ITB database from devices with circular plasma
cross section and dominant electron heating predicts for

JEr t31l

11

36

2.1

1.7

JT-60U [361at.oITER a low threshold power of -10 MW with very5

1.7

weak density dependence. JT-60U demonstrated such an

Wakatani M. et aI., Internal Transport Barrier Physics for Steady State Operation in Tokamaks

pessimistic than the P1 scaling for ion ITBs. While
ITBs at high density have been achieved experimentally,
it remains to satisfy all the conditions needed fot Q - 5
steady state operation. Theoretically it is harder toachieve ITBs with T, - T" in the presence of ITG
turbulence, but experimental evidence is not always inagreement with this. Although some results with 4 - T"electron ITB [28]. It should be noted that further analysis of the database and further improvement of the database may change these predictions significantly.

6. Conclusions
To satisfy electric utilities it would be desirable tooperate a tokamak fusion power plant in steady state.

The improved confinement properties exhibited byplasmas with ITBs, together with the associatedbootstrap current, make them potential candidates forare encouraging, more data is required. Experimentally,steady state scenarios, although some additional current
drive will be necessary. However the maintenance ofstability to MHD modes at high BN and the prevention

edge instability which enhances particle transport, as
observed in a number of devices, may offer a solution.
Control of ITBs in ITER, a complex issue because of
the nonlinear coupling of the q proflle, pressure

impurity accumulation and insufficient He exhaust in
the presence of ITBs, is a potential threat; some type ofof impurity accumulation in the plasma core, as well as
the need to control the barrier evolution in burning

gradient, bootstrap current and fusion power as theseevolve with the ITB, has been modelled successfullyusing current drive techniques.

plasmas, pose challenges and adequate control
techniques must be developed to meet these.
To be useful in a power plant, these ITB scenarios

Acknowledgement

need to be maintained in steady state, as described inSec. 4. Some combination of current drive techniques isneeded to achieve the q profile required for broad

We acknowledge ITER Physics Expert Group on
Transport and Internal Barrier Physics and its successor
ITPA (International Tokamak Physics Activity) Topicalbarriers in the presence of the bootstrap current. A
number of methods have been demonstrated, e.g.
LHCD. NBCD. FWCD and ECCD. However the firsthurdle to surmount is maintaining MHD stability at highBN. Feedback control of B11 has been successfully

Physics Group on the same topics for preparation ofcontents in this review paper.

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