25C06
Effects of Micro-Turbulence on Excitation of NTM
新古典テアリングモード励起への微視的乱流の影響
A. Ishizawa*, F. L. Waelbroeck**, R. Fitzpatrick**, W. Horton**, and N. Nakajima*
石澤明宏*, F. L.ウォルブロック**, R.フィッツパトリック**, W.ホートン**, 中島徳嘉**National Institute for Fusion Science,322-6, Oroshi-cho, Toki, 509-5292, Japan**Institute for Fusion Studies, University of Texas at Austin,
Austin, Texas 78712, USA*核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6**テキサス大学オースチン校 オースチン テキサス 78712 アメリカ
Effects of micro-turbulence on the excitation of neoclassical tearing modes (NTMs) are investigated bynumerically solving a set of reduced two-fluid equations. It is found that the kinetic ballooning mode
driven turbulence produces long-wavelength magnetic islands on q=1.5 rational surface, even if the profileis stable against tearing instabilities. The island width is several times the ion Larmor radius, and thissuggests that the turbulence can produce the seed island of NTM. It is also found that ion temperature
gradient mode driven turbulence enhances the drag force acting on magnetic island and can makepolarization current effect in the Rutherford equation destabilize.

1. Introduction
Magneticislands
areubiquitousinmagnetically confined torus plasmas, and they
limit achievable plasma beta and sometimes cause
disruptions in large scale tokamaks such as ITER.
Tearing instabilities are caused by spontaneous
magnetic reconnection that may occur at arational surface in a sheared magnetic
configuration, such as a current sheet in amagnetically confined plasma. According toMagnetohydrodynamic (MHD) theory, the ∆’stability parameter of tearing instabilities
determines the instability threshold and thus theformation of magnetic islands. An equilibrium isstable (unstable) against tearing instabilities when
this stability parameter is negative (positive).
Tearing
instabilities
arecurrent
driveninstabilities, and thus are most unstable forlong-wavelength
perturbation.
Inmoderntokamaks magnetic islands appear in high beta
discharges, even if the linear analysis tells thattearing modes are stable. This nonlinear
instability is caused by perturbation of bootstrap
current and is called neoclassical tearing modes(NTMs) [1, 2].
The growth of NTM requires a threshold called
seed magnetic island, and there are two issues
regarding the seed island. One is the formation
process of the seed island. It is considered that theother MHD activities such as sawtooth or ELM
cause the seed island. The other issue is theevaluation of the threshold, i.e. the width of theseed-island. In this work we investigate the effectof micro-turbulence on the two issues, because
turbulence can be driven by pressure-gradientinstabilities around rational surfaces. In Sec. 2 weconsider the effect of turbulence on the formationof seed magnetic islands. In Sec. 3 we consider
the effect of turbulence on the threshold.
2. Formation of seed-island by turbulence
In this section we will show that long-wavelength
magnetic islands are produced by micro-turbulence
driven by kinetic ballooning instabilities, even if theprofile is stable against tearing instabilities. Theisland formation is examined by three-dimensional
simulation codes in torus plasma [3]. The island
formation by ion temperature gradient instabilities(ITG) in a plasma slab was reported in our previouswork [4]. Figure 1 shows color map of electrostatic
potential and the equi-contours of helical magnetic
flux for m/n=3/2 on a poloidal section. Theturbulent flow gives rise to magnetic reconnection
at the q=3/2 rational surface. The equi-contours ofhelical magnetic flux clearly show that
long-wavelength magnetic islands are formed at therational surface of q=3/2. The stability parameter of(m,n)=(3,2) mode is approximately -2. Hence, we
see that long-wavelength magnetic islands can exist
even if the tearing mode is stable. The wavelengthof the magnetic island is much longer than the ion
Larmor radius and is the same order as the minor
radius, and the width is several times the Larmor
radius. The shape of the magnetic islands isdifferent from that of a typical tearing mode
because the turbulent flow causes fluctuations in themagnetic field.
3. Effect of turbulence on the threshold
The excitation threshold of NTM is determinedby the bootstrap current term and the polarization
current term in the modified Rutherford equation.
In this section we consider the effect of ITGturbulence on the polarization current term bymeans of numerical simulations of a reduced set of
two-fluid equations in slab geometry. Simulations
are carried out in the island fixed frame, where thewidth and poloidal location of magnetic island do
not change. Uniform ExB flow is applied to theisland, and the drive as well as the drag force acting
on the island are calculated as a function of theexternally applied flow velocity. This work extends
previous work [5, 6] by including finite ion
temperature effects. Figure 2 shows that turbulentelectron flow appears within the island separatrix,
while turbulent ion flow spreads outside of theseparatrix. It is found that the turbulent flowenhances the drag force acting on the island. The
effective
viscosity
increases
tentimes
approximately. The ion fluid inertia, which
determines the ion flow velocity shear around theisland separatrix, is responsible for the productionof the polarization current. The polarization current
term is destabilizing in the presence of turbulence.
4. Summary
We have carried out numerical simulations of areduced set of two-fluid equations in torus plasmas.
We have found that kinetic ballooning driven
turbulence causes coherent magnetic islands at theq=1.5 rational surface, even if the stability
parameter of tearing modes is negative. The widthof magnetic island is several times of ion Larmor
radius. The typical width of the required seed-islandis evaluated to be several times ion Larmor radius
by using experimental data [2]. Thus, the turbulence
can produce seed magnetic islands and explain the“spontaneous” NTMs that have been observed tooccur in the absence of a triggering event such as asawtooth crash. We have also found that ITG driven
turbulence enhances the drag force acting on
magnetic island, and can make the polarization
current term destabilizing.

∆' ≈ −2
Fig.1. Electrostatic potential profile and equi-contoursof helical flux. Turbulence driven kinetic ballooning
modes is strong at the bad curvature region. Coherent
magnetic islands appear at the q=1.5 rational surface.

Fig.2. Magnetic surfaces (left), electron flow streamlines (center) and ion flow stream lines (right).

Acknowledgments
This work is supported by the Japanese Ministryof Education, Culture, Sports, Science andTechnology, Grant No. 23561003.
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