Proceedings of ITC/ISHW2007

Tokamak Plasma Transport Simulation in the Presence ofNeoclassical Tearing Modes
Y. Takahashi, K. Yamazaki, J. Garciaa, H. Arimoto, T. Shoji
Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, JapanaUniversitat Polite`cnica de Catalunya (UPC), Barcelona, Spain
For the prediction of the ITER plasmas, the effect of the neoclassical tearing mode (NTM) on the plasma
confinement has been calculated using the 1.5-dimensional equilibrium and transport simulation code TOTAL. Thetime evolution of the NTM magnetic island has been analyzed using the modified Rutherford equation for a ITER
normal shear plasma. The anomalous transport model used here is GLF23. The saturated magnetic island widths arew/a~0.048 at 3/2 mode and w/a~0.21 at 2/1 mode, and the reduction in fusion power output by NTM is 27% at the3/2 mode, 82% at the 2/1 mode, and 89% at the 3/2 + 2/1 double mode. The stabilization effect of the electron
cyclotron current drive (ECCD) with EC is also clarified. The threshold of ECCD power for the full stabilization is~10[MW] against the 3/2 mode, and ~23[MW] against the 2/1 mode.
Keywords: ITER, tokamak, simulation, neoclassical tearing mode, electron cyclotron current drive, stabilization

1. Introduction
The neoclassical tearing mode (NTM) might limit theplasma pressure and would lead to a disruption in future
tokamak reactors. The NTM makes the temperature profile
flat inside magnetic island, and the central plasma
temperature is reduced. Therefore, when the magnetic
island is formed in the plasma, the fusion output power isdecreased. The analysis and control of NTMs are one of
the crucial issues in tokamak reactor [1]. The NTM iscaused by a lack of the bootstrap current inside themagnetic island where the pressure profile is flattened [2].
The electron cyclotron current drive (ECCD) gives theNTM stabilization to replace the missing bootstrap current.
The effect of NTM on the ITER plasma should beinvestigated, and the stabilization method of NTM should
be clarified.
For the prediction of ITER plasmas, the time
evolution of neoclassical tearing modes has been
calculated by using the 1.5-dimensional (1.5-D)
equilibrium and transport simulation code (toroidaltransport linkage code TOTAL [3,4]). The magnetic island
width is evaluated using the modified Rutherford equation[5,6]. In the simulation code, we used the GLF23
anomalous transport model that can simulate H-mode
plasmas [7].
The purpose of this paper is to clarify the effect of theNTM magnetic island formation on the plasma
confinement and to demonstrate its stabilization by theelectron cyclotron current drive (ECCD) in ITER. In thenext section, a numerical model is described. The details ofmodified Rutherford equation, the ECCD current profileand the current drive efficiency are also shown in thisauthor’s e-mail: takahashi-y@ees.nagoya-u.ac.jp

section. In section 3, simulation results are shown. Thesummary is given in section 4.

2. Numerical model
The time evolution of NTM has been calculated using
1.5-D equilibrium and transport code (toroidal transportlinkage code TOTAL [3,4]). The plasma equilibrium issolved by the free-boundary Apollo code [8], and theplasma transport is evaluated including the impuritydynamics [9]. The anomalous transport model used here isthe glf23 [7] that can simulate H-mode plasmas.

2.1 Modified Rutherford equation
The time evolution of a NTM island width, W, iscalculated according to the modified Ruther ford equation.
Here, W is the normalized magnetic island width withrespect to the minor plasma radius, a.

dWdt

BSk1

GGJ

pol

(1)

EC2(W )

(2)

0BS

GGJ

W

k 2 Lq j BS

k3

Bp

L2q

2spss0

pol

k4

g0

Ws, iLp

1q s21pips(3)Wd22L2q

Lp21W221W3(4)Proceedings of ITC/ISHW2007

ECk5LqBpsf EC

I EC 1a2 W 2(6)Here, ' is the classical stability index defined as thelogarithmic jump of the radial magnetic field perturbation
across the rational surface [10]. BS, GGJ, pol and EC
are the perturbed bootstrap current, the stabilizing effect of
the field line curvature [11], the ion polarization current
and the EC current effect [12]. is the coordinate of thenormalized minor radius. , s, ps, pi and s are theneoclassical resistivity, the inverse aspect ratio, the local
poloidal beta, the poloidal Larmor radius normalized byminor radius a and the rational surface position,respectively. The scale lengths, Lq and Lp, are defined as
Lq=(dq/d )-1 and Lp=-(dp/d )-1.

2.2 Modified Rutherford equation
In this paper, the EC current profile is modelled by aGaussian distribution as

Table 1. Plasma parameters used herefor ITER.
R0 : major radius (m)a : minor radius (m)Bt0 : toroidal field at R0 (T)IP : plasma current (MA)<ne> ( x 1020 m-3)
<Te> (keV)<Ti> (keV)

Table 2. Parameters relevant to therational surface.
m/n

3/2

2/1

JBS (MA/m2)

0.67
0.65
0.11

0.84
0.46
0.11sps

Table 3. Coefficients of each term in themodified Rutherford equation used here

2j ECj EC 0 exp

CsWEC

k1
k2
k3
k4
k5(7)

,

6.2
2.0
5.3
15
1.01
10.9
9.8
3.1

Magnetic island

1.0
10.0
1.0
1.0
5.0

jEC
61.5 10

WEC

0.25
0.2

62

j[A/m ]

d /2

cos mj EC

0.1

RF55 10

000.2

0.05

bs

0.4

0.6

0.8

10r/a

where C=4ln2, jEC0 is calculated from the total EC
current IEC. The value s is the position of the current
density peak. The efficiency of the EC current is given by[2]dˆRFWjFigure 1. Model of EC current profile. The EC current
density, jEC is modelled by the Gaussian distribution.

0.15

totalW [MW]j1 10

Figure 2. Plasma current density and input heating
power profile as a function of normalized minor
radius. The total input power is 40 MW, theaverage electron density is 1.0×1020 m-3 and thetotal current is 15 MA.

(8)

3.1 Reduction in plasma temperature and fusion
power by NTM

The value of IEC is assumed to be proportional to theEC power, PEC, as IEC [kA]=4.35PEC[MW] for the 3/2
mode and 4.15PEC[MW] for the 2/1 mode [6].

In a ITER plasma the NTM magnetic islands are
saturated around ten seconds after introducing the seedisland. Figure 3 shows the electron temperature profile andthe q profile when the magnetic island is saturated. The 3/2
mode island (q=1.5) exists at r/a=0.67, and the 2/1 modeisland (q=2) exists at r/a=0.84. We assumed the transportcoefficient is quite large inside the magnetic island.
According to figure 3, the electron temperature at plasma
center decreases due to the magnetic island formation. Thatis, the fusion power decreases too due to the NTM
magnetic island. Table 4 shows the plasma parameterswhen the magnetic island exists in the plasma. Here, Te(0),ECdˆd /2

j EC,

3. Numerical result
Table 1 shows parameters of a typical ITER plasma
analyzed in this paper. The local parameters at the rationalsurfaces of q=3/2 and 2/1 are shown table 2, where s, psand jBS are the normalized rational surface position, thelocal poloidal beta, and the local bootstrap current density,respectively. The coefficients of each term in the modified
Rutherford equation used here are shown in table 3.

Proceedings of ITC/ISHW2007

30

0.002

-1

0(b)

-1

[s ]

normal2.5

NTM(3-2)
NTM(2-1)

152

10

0.004
0.002
0-0.002
30

1.5

0.2

0.4

0.6

r/a

0.8

1

Table 4. Central temperature, bootstrap current
fraction and Q value in three cases
NormalNTM(3/2)
NTM(2/1)
Double NTM

Te(0)[keV]

IBS/Itotal(%)

28.7
24.9
14.9
12.2

23.2
20.3
12.6
9.2

Q
14.6
10.7
2.6
1.6

3.2 Time evolution and saturation of magneticisland width
The NTM magnetic island grows in time, and theisland width is finally saturated. We assumes a seed islandwith w/a=0.05 introduced at time=30 [s]. Figure 4 shows
the time evolution of the magnetic island width with 3/2,2/1, and double modes. The 3/2 mode island width issaturated at w/a=0.048, and the 2/1 mode is saturated atw/a=0.21. As double mode, saturated each magnetic island
width is nearly equal to single mode. The time constant for
saturation is about 10 seconds. In 3/2 mode, the time forsaturation of double mode is longer than single mode. In
2/1 mode, the time for saturation are same with single anddouble.

(a)

0.22
0.2 double NTM
0.18
0.16
only (2-1) mode
0.14
0.12
0.1
0.08
0.06
30
35
40

time[s]4550

We simulated the reduction in the magnetic island
width by adding the electron cyclotron current drive(ECCD). Figure 6 shows the effect of the ECCD injected at40[s] using the model described in section 3.2. The
magnetic island width is fully erased by adding the large
ECCD power. And, We simulated the different of reduction
single and double mode. Figure 7 shows the reduction ofmagnetic island width in case of single and double. In 2/1
mode, their difference is very small. But in 3/2 mode, theeffect of ECCD is big. Because, the temperature at 3/2
surface position in case of double is small in compare withsingle (Figure 3). The temperature at surface position 2/1 issame with double and single. We change the injection timeof ECCD as shown in figure 8. Early injection of ECCD
can easily reduce the magnetic island width. The value ofthe total EC current IEC is assumed to be proportional to theEC power, PEC,
0.06
0.05

(b)
50

Figure 4. Time evolution of central temperature andmagnetic island width of each modes (a) 3/2 mode,and (b) 2/1 mode.

20kA

0.04
0.03
0.02

100kA

40kA

(a)

0.01
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06304540

time [s]3.3 Time evolution and saturation of magnetic
island width

w/a

0.052
0.05
double NTM
0.048
0.046 only (3-2) mode
0.044
0.042
0.04

35

Figure 5. Total current and bootstrap current profile
with (a) 3/2 and (b) 2/1 modes.

1

w/a0deltap
dbsj
dgg
dpol

0.006

q

Te[keV]

0.004-0.002320

deltap
dbsj
dgg
dpol

0.01

Figure 3. Electron temperature and safety factor q profile
without and with 3/2, 2/1, and double neoclassical tearing
modes.

w/a(a)

0.006

0.0085 double NTM

w/a0.01
0.008

3.5250Figure 5 shows the time evolution of every terms inthe modified Rutherford equation as single mode. It should
be noted that in equilibrium, the term ’ changes frompositive to negative.

[s ]IBS, ITOTAL and Q are the central electron temperature, thetotal bootstrap current, the total current and the Q value,respectively. The Q value is defined by the ratio of thefusion output power to the input power. At 3/2 mode, the Qvalue decreases to 73% of no NTM case, at 2/1 mode, theQ value decreases to 18% of no NTM case, and at double
tearing modes, the Q value decreases to 11% of no NTM.
To reduce the magnetic island width is important in order
to raise the fusion power output.

20kA
40kA
80kA
100kA

(b)
35

40

time[s]4550

Figure 6. Time evolution of magnetic island width at (a)3/2 mode and (b) 2/1 mode. Magnetic seed island with
w/a=0.05 is introduced at time=30[s], and the EC current
was injected from 40[s] with current width WEC/a=0.04
and with EC total current of 20, 40, 100 and 200[kA].

Proceedings of ITC/ISHW2007
0.06

w/a

0.05
0.03
0.02

w/a

For the reduction in ECCD power and the increase in
the stabilization effects, the EC current width should benarrow. When the injection current width is half, thethreshold power for the full stabilization is considered
about half. The other method for ECCD power reduction isto modulate the EC current. The efficiency of ECCD canbe raised by the current injection to the O point in magneticisland. The details of these analyses will be describedsomewhere in the future.

single mode

0.04

double mode

0.01
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
30(a)

single mode
double mode

(b)
35

40

time[s]4550

Figure 7. Time evolution of magnetic island of the seedisland with w/a = 0.05 at time=30 [s] at (a) 3/2 mode
injected current 20[kA], and (b) 2/1 mode injectedcurrent 100[kA]. The ECCD power is injected at time =40 [s] in single (blue) and 3/2+2/1 double mode(red)
case.
0.25
40[s]

w/a

0.2
0.15

32[s]

0.1

31[s]

0.05
00102030time [s]4050Figure 8. Time evolution of magnetic island of the seedisland with w/a = 0.05 at time=30 [s]. The ECCD powerof 100kA is injected at the time shown in the figure.

as IEC [kA] = 4.35PEC[MW] for the 3/2 mode and4.15PEC[MW] for the 2/1 mode. We need 10MW ECCD
power for 2/1 mode stabilization, and 23MW for 3/2 modestabilization, when the NTM is saturated.

4. Summary and discussions
The ITER plasma with the neoclassical tearing mode(NTM) is simulated using integrated transport code
TOTAL. The anomalous transport model used here is
GLF23, and the magnetic island width of NTM iscalculated by the modified Rutherford equation. The
magnetic island formation reduces the plasma temperatureand the fusion output power. The decrease in the Q value
due to NTM is estimated. The reduction in fusion output
power by NTM is 27% at the 3/2 mode, 82% at the 2/1mode, and 89% at the 3/2+2/1 double mode. The saturated
magnetic island widths of each modes are w/a~0.048 at 3/2
mode and w/a~0.21 at 2/1 mode.
The Injection of ECCD is considered to stabilize theNTM and to recover the plasma confinement. We calculate
the stabilization effect of ECCD with EC width wEC/a=0.04.
The threshold power for the NTM full stabilization by
ECCD is ~10 MW against the 3/2 mode, and ~23 MW
against the 2/1 mode.

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