J. Plasma Fusion Res. SERIES, Vol.5 (2002) ll2-111

Mechanisms of Transport in Radiative lmproved Mode
ToKAR M.2., DUMORTIER p.1, JecrsoN G.L.2, KALUPIN D.', MURAKAMI M.2'3,MESSIAEN A.M.r, NoRDMAN H.4, oNGENA J.1, REISER D., SINGH R.s, STAEBLER G.M.2,
SYDORA R.6. UNTERBERG B.. WEILAND J. ANd WEYNANTS R.R.1
lnstitut fur Plasmaphysik, Association EURATOM-FZJ, 52425, Julich, Germany
ERM - KM S, Association,, EU RATO M -Belgian State ", Brus sels, Belgium
12DIII-D Natio.nal Fusion Facility, San Diego, CA 92 186-5698, USA'ORNL, Oak Ridge, TN 3783 1-8072, USAaChalmers University of Technology, Association EURATOM-NFR, Gdteborg, Sweden
slnstitutefor Plasma Research, Bhat, Gandhinagar, India
6(Jniversity of Alberta, Edmonton, Alberta, Canada T6G 2Jl(Received: 11 December 2001 / Accepted: 20 March 2002)

Abstract
Improvement of confinement by a deliberate seeding of impurities like neon and argon has beenfound in many devices. Most intensively this phenomenon was studied in the limiter tokamak TEXTOR,
where it was called radiative improved (RI) mode, and in the divertor machine DIII-D. Recentexperiments on TFTR, JT-60 and JET have demonstrated that by an optimization of seeding procedure a
positive effect of impurities can be achieved in reactor scale devices.
Extensive theoretical and modelling activities were performed during past years in order tounderstand the mechanisms of confinement improvement in Rl-mode. Characteristics of drift instabilities

namely the ion temperature gradient (ITG) and dissipate trapped electron (DTE) modes, which provide
the main contribution to the anomalous transport in tokamaks, have been analyzed by the code for GyroKinetic Stability. The behavior of non-linear turbulent eddies and vortices was studied in "particle incell" simulations. Fluid approximation has been applied to asses the effect of impurities on anomaloustransport. All these studies predict a reduction of turbulence originated from the most dangerous ITG
modes. Computations by a transport code with models for anomalous transport coefficients due to drift

micro-instabilities reproduce many peculiarities of Rl-plasmas.

Keywords:drift instability, confinement improvement. impurity, turbulence suppression
such a surprising effect of impurities on plasma
performance, is important to assess the relevance of

1. lntroduction
Operational regimes with reduced anomaloustransport resulting from seeding of impurities werethese regimes to reactor conditions.

obtained in different tokamaks, e.g., in ISX-B, ASDEX,TEXTOR, DIII-D, TFTR []. In these experiments adeliberate pollution of the plasma led to an improvementof the energy confinement in spite of increased radiation
losses. Understanding of mechanisms, which underlie

2. Features of L-Rl Transition
In the limiter tokamak TEXTOR the transition toradiative improved (RI) mode from a state of low (L)@2002 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchCorresponding author's e -mail: m.tokar@fz-juelich.deIt2

Tokar M.Z. et al., Mechanisms of Transport in Radiative Improved Modein the L-mode and Rl-mode stages in shot 68803 [2].
Although all profiles are more peaked in the Rl-mode

confinement was triggered by puffing of neon impurity
in plasmas additionally heated by neutral beam injection(NBI) and ion cyclotron resonance heating (ICRH). As

the most pronounced feature is the principal change inthe density shape. In Fig. 2 the reduction of anomaloustransport is demonstrated by the radial profiles of thean example Fig.l displays the measured radial profiles

ofthe electron and ion temperatures and electron density

effective heat diffusivity obtained from TRANSP
modeling [2].

3. Changes in Transport Characteristics
The analysis of drift mode stability by different
approaches shows that the observed reduction inanomalous transport in the Rl-mode is caused by asignificant suppression of Ion Temperature Gradient(ITG) unstable modes. These modes are widely

I\Sconsidered as the main cause of anomalous losses ofenergy and particles in the L-mode. Figure 3 shows theperpendicular wave number spectrum of the ITG growthrate f s6 found in ref. [3] on the bases of a fluid model[4] generalized for the case of arbitrary number of ionspecies.

n"(10l3cm-3;

In order to understand the reasons for the decreaseof Jrrrc in Rl-mode we proceed from an approximate
formula derived for plasmas with a not very flat density
profile [5]:f anr,,2dlnn",-3^,mu*',
rffc*V l-dr.,dr- -8\Pldlnn"\'z"trd, )The plasma effective charge Z"y comes into play because the trigger of ITG instability, non divergence free
due to tokamak geometry diamagnetic flow, is inversely

Fig. 1 Radial profiles of plasma parameters in shot
68803 in TEXTOR measured in L-mode before

neon puff (broken curves) and in Rl-mode (solidlines).

1.6

t.4

Yrrc(lu"s ),\t.2

X sfflrhg t=1.*l(Lo1od") #68&Xt

L_mode^,..-.....-t,t.larttt
tr,I,l1.0II

0.8

RI-mode

0.6
0.4

t=2(b (Rl-mode)

0,20,2 0,3 0.4 0.5 0.6 0.7 08

0.1

Normalized Minor Radius

0.2 0.3 krp , 0.5 0.6 0.7

Fig. 3 Spectrum of the ITG instability growth rate at

r=30 cm under L- and Rl-mode conditions in

Fig. 2 Radial profiles of effective heat diffusivity found in
TRANSP analysis.

TEXTOR.

ll3

Tokar M.Z. et al., Mechanisms of Transport in Radiative Improved Mode

proportional to the ion charge. There are two channels
for the influence of the density gradient: (i) the work ofpressure gradient and (ii) phase shift between the density and temperature perturbations. One can see that
only an increase rn Z"nis not enough to suppress the instability and a simultaneous increase of the density gra-

The results of simple stability analysis agree withthe data of sophisticated modelling by the "particle incell" approach [6]. Figure 4 demonstrates themodification in the poloidal distribution of theelectrostatic potential occurred by the L-RI transition.

After the transition the turbulence is strongly reduced in
the main part of the plasma cross-section and this ismostly due to the more peaked density profile in the RI-dient, i.e., density peaking is required.

mode.

It is necessary to stress that the discussed
mechanisms of turbulence suppression in Rl-mode dono rely on the traditional scenario due to a shearedradial electric field E,. However the latter can be ofsignificant importance in discharges with unbalanced

NBI injection where a strong toroidal rotation
contributes essentially to E . Figure 5 shows the time
evolution of the maximum growth rate of drift modes
and the radial shear of ExB rotation in two shots inDIII-D [7]. Neon injection triggers the process ofcontinuous rise in the lar6sl. This happens, however,after the initial drop in the maximum growth rate due tothe presence of impurities [7]. The turbulence becomescompletely suppressed when ymd < laBsl.In discharges
with balanced NBI la6"l does play an essential role andonly direct effect of impurities leads to confinement

Fig. 4 The pattern of the electrostatic Dotential in thepoloidal cross-section found by "oarticle in cell"
modelling of drift turbulence in L- (left) and Rl-mode (right).

300

improvement.

no Neonj zoo

P = 0'66

4. Role and Mechanism of Density Peaking
Observations on TEXTOR show that density

98777D01

peaking is indeed an important prerequisite of the L-RI

3 100

transition [8]. In Fig. 6 the improvement factor fge3 is

F0
0.6

0.8

1.0 1.2 t.4

1.6

1.0

1.8

TIME (s)

,r

0.9

300

Neon (2 T-Us)

i: 200**8o5,4ft1fr83$

rt93

0.8

P = 0.66

P*/Pn*^{98775D05
0.7
lole*sl$ roo

0,60.5

0L
0.6

1.2

1.4

1.60.8 1.0 1.2 1.4 1.6 1.8

1.8n.(0) / <n.>

TIME (s)Fig. 6 lmprovement factor /"r. versus density peaking

Fig. 5 Time evolution of the maximum growth rate andshear of ExB rotation in Dlll-D L-mode discharges
without and with neon seeding.

for discharges with different radiation level. The
curve shows the time evolution of both parameters in TEXTOR shot 68805.

t14

Tokar M.Z. et al,, Mecharisms of Transport in Radiative Improved Modethat this happens mainly because of reduction in the particle diffusivity (see Fig. 7).

displayed as a function of the ratio between the central

and line averaged values of the density. A certain
critical level of peaking should be achieved before thetransition. In order to get an idea what is the cause of
the peaking we proceed from an electron particle

5. Predictive Transport Modeling
5.1 Transport model for L-Rl bifurcation
In the literature one can find theoreticalbalance equation. For stationary conditions in theplasma core where particle sources are weak thiscondition reduces to zero flux density:

approaches, which allow to interpret the modification intransport characteristics observed by the L-RI transition[0,11]. When the anomalous transport is due toinstabilities on ion dynamics, e.g. ITG, the relative levelof pinch-velocity is small. In the case with turbulence
dominated by trapped electrons (TE) this level isThus a peaking of the density profiles should occur due
to increase in the ratio of pinch velocity Vf andsignificantly larger. The following half-empiricaltransport model takes this into account:diffusivity Dj. An interpretive analysis has shown [9](Di = D fo + D or", Vi = -l o [" *\-3R+D\or'u-ldrl4W

where the q is the safety factor and the diffusivity ingredients due to different unstable modes are computed in
the mixing length limit:

DI|G'otr' * r'Ft'o'/t?
/ tr-L.mu

with t1,.u, being the perpendicular wave number atwhich the growth rates achieves its maximum (7oru iscomputed according to Ref. [12]).

Figure 8 displays the electron flux density lf
versus the density gradient for parameters at r=3ocm in
TEXTOR in L-, Rl-mode and under some intermediate

critical conditions. In the L-mode with a low plasma
effective charge 3 stationary values of dn"ldr arepossible. The discharge history predetermines that theFig. 7 Electron diffusivity and pinch velocity reconstructed by an interpretive analysis for L- and Rlmode conditions in TEXTOR.

plasma is in the stable state of a low gradient. An
increase of 26 results in the reduction of the ITG
contribution and fj maximum decreases. When thecritical state is reached a dynamic bifurcation to the RImode state with a large density gradient occurs.

5.2 Numerical predictive modelling by code
RITM

TEXTOR: The transport model described above has
been incorporated into l-D transport code RITM [3]developed especially to model the plasma states strongly

influenced by impurities through radiation, ion dilution
and, now, effects on transport coefficients. RITM describes the transport of hydrogen and impurity neutrals
and allows to model the role of recycling. The sources
due to ionization of neutrals are included into continuity

Fig. 8 Dependencies of the electron flux density on thedensity gradient and stationary plasma states forequations for electrons and all charge states of such impurities as He, C, O, Ne, Si. Heat balance equations fordifferent conditions.
115

Tokar M.Z. et al., Mechanisms of Transport in Radiative Imoroved Modeelectrons and ions are solved with the energy sourcesfrom ohmic, NBI and ICR heating. The profile of ohmic
current is computed from Maxwell equations and GradShafranov equation determines the shift of magnetic
surfaces. Together with analytically prescribed profilesof ellipticity and triangularity this allows to calculate theprofile typical for L-mode is formed. Later the presenceof impurity leads to a subsequent penetration of the LRI bifurcation towards the plasma core. At a time of 0.3
s quasi-stationary Rl-mode conditions are reached,which are characterized by a peaked density profile, ahigh radiation fraction P,ud/Pbr}.1 and ITG mode

metric coefficients.

suppressed over a wide radial zone of the plasma. From
this moment the intensity of gas puff is fixed at a very
low level. Nevertheless the density profile continues toFigure 9 demonstrates the time evolution of thedensity profile modeled with RITM for a dischargewhere seeding of neon leads to the L-RI transition.
Starting from some initial profiles the prescribed
program for the line averaged density is controlled by
the gas puff intensity. To a time of 0.12s a centrally flat?l;

JET: Earlier trials to improve confinement in JET byseeding of impurities [4] sowed doubts that this can beachieved in large machines. New series of experiments

have shown that also in this case a positive effect ofimpurity seeding can be attained through an optimization of the puffing scenario both for the working andimpurity gases. It was possible, e.9., to maintain a good
confinement in the H-mode discharges at an electron
density close to the Greenwald limit. In the L-mode discharges seeding of neon led as in TEXTOR and DIII-D
to a significant, however transient, peaking of density

8.4

1.2-l

3cm-3 (see Fig. 10).

12-i- | 10.a5|

peak and the central electron density exceeds 1.lxl0ra

u.o
6c-_

4.8
6

J.6

and pressure. Figures

1.2in #50329 before and after neon puff. The modeling allowed to interpret the necessity of a significantty higher
plasma effective charge in JET,5-7, than in DIII-D andTEXTOR, 2-3, in order to set an Rl-mode effect. The

1.2oWUW3---.-q-*.;.,mu[sJ . n," -l.oll

and 12 show the measured andcomputed by RITM, resp., profiles of plasma parameters

2.4- (\-Fig. 9 Modeled by the code RITM time evolution of theelectron density profile during the L-Rl transition

by neon puffing into TEXTOR.

ITG,DTEDrt?

n, {lol3cm-3 )(m'ls )Ine (10'-crrr' )

t.6
r.2
0.8
0.4Fig. 10 Final density profile after the L-Rl transition inTEXTOR measured (broken line) and computed
by RITM with contributions of different channels
to anomalous particle diffusion (solid lines).

Electron density and pressure profiles in JET#50329: L-mode (broken curves) before and Rlmode like state (solid curves) after neon seeding.

ll6

Tokar M.Z. et al., Mechanisms of Transport in Radiative Improved Modeoi(lo4cm2/s)

P. (a.u.)n.1lol3cm-l )r (cmr (cm)l02030 406070 80 90IO20JU 40

r (cm)

60 70 80

Fig. 12 Computed profiles of the electron density, pressure and diffusivity for JET shot # 50329: L-mode (broken curves)
before and Rl-mode like state (solid curves) after neon seeding.

ratio VilDl, which controls the density peaking, is governed by the value ol'"tofc and for a bifurcation to
the Rl-mode the latter should exceed a critical level [5].
On the one hand in plasmas of low collisionality as inJET, the electron drift frequency exceeds the effective
collision frequency for trapped electrons and DlrE-n.
t121. On the other hand D-llG decreases with increasing
Z"s and ITG transport is suppressed completely when
the plasma ef1'ective charge exceeds a certain criticallevel [5]. Thus the lower the plasma density the higher
2"6, at which DfrElD-llG approaches its critical level.
Since the plasma in JET L-mode is hotter and of a lower
density than in DIII-D and TEXTOR the required Z"ii ismodels with contribution from ITG and TE modes to thelarger.

I5l M.Z.Tokar et a/., Phys. Rev. Lett. E4,895 [2000].
t6l R. Sydora et al.,Plasma Phys. Control. Fusion 38,

particle flux reproduces well the profile evolution inTEXTOR and JET caused by impurity seeding.

Referenceslll J. Ongena et al., Phys. Plasmas 8, 2188 [2001].
[2] R.R. Weynants et a/., Nucl. Fusion 39, 1637
ll999l.

l3l M.Z. Tokar' et al.,Plasma Phys. Control. Fusion
4r,L9 lr999l.

[4] J.Weiland Collective Modes in Inhomogeneous
Plasmas, Kinetic and Advanced Fluid Theory(Bristol: IOP Publishing, 2000).

A281 [1996].

6. Conclusion
Radiative improved mode was found in diverse
tokamaks by seeding of different impurities. It is[7] G.R. McKee et al.,Phys. Plasmas 7,1870 [2000].
t8l B. Unterberg et al.,Plasma Phys. Control. Fusion
39, 8189 11997).

accompanied by a significant reduction in theanomalous transport of energy and particles. Bothl9l M.Z. Tokar, Contrib. Plasma Phys. 40, 443 [2000].
[0] V.V. Yankov and J.Nycander, Phys. Plasmas 4,simple transport models and sophisticated simulations

2907 [19971.
D.R.
Baker and M.N. Rosenbluth, Phys. Plasmas 5,[11]2936 [1998].
[2] B.B. Kadomtsev and O.P. Pogutse, Nucl. Fusion

confirm that this happens due to suppression of ITG
turbulence which is the main transport channel in Lmode. The suppression is initiated by the increase of Zerr
and enhanced by peaking of the density profile occurred
due to increase of the VllDlratio. At a high enough Z"sa bifurcation leading to the L-RI transition takes place.

In computations with the code RITM the transport

rr,67 [r97rl.
|3lM.Z. Tokar, Plasma Phys. Control. Fusion 36, 1819
[ree4).

[l4] G.F. Matthews et al.,Nttcl. Fusion 39, 19 ll999l.