J. Plasma Fusion Res. SERIES, Vol.5 (2002) 82-87

ITER Gonfinement and Stability Modelling
POLEVOI Alexei R., MEDVEDEV Sergei Yu.r, MUKHOVATOV Vladimir S., KUKUSHKIN Andrei S.2
MURAKAMI Yoshiki3, SHIMADA Michiya and IVANOV Andrei A.l
ITER CTA, Naka JWS, Naka, 311-0193, Japan
lKeldysh Institute of Apptied Mathematics, 125047 Moscow, Russian Federation

2IEn CfA, Garching JWS, Garching bei Munchen, Germany
3Power and Industrial Systems R&D Center, Toshiba Corp., Kawasaki 210-0862, Japan(Received: ll December 2001 / Accepted: 18 April 2002)

Abstract
The results of self-consistent transport and stability studies of the ITER reference inductive andsteady-state reversed shear scenarios are discussed. The semi-empirical transport models used for ITER
simulations with 1.5D transport codes ASTRA and PRETOR are described. The analysis reveals a weak
dependence of plasma performance on the radial profiles of transport coefficients provided thecoefficients are adjusted to make the computed energy confinement time equal to that given by a global

H-mode scaling relation (IIn= 1). It is shown that the ITER reference inductive scenario with O = 10,
Pru, = 400 MW, Ie = 15 MA is stable against the high and low n ideal MHD modes without a conducting
wall. Steady-state operation with Q > 5 would require a reduced current 1e - 9 MA, enhanced
confinement with llr - 1.5, BN - 3, high bootstrap fraction - 5OVo and a reversed magnetic shear
configuration. This configuration is ideally unstable without a wall and stable with a conducting wall at
1.4a.

Keywords:
tokamak, transport, stability, ITER

1. lntroduction

a strong dependence of core plasma parameters on

Predictions of plasma performance in ITER during

boundary conditions presently taken from experiments.
The absence of a reliable model for the edge pedestal

the Engineering Design Activity (EDA) have been based

parameters reduces significantly the projection

largely on the empirical global confinement scalings
while two other possible approaches, i.e. thecapability of these transport models.
In 1999, the ITER Confinement Database andModelling Expert Group has recommended for ITER
design the ITERH-98P(y,2) confinement scaling [5]dimensionless physics parameter scaling technique andapplication of physics-based transport models, havebeen used for comparison [1]. All these techniques haveprogressed well during recent years. In particular, themodels based on transport governed by drift wave

xHss(v2)

turbulence have demonstrated their capability todescribe energy transport in the plasma core of L- and- O.O562l0.e3Bo.rs no 4t p4.6eRt.e7td.78€0.58M0.re, ( 1 )where the units are s, MA, T, 10le m-3, MW, m, AMU.
From recent analysis of the enlarged global confinement

H-modes and predict the formation of internal transportbarriers in some experiments [2-4]. These models show

Corresponding author's e-mail: polevoa@ itergps.nakajaeri.go.jp
82@2002 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchPolevoi A. er aJ., ITER Confinement and Stability Modellins

database (ITERH.DB3), the practical reliability of theconditions is discussed.

ITERH-98(y,2) scaling was confiflned, and the 2ologlinear interval was reduced from +18 to +147o [6]. The
practical application of the global confinement scalings
for ITER performance projection consists in normalisingtransport codes in such a way that the energy confine-The core transport in the central zone with low
safety factor 4 < 1 is affected by sawtooth (ST)oscillations. In Sec. 2 we compare semi-empirical andtheory-based ST model predictions for ITER. If the ST
period is longer than the central zone temperature anddensity recovery time (as expected in ITER), then in ament time computed by the code coincides with thatgiven by the scaling relation. The radial profiles oftransport coefficients are chosen in a form that allows

zone with low magnetic shear caused by ST mixing andhigh-pressure gradient, the ballooning mode stability
limit may restrict plasma performance. The results ofsatisfactory description by the code of the temperatureand density profiles in present experiments. An exampleof the results of such 1.5D simulations is shown in Fig.
I where the ITER operation domain with Q = 10 is represented on the plane Pro, - l1Hss(r,zy [71. Here Q: Pn"/
Proo, Pro. is the fusion power, Papp is the auxiliary
heating power, /1ses1, ,D = tElrE,p1es(y.zy is the confinement

ballooning stability analysis for the reference inductive
scenario are presented in Sec. 3.
To provide steady-state operation, low plasma
current 1 - 9 MA operation with high normalised-beta
fi1 - 3 is required. In these regimes ideal MHD modes
can be excited. The possibility of mode stabilisation by
conducting wall for the SS scenario is discussed in

improvement factor relative to the scaling (1). Twomodels of this type used for ITER predictions are discussed in Sec. L. The results of model benchmarking
versus the discharges from the ITER profile database areSec. 3.

the plasma thermal diffusivities, 26i and 7", used in 1,5D

So, the present analysis comprises semi-empiricalmodel benchmarking versus the experimental profile
database. We also consider the sensitivity of ITER
plasma performance predictions to model assumptions

presented.

Such a lD treatment of the core transport requires

such as the profile of diffusivity, boundary conditions,some sort of boundary conditions at the core edge
(separatrix). Modelling of the scrape-off layer (SOL)and divertor (DIV) requires at least a 2D consideration
with neutral particle simulations by sophisticated Montesaw-tooth oscillations, He transport, and limitations
caused by ballooning and ideal kink mode stability.

2. Gore Transport Modelling
ITER performance simulations were carried out by
PRETOR [9] and ASTRA [0] transport codes. Radial
lD transport of charged and neutral particles, electron
and ion heat, toroidal momentum M6 and poloidal
magnetic flux tywas simulated with a self-consistent 2Dequilibrium calculation. Such an approach is called 1.5D

Carlo technique [8]. So, core boundary conditions haveto be consistent with the SOL/DIV transport simulations
and limitations. The operational window for boundary
conditions ancl edge transport are discussed in Sec. 2.

The sensitivity of model predictions to boundarymodelling.

In the reduced version, charged particle transport issimulated only for the electron and helium components
n. ar'd ns". Other impurity species are supposed to be

l.-5D simulation (PRETOR)
1000

I

aoo

F
;

ooo

I

known fractions of the electron density n.y= fyn", thefuel densities /lp, n"1 ala calculated from thequasineutrality conditionst ne = nD * n7 | 2 ns" t

4oo

E zoo

ZyZyn"y.

The electron source S" is calculated from edge gas
puffing, pellet and neutral beam NB injection modelling.
The helium source Ss" is defined from fusion reaction
calculations and ionisation of the He atomic influx at theboundary. The impurity charge Z1 is determined fromthe coronal equilibrium model I l].
The poloidal magnetic flux tg.diffusion equation
takes account of the bootstrap current densityj6, u2l0.90 0.95 1.00 1.05 1.10 1. t5
HHss(y,z)

Fig. 1 Operational domain in H"ns{r.2)-factor/fusion power

space for /p= 15 MA and O = 10. Operationalboundaries (shaded area) are given by <n">lno=
1.0, BN = 2.5 and P.o""/P.* = 1.3 where n. is theGreenwald density. ne = lp/(na2l, Ploss is the power
conducted and convected through the separatrix,
and P.-, is the H-mode power threshold.

and the externally driven current densityftp.
83Polevoi A. et al., ITER Confinement and Stability Modelling6 x 10re m-3 and temperature Z - I keV are used asboundary conditions for the reference inductive scenario

Transport coefficients
For the simulations of ITER performance, thermal,
toroidal momentum and particle diffusivities, h, )(i, La,

simulations (see Fig. 2). In ASTRA the boundary
conditions at the separatrix are calculated frominterpolation of the B2-Eirene (B2E) calculations forDg", D" of similar form are chosen:

o = c f(p) h(p) + (1 - h(p)) z'"'",

SOL/DIV heat, charged and neutral particle transport. In
this approach, the densities, temperatures of charged
particles, as well as neutral fuel and impurities influxes
are calculated self-consistently as functions of power
output, and the outflows of DT, He and impurity ions:l-ot,., 1r",, -li.p,.. Proper control of plasma parameters isprovided by realistic actuators: such as gas puffing ratel-s, pumping speed So, deep fuelling rate [o," (neutral
beams (NB) [15], pellet injection), tritium fraction in thefuel and auxiliary heating power Papp. For the reference
Pro, = 400 MW inductive operation with loss power
Pr_oss ( 100 MW this interpolation predicts rather low(2)

whereft(p) = I for p<0.9 andh(p) =0 forp> 0.9 (corresponding to the H-mode edge pedestal transport improvement to neoclassical value), P = rlru is thenormalised radius, connected with the toroidal magnetic
flux @ (r = (iDlnB)tt2 and B is the toroidal magnetic
field). For ITER scenarios this simplified description of
the edge pedestal gives a pedestal pressure gradient
within the ballooning limit which is consistent with the
ELM-Type-I operation considered.
The relation between normalisation constants ischosen on the basis of experiments; XilX," = 2, Xilya = I.
D./L" = l, DH"lDe = 1. The normalisation is fitted toprovide the prescribed behaviour of the energy
confinement time zB according to experimental scaling,i.e. HHss1r,2:)= l.

12 t----t----t----t----t-----

I-l

e l0
Y

241
=;f
i'zl
Fl

simplest form approximating a radial dependence of thetransport coefficients observed in experiments :f(p)=t+3f.

20

S Rr*N nDr

In ASTRA simulations it was chosen in thelXI*

gl ' ' ' '

2.0

(3)

25

A roF-il--------\r

l5

5

I

0

).u

[--r---r-------r--r---.1

r.sl'--4.
€gli'\ \.qt\l r.oF
J4t\ljes \N: otflr--"=--i-----'r'-

4.0

-l

In PRETOR simulations, the radial shape was chosenIaccording to the transport model described in [13].

0.0

0.5 r____r__-r-_---rtl€ o.+\
= t\

ot

1.0

I

6.6

Model validation
The semi-empirical ITER model with diffusivity
profile (3) was benchmarked with the experimental datafrom the international profile data base [4]. The subsetof experimental data with Flnqs - l, high density, z/n6 >
0.5, and flat density profiles was chosen for suchbenchmarking. The boundary conditions and input
power profiles are taken from experiments. Heat andparticle transport is simulated. The simulations reveal
satisfactory agreement between ITER semi-empiricalmodel predictions and experimentally-measured
temperature profiles. For the considered data subset the
average standard deviation (AZ,,a = (> (Z,-T-)'z)/(tT*r)tt1 is l4Vo for ions and l2%o for electrons, where Z,

3.0

z 2.0

2.O

I

-l

| ^

::f \," I-.1 r'* i.l )')-k"JE^

R 0.21- \. -<t^\.1-o.
nrLrADD\-J

0.0 0.2 0.4 0.6 0.8 1.0
p

1.5

1.0

>< 0.50.0 L
0.0

0.2 0.4 0.6 0.8 1.0
pFig. 2 Radial distribution of plasma parameters pre-dicted for the same boundary conditions and ir.l?: = 5 bV ASTRA (solid line) with the heat conductivity 7 profile described by Eqs. (2), (3), and by
PRETOR (dashed line) with another 7 profile, described in Ref. [13]. n and n61 are electron andfuel ion densities, I is the ion temperature, h, jr"
are the total and bootstrap current densities, q, isthe safety factor, Pooo, P" are the additional and alpha heating power densities. Corresponding glo-

is simulation, Z. is an experiment (summation is
performed over the radial point positions).
Boundary conditions
In PRETOR simulations relatively high density n" -bal parameters are represented in the middle
column of Table 1.
84Polevoi A. et a/., ITER Confinement and Stability Modellins

boundary density n"(a) - 3 x 10re m-3, temperature T(a)- 200 eV and He atomic influx 4-1",0 - 0.5-0.6 1lr",,.
Two different approaches were used for heliumtransport analysis. The simplest one supposes thatrecirculating atomic helium is completely ionised before
reaching the core (i.e. the helium ions in the core
originate from fusion only Sg" = Sn".rur). The helium ion
density is controlled independently by He pumping at
the edge. In this approach the details of transport are not
too important for the integral He contamination, sincethe He content is supposed to be controlled by pumping[6] to provide helium contamination at the desirable
level is"lrs = 5, where f 11, = ln11"dVlls""dv. The
second approach is based on the B2-Eirene calculations.
In this approach, the recirculating He atomic influx andthe He boundary density are calculated self-consistently

t2

40

? l0
6

30

6

8ro
5

6
4

ra tO

2
0

0

0.6

[

2.0

0.s F

1.5

I

F o'o
r'
()1t-"1
o

tI tn
F
''"

*-l

nt L

:i 0.5

o't

r
0.0 L
0.0 0.2 0.4 0.6 0.8 1

0.0oo.o 0.2 0.4 0.6 0.8 l.oppFig. 3 Radial distribution of plasma parameters predicted by ASTRA (solid line) and PRETOR (dashedline) calculations for different boundary conditionsand He transport. 7 is the heat conductivity, n.
and no, are the electron and fuel densities, f, iswith particle and energy circulation in the SOL/DIV
area. In that case the ratio f"rl tt is the result of
calculations rather than an input parameter.

the ion temperature, Pooo, Po are the additional

and alpha heating power densities. The ASTRA
modelling includes boundary conditions and He
transport compatible with B2-Eirine calculations.

Sawtooth oscillations
We consider two approaches for ST oscillations in
ITER simulations. The semi-empirical, simplified modelis used in ASTRA, where the ST mixing is supposed to
be triggered by some specific current profile in the zone
Psr < 1.4 P (q = l). In PREToR simulations thecomplete reconnection model by F. Porcelli et al. [17] isused for ST description. The ST is triggered when the

Corresponding global parameters are represented
in the last column of Table 1.

Table 1 Sensitivity of plasma performance to boundary
conditions

perturbed magnetic energy exceeds some threshold
SWmae > W,5., and the mixing radius p51 is calculated
from flux continuity. In both approaches particles andtemperatures are flattened over the ST zone taking
account of particle and energy conservation.

R/a (m/m)

Sensitivity studies
Simulations reveal a weak sensitivity of plasma
performance to the detailed shape of transportcoefficients /(p) (see Fig. 2). For the same boundary
conditions, the normalisation F1ge3 = I gives transport
which is similar in the hot central zone resultine inalmost identical plasma parametdr profiles.
The details of the ST modelling have a minor effecton plasma performance too, since the temperature anddensity profile recovery proceeds faster than plasma

ASTRA+B2E

6.2 t 2.O

6.2 t2.O

B. (T)

5.3

5.3

LffA)
r./tL

15.0

15.0

1.7 t0.33

r.7 t0.33<rL> (101'qm'r)

l0.l

10.1

Iync

0.85

0.84

<T,> (keV)<T> (keV)

8.0

8.9

8.8

9.7

$, (Vo)

2.49

2.78

0*

r.76

1.97

Pf,,"(MW)

400

471

Q =Pm/(Pm+Pm)
w,, (MJ)

t0

l1.8

320

. 348

Pl

/P,

Tn (s)

current profile recovery T51 ) ?6 (ST period - mixing
zone skin time). The performance dependence on the

PRETOR&ASTRA

1.8

t.9

3.71

3.45

fs"^". (Vo)

J.a

4.7

Z.n

1.66

t.69

(Mw)

47

46

boundary conditions is much stronger (Fig. 3 and

0.85

0.81

Table. 1).

5.0

6.7

P*

85

Polevoi A. et al., ITER Confinement and Stability Modelling

3. ldeal Mode Stability Analysis

increases with q.1n. So, the ITER wall position, a*/a =1.4 for a = 1 85 m, implies a lower limit on 4,in (upper

The ballooning and low-n ideal kink mode stability
was carried out using the KINX code [18]. The result ofanalysis of the ballooning stability between the ST
oscillations in the reference inductive ITER scenarios ispresented in Fig. 4. The analysis reveals that in the wide
central ST mixing zone, the pressure gradient is close tolimit on @) for chosen global parameters.
The results of stability analysis for equilibria withscaled pressure profile (and By) with fixed 4 profile fordifferent 4^in for the SS operational regimes presented inTable 2 are shown in Fig. 6. The operational parametersin Table 2 are calculated for R = 6.35 m, e = 1.85 m,
6st/ht - O.4l/1.84, B = 5.175 T, Io = Q N4A, <n.> = $;l!
x l0rem-3, PNn = 34 MW with the neoclassical ion heat

the ballooning/Mercier stability limit p' - pi6. Possible

excitation of ballooning modes in this case may affectplasma performance and would require further analysis.
Steady state (SS) operation with high Q > 5 andmoderate internal inductance li - 0.6^0.7 requires highbeta B* > 4 /i operation, where the ideal kink modes
become unstable without a conducting wall. A highbootstrap current fraction in SS operation produces
reversed shear configurations q(O) > q^in (Fig. 5). SS is
possible for the same global parameters: geometry, B, 10,n" with different safety factor profiles (different 4-;,)and multiplication factor Q (which decreases when 4,1n
increases) controlled by a variation of lower hybrid
current drive. The maximum distance to the conducting

diffusivity in the reversed shear zone.
The calculations reveal that the operational pointwith B1 = 2.8 for q^in = 2'l is located in the unstablezone. The operational point with kt = 2.56, Q = 5 fore^in = 2.4 is stable and is close to the no wall limit B* =j, MA/m2
0.5

wall that can provide the kink mode stabilisation

0

o.2

0.4

0.6

o.2

0.8

0.4

0.6

0.8

p

0.8
Fig. 5 Calculated profile of the safety factor q and densi-

ties of the bootstrap current (/0"), neutral beam

0.6
-o-

driven current (,ue), and lower hybrid wave (1")
driven current. The minimum q value is above 2.

0.4
0.2
0

0

0.2 0.4 0.6 0.8\roTable 2 ITER plasma parameters for the SS scenario
with different q profiles
1uFig. 4 Safety factor q (top) and pressure gradient y' (bot-tom) radial profiles before sowtooth mixing. Pressure gradient given by transport simulation isshown by solid line and the ballooning/Mercier
stability limit is shown by a dashed line. The
normalised square root of the poloidal flux isused as the radial variable.

86

Unstable

StableP,, (Ivlw)

29

tJ- I

Qm"

2.1

2.4

li

o.72

0.63
2.56

P"

2.8

a
4,n)

5.7

5

2.2

2.17

Pf,,. (MW)

36r

338

Polevoi A. et al., ITER Confinement and Stabilitv Modellins

Community, Japan, and the Russian Federation, under
the auspices of the Intemational Atomic Energy Agency.

The views and opinions expressed herein do not neces-sarily reflect those of the Participants to the CTA, the
IAEA or any agency thereof. Dissemination of the information in this paper is governed by the applicable termsof the former ITER EDA Agreement, which continue toapply during the CTA.

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for different q profiles and a = 1.85 m. The no-walllimit is shown by dashed lines.

ference, Sorrento, Italy (2000) TH4ll.
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t6l O. Kardaun, "On estimating the epistemic probabil2.5 (see Fig. 6).

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lower bound in ITER." Nucl. Fusion QO}l). in

4. Conclusions

press.

l7l Y . Murakami et al., J . Plasma Fusion Res. 77 , 7 12

The semi-empirical model used for ITER predictions satisfactorily reproduces experimental profiles
from the profile database.
The semi-empirical approach predicts for ITER
weak sensitivity of plasma performance to diffusivity
profiles for similar boundary conditions.
The details of sawtooth modelling do not affectplasma perforrnance provided the sizes of the mixing
zone are similar and the ST period is longer than thepressure recovery time. The pressure gradient in the
mixing zone is marginally stable vs. ballooning modesin the referencc inductive scenario.
So, the reference ITER scenarios are robust asainst(2001).

t8l A.S. Kukushkin et al., ISth IAEA Fusion Conference, Sonento (2000) ITERP/IO.

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[3] P.H. Rebut et al.,Plasma Physics and Controlled
Nuclear Fusion Research (Proc. I2'h Int. Conf.

the considered effects.

High Q > 5 steady-state operation would requirestabilisation of low-n ideal kink modes. There is anoperational window with Q > 5, A{ > 2.56, for thestabilising wall position compatible with the ITER

Nice, 1988) Yol.2,IAEA, Vienna 191 (1989).
[14] ITER Physics Basis, Nucl. Fusion 39,2215 (1999).
[15] A. Polevoi, H. Shirai and T. Takizuka, JAERI
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[7] F. Porcelli et al., Plasma Phys. Control. Fusion 38,

design, anla> 1.4.

This report was prepared as an account of work undertaken within the framework of ITER Coordinated Technical Activities (CTA). These are conducted by theParticipants: Canada, the European Atomic Energy

2163 (1996).

[8] L. Degtyarev et al., Comput. Phys. Comm. 10, 103(1997\.

87