J. Plasma Fusion Res. SERIES, Vol.5 (2002) 386-389

Analysis of Toroidal Rotation Effects of the lon Polarization
Current on the Neoclassical Tearing Mode
TAKEI NAhOKO, OZEKI TAKAhiSAI, SMOLYAKOV ANdrCi I.2, ISAYAMA AKihiKOI,HAYASHI Nobuhikor, TSUJI-IIO Shunji and SHIMADA Ryuichi
Research Laboratory for Nuclear Reactors, Tolcyo Institute of Technology,Tolq)o 152-8550, JapanlNaka Fusion Research Establishment, Japan Atomic Energy Research Institute,801-1 Mukouyama, Naka, Ibaraki 311-0193, Japan
2Plasma Physics lnboratory, Departmant of Physics, University of Saskatchewan, Saskatoon,

Canada S7N 0W0(Received: ll December 2001 / Accepted: 24 May 2002)

Abstract

A model of the polarization current, which would be associated with the excitation of theNeoclassical Tearing Mode (NTM), was investigated. In this paper, the model of the polarization current
term which includes the effects of the toroidal rotation and the pressure gradient was evaluated using JT-60U experimental data. Destabilization and stabilization by the polarization current term with theobserved toroidal rotation were analyzed to be consistent with the excitation and suppression of theNMT. When the toroidal rotation has a destabilizing effect on the NTM, the NTM will grow rapidly
without a seed island by both effects of the bootstrap current term and the polarization current term.

Keywords:
neoclassical tearing mode, plarization current, toroidal rotation, pressure gradient, mode frequency

1. lntroduction

the diamagnetic drift frequency [1,2]. In this paper, thepolarization current term model, including the toroidalrotation and the pressure gradient, was analyzed using
experimental data from JT-60U.

The neoclassical tearing mode (NTM) is considered

to reduce the B-limit in low collisional plasmas andcause confinement degradation in tokamaks. Hence, it isimportant to prevent the occurrence of the NTM andclarify the nonlinear mechanisms for excitation of theNTM. It is accepted that the polarization current isnecessary to resolve the nonlinear mechanisms forexcitation of the NTM. The role of the polarization
current in the nonlinear island evolution has been
analyzed theoretically [1-5] and experimentally [5-6].

2. Modified Rutherford Equation
The modified Rutherford equation [1-3,5,7] is acommonly used analytical method for evaluating theNTM srowth. It is written as follows:g)= r"NQts)+ fr,I r.s'-s""r*+,[18,,7 ,'"dt'f,''

One of the authors (A.I.S.) has shown that thegeneralization of the theory of drift effects could give

LrllS2+U2o.+gl,.e)Llw.ol,tD-rise to stationary small-scale magnetic islands rotating in
the poloidal direction with a frequency on the order ofke uie

Corre spondin g author' s e -mail : 00m I 9203 @ nr.tit e ch. ac j p386

@20O2 by The Japan Society of Plasma

Science and Nuclear Fusion ResearchTakei N. et al., Analysis of Toroidal Rotation Effects of the Ion Polarization Current on the Neoclassical Tearing Mode

Here, subscript s denotes the rational surface, r is thedirection of the ion diamagnetic drift.

minor radius, ?r, is the full island width, wa = 5(Xtlht)''u fr"L,rql(em))rtz lll is the critical island widththat will lead to an incomplete flattening of the pressure

In order to evaluate the effect of the polarization
current term, the function of /is considered as a figure
merit of the polarization current term:

profile within the island for small '.D, Ls= -(d ln p/dr) 1,Zn = (d ln q/dr)'t, L" = qLrlt". ar is the mode rotation
frequency, @E is the plasma rotation frequency which isinduced by the radial electric field, o*1 is the ion diamagnetic drift frequenc!.ke= mlr" is the poloidal wave
number, ate= Be(lhnrmr)-tn is the poloidal Alfv6n velocity, cp = ptrllqn" is the resistive field diffusion time,
4n" is the neoclassical resistivity, Fp = 2ttoplB& is thepoloidal beta. The strength function g(vi, e) takes theasymptotic valae t3t2 and 1, when v1 11 ta*" and vi >>(2)2'lw/ NNB^:
O: w/o NNB

1.5o-lr

E1

t6o*s, respectively. The first term on the right-hand siderois the contribution of the equilibrium current profile,:. oooo-oO/ ^.l\a/-:ond term describes the bootstrap current drive. The lastterm is the contribution of the polarization current basedon the theory of Refs. [1,2]. This term has the stabilizing
effect in the case of al.1 < a - an < 0. In the following
section, the effbcts of the toroidal rotation and the pressure gradient were examined for the polarization current
term in the modified Rutherford equation.

-s0-^AAr,

F 0.5

characterized by the stability parameter A'(To). The sec-o-0.5-103. Evaluation of the Polarization Current
Term0.2

0.4

p0.6

0.8

Fig. 1 Toroidal velocity profiles for the discharges withand without N-NBl. The vertical line indicates thelocation of the g = 2 surface.

The polarization current term was evaluated using
the data of two discharges [6]. The discharge conditionis the same except with and without the negative ion
based NBI (N-NBD injection into the discharge. The2ll
mode was observed in the discharge where the N-NBI
was not injected, while in the other discharge with NNBI, the mode was not observed though the beta value
was rather higher. Differences of parameters in the twodischarges are the toroidal velocity and the pressure

E36706

aF4I32X
q-i* oolo io

gradient atthe q = 2 surface. The total pressure gradientis 1.36 x 105 Palm and 8.9 x 104 Pa./m in the discharges
with NTM and without NTM [6], respectively. Figure I
shows the toroidal velocity profiles, whose values areabout 1.0 x 101 nl/s and 4.9 x 104 m./s in the discharges
with NTM and without NTM, respectively. The mode

8NE!

otro

r=orotation frequency, al, was estimated from the observed
frequency, @Nri-ou (= ZIt f;y1ooo), by ECE and Mirnovl!

coils. Since the toroidal rotation was small at therational surface, we assumed that the poloidal

5.6

5.7

5.8

time (s)component of the mode rotation was dominant and ar oMi-ou. The mode started at a frequency of 4 kHz andthe frequency reduced to 2 kHz in the discharge withNTM as shown in Fig. 2. The mode rotation was in theFig. 2 Time evolutions of the Mirnov oscillation ampli-tude and the mode frequency measured by ECEin the discharge with NTM.
38',1

Takei N. et aI., Analysis ofToroidal Rotation Effects ofthe Ion Polarization Current on the Neoclassical Tearing ModeThe drift frequency by the radial electric field ars anddischarge with NTM, by contrast, in the discharge

the ion diamagnetic drift frequency a*iare expressed aswithout NTM, the polarization current term has afollows, respectively:|a,=-n!,(r'Zr.re ndPi^P,^o drrB,-ue Bo+ u, Bq)

a*i=-frhhq

dp,drlO(3)

o 0.5IX(4)0\-0.5Here, .B4 is the toroidal magnetic field, Zi^, and /rimp are

10

impurity effective charge number and the impurity density, respectively. oe is the poloidal rotation velocity and'ira is the toroidal rotation velocity. In the case of a*i< ctl- (Dxi10, the sign of/is negative, by which the polarization current term has a stabilizing effect on the NTM.
The mode frequency,-fr,.nou, was not measured in thedischarge with N-NBI, since the mode was not observed. Hence, it is assumed that the mode frequency is
the same with the discharge without N-NBI in the analy-a8E{6P54gsis.

The effect of the toroidal rotation was evaluated on
the value of/for the above two discharges in Fig. 3. In
this analysis, rrr was fixed, and alp was varied with thepressure gradient dpy'dr and the toroidal velocity aq.Tlte

0-3.0 -2.O -1.0 0 1.0 2.O@-C+ ( xtOc rad/s )value of observed toroidal velocity was outside thestabilizing range (f > 0) when the NTM set in, and theFig. 3 Stabilizing (f < 0) effect ranges of a- as together

with the relationship with v, for discharges withvalue of the toroidal velocity existed inside thestabilizing range (/ < 0) when the NTM was not

and without NTM. The vertical solid line and broken line denote the value of a>, of the discharge
with NTM and without NTM, respectively. 'S'and'U'stand for the stabilizing range and the destabilizing range, respectively.

observed. As a result, the effect of the toroidal rotation

appears to be consistent with the excitation andsuppression of the NTM.
In order to evaluate sensitivity of the polarization
current term, the dependence of/on the toroidal rotationand the pressure gradient was investigated. And further,
the dependence on the mode frequency was evaluatedfor 1 kHz, 2ktlz arrd 4 kHz, because the mode started ata frequency of -4 kHz and slowed down to -2 kHz in
the discharge with NTM, and the mode frequency wasassumed to be 2 kHz in the discharge without NTM.
The results are shown in Fig. 4. When -o-1 is low, the10;8E
r6o54

stabilizing region against the toroidal velocity is sonarrow that adequate toroidal rotation is required tohave a stabilizing effect on the NTM. However, irs -d)x100.5

1.0

1.5

2.O 2.5

3.0- @*i (x104 rad/s )increases, the stabilizing region expands. Accordingly
higher -4r.1 is preferable to extend the stabilizing region
against the toroidal velocity. Figure 4 also indicates thatthe stabilizing region shifts with the mode frequency. If
the mode frequency is 1 kHz, the polarization current
term has a stabilizine effect on the NTM in theFig. 4 Negative and positive sign regions of f plotted in
the domain of the ion diamagnetic drift frequency
and the toroidal velocity. The stabilizing effect re-gion shifts with the mode frequency. The dotted
area indicates the stabilizing region when a;"',.."/2tt = 2 kHz.
388

Takei N. et al., Analysis ofToroidal Rotation Effects ofthe Ion Polarization Current on the Neoclassical Tearing Modedestabilizing effect. For 2 kH4 the result is consistent
with the expeiimental results. For 4 kHz, the plasma
with and without NTM are outside of the stabilizingregion. Consequently, the stabilizing effect region islower than the other. However, the results are not clear
to explain the drive mechanisms of the NTM. Botheffects of the polarization current term and bootstrap
current term were evaluated in Fig. 6. Results are
drastically changed since the NTM will grow rapidly
without a seed island in the case of the discharee withNTM.

sensitive to ther mode frequency.

The 2ll island growth was examined with thebootstrap current term and the polarization current termin the modified Rutherford equation. The pressure
gradient affects both terms. Figure 5 shows the effect of
the bootstrap current term alone. The growth rate of the4. Summary
The model of the polarization current term which

includes the effect of the toroidal rotation and thedischarge without NTM is smaller than the other, since
the pressure gradient in the discharge without NTM ispressure gradient tI,2) were evaluated using
experimental data from JT-60U. Results show that theeffect of the toroidal rotation appears to be consistent
with the excitation and suppression of the NTM whenthe mode frequency, ar, is equal to 2kFlz. However, the60:w/NTM: w/o NTM

40ff,, 20elE-l+.
tE0-20stabilizing effect of the polarization current term issensitive to the mode frequency. Stabilizing region+against the toroidal velocity expands with an increase in-(o*i, thus higher -ar.i is preferable. The effect of thepressure gradient through the bootstrap current term in
the modified Rutherford equation is not clear to explain
the trigger of the NTM. However, both the polarization
current term with a destabilizing effect and the bootstrap

current term are important to explain the excitation ofNTM without a seed island.

0 0.02 0.04 0.06 0.08 0.1
l4l (m)Acknowledgments
One of the authors (N. T) would like to thank Drs.
S. Takeji, T. Suzuki, H. Ninomiya and A. Kitunezaki forFig. 5 The gro'Mh rate against the island width by thebootstrao current effect.

their discussions, supports and encouragements during
her stay at JAERI.

60:w/NTMtll: w/o NTM

40(1989).

t2l A.I. Smolyakov, A. Hirose,E.Lazzarc et al.,Phys.

il*'-j 20EIE

Plasmas 2,l58l (1995).

t3l M. Yagi and S.-I. Itoh, Proc. 18 th IAEA Fusion
Ene rgy Confe rence, Sorrento, 2000, IAEA-CN-77// ----.--..:

Gt0

THPZ|O9.
t4) H.R. Wilson, J.W. Connor, R.J. Hastie et al.,Phys.

r-20

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t7l

Fig. 6 The growth rate against the island width taking

account of both effects of the bootstrap current
and the polarization current.
389