Transcript XuTao_tearing_modes_..

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Locking of tearing modes by error field
in J-TEXT Tokamak
Tao XU
Xiwei HU
Qiming HU,
Qingquan YU
College of Electric and Electronic Engineering,
Huazhong University of Science and Technology
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Contents
1. Background
2. Basic Equations
3.Modeling Results
4. Conclusion
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1. Background
Error field are generated primarily by field-coil misalignments and
nonaxisymmetric coil-feeds.
Considerable theoretical [1-8] and experimental [9-12] effort has been
done on the interaction of small resonant helical magnetic field errors
with neoclassical tearing modes (NTM) in tokamaks. The Locking
threshold was found to be very small, typically
bra/Bt∼10⁻⁴-10⁻³,
where bra is the radial component of the error field at the plasma edge
r=a, and Bt is the toroidal magnetic field.
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 The magnetic reconnection can be driven by error field, which result
in the formation of locked magnetic islands in even intrinsically
tearing stable plasmas. The locking of neoclassical tearing modes
by error field degrade the plasma confinement. In order to avoid
these excitation, we will study the interaction of error field with
tearing mode in J-TEXT tokamak.
 Because the 2/1 tearing modes can lead to a disruption , we will
discuss it mainly in this paper.
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2. Basic equations
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In this paper, large aspect ratio tokamak plasmas (ε=a/R≪1, where ε, a,
R are the inverse aspect ratio, the minor and the major radii, respectively)
are considered. The equilibrium toridal magnetic field is Btet.
The purturbed error field is expressed in term
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3 Modeling results
3.1 Locking of tearing mode by error field
 In this subsection, we will study the interaction of the error
field with m/n=2/1 magnetic island. We will use the J-TEXT
discharge 1011914, for this discharge a large data set was
available. The boundary is chosen as ψb=1.2×10⁻⁵(aBt), the
initial magnetic island width is about 0.01a.
Te₀=0.8kev, S=8.7×10⁶, χ∥=1.9×10⁹(a²/τR), X⊥≈μ≈0.6(a²/τR). jb=
2.5×10⁻⁴(Bt/μ₀a), ne=1.14×10¹⁹m⁻³, τR=0.15 s, the initial rotatin
angle frequency is ω₀=5.6×10⁴ s⁻¹.
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Three cases are examined: one is the case with superposition of
error field, and with bootstrap current, 'with error field'; the
second is the case with superposition of error field, and
without bootstrap current, 'without bootstrap'; the third is the
case without error field and without bootstrap current, 'without
error field'.
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3.2 The time for the magnetic island to be locked
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 For a given system, once the error field amplitude is larger
than a critical value ψc, the magnetic island will eventually be
locked as shown in Figures 1 and 2. The stronger the error field
is, the less time is required for the magnetic island to be
locked. Figure 3 shows the relation between the required time
for mode locking and the error field amplitude, assuming the
island width starts to grow from 0.01a. In figure 3, the input
parameters are: Te=0.8Kev, S=7.6×10⁶, χ∥=1.5×10⁹(a²/τR),
χ⊥≈μ≈0.8(a²/τR), jb= 3×10⁻⁴(Bt/μ₀a), τR =0.15 s, ne=1.5×10¹⁹m⁻³.
Figure 3 shows two case: the first case is ω₀=4×10⁴ s⁻¹, the
second case: ω₀=2×10⁴ s⁻¹. where ω0 is the mode frequency
without the error field. The critic value of error field is
ψc=3.65×10⁻⁶ (aBt) for the first case, and ψc=1.2×10⁻⁶ (aBt) for
the second case. The time t→∞ for the magnetic island to be
locked as error field ψ→ψc.
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3. 3
The threshold for mode locking
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 We are interested in the dependence of the threshold on the plasma
rotation. Numerical simulations have been carried out for m/n=2/1
mode in J-TEXT. In figure 4 J-TEXT input parameters are:
S=1.19×10⁷, χ∥=4.5×10⁹ (a²/τR), μ≈χ⊥≃1.1 (a²/τR), Te=1Kev,
ne=1.14×10¹⁹m⁻³, jb= 3×10⁻⁴(Bt/μ₀a).
 Figure 4 shows the mode locking threshold versus the island
angular rotation frequency ω.

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 In figure 5, input parameters are: S=7.6×10⁶, χ∥=1.5×10⁹ (a²/τR),
ne=1.5×10¹⁹m⁻³, μ≈χ⊥≃0.8 (a²/τR), jb= 3×10⁻⁴(Bt/μ₀a)
 Figure 5 shows the threshold ψ_{threshold} for mode excitation
changed with plasma viscosity μ in the 2/1 resonant surface.
 Figure 5 shows that
 We also get
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4. Conclusion
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 In summary, we have found the mode locking threshold, equation
(11), for J-TEXT tokamak plasmas. The threshold is proportional to
μ^0.5 and S^(−2). We have also found that faster rotating plasmas
are more resistant towards mode locking.

In order to research the effect of the helical field on tearing
modes, saddle coils will be installed in J-TEXT tokamak soon. The
mode locking threshold will be studied in future experiments and
compared to our theoretical results.
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Thanks
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