Mitigation of Kink Modes in
Pedestal
Z. T. Wang 1,2 , Z. X. He 1, J. Q. Dong 1 , X. L. Xu 2 ，M. L. Mu2,
T. T. Sun2, J. Huang 2, S. Y. Chen2, C. J. Tang2
1. Southwestern Institute of Physics, Chengdu 610041, China
2. College of Physics Science and Technology, Sichuan University,
Chengdu 610065, China
The Second A3 Foresight Workshop on Spherical Torus
Jan. 6-8, 2014,
Tsinghua University, Beijing, China
• Kink modes are investigated in pedestal for
shaped tokamaks. Aanalytic combining
criterion is presented.
• For large poloidal mode number the modes
are highly localized in both poloidal and
radial directions. The modes increase
rapidly when they approach to the resonant
surface. They are typical of ELMs.
• There seems to be a second stable region
when current gradient is large. It is pointed by
Wesson [10] that “There is no way of avoiding
this destabilizing current density gradient….
Fortunately the current density gradient also
provides a strong stabilizing effect, namely
shear of magnetic field”.
• Several mitigation methods for controlling
ELMS are proposed. The principle of the
mitigation could apply for spherical torus.
• In the recent results given by Webster and
Gimblett，the peeling mode could occur, but
growth rate can be arbitrarily small near the
separatrix.
• Numerical calculations have suggested that a
plasma equilibrium with an X-point-as it found
with all ITER-like tokamaks is stable to the
peeling mode [1-3].
• We extend Zakharov’ work [5] to the shaped
tokamaks.
• Based on energy principle, The potential
energy is written in a form:
•
(1)
• In the Hamada coordinates
, the
potential energy is turned out to be
where
• In the neighborhood of the magnetic axis, the
square root of volume is taken as small
parameter [8]. To the lowest order we have,
(5)
• We consider the step current proposed by
Shafranov [13],
• We get a combining criterion [9],
2
6
4
4

1


2
(40)
 
Q
 2 
 2 d
•
2
2
2
1 
  
     1
• When   0, Eq.(40) is the sufficient criterion of
Lortz [8-9] and    Eq.(40) is the necessary
criterion of Mercier [7],   1 Eq.(40) is the
result of present Paper.
• We define triangularity,
•
(12)
• The potential energy
•
(13)
• We can get an analytical criterion,
(14)
• Where ι is rotation transform, the reciprocal of the safety
factor q.
• The growth rates of the unstable modes can be given
by
•
•
•
(15)
Numerical solution
• For large tokamaks, such as, ITER, JET, DⅢ-D , JT-60,
HL-2M there are large elongation and triangularity.
We choose the parameters,
• We get the growth rates versus
in Fig. 1. Fig.2
gives the growth rate related to the current gradient.
Both pressure gradient and current gradient are the
drives of the kink modes. The elongation is
essentially destabilizing. The growth rates versus
elongation is given in Fig. 3. The triangularity has
stabilizing effects in Fig. 4. The mode structure is
presented in Fig.5.
• There are two stable regions in Fig. 6.
Fig. 1. The growth rates
versus
Fig. 2 . The growth rate versus
Fig. 3. The growth rates versus
elongation
Fig. 4. The growth rates versus
triangularity.
Fig.5. The mode structure near the
resonant surface where
Fig. 6. There are two stable regions
Summary
• Using the energy principle we derive a combined
criterion of kink
• Numerical results show that the growth rates
vary with elongation which essentially has
destabilizing effects. The triangularity has
stabilizing effects.
• Changing elongation and triangularity by shaping
coils may mitigate kink modes which may related
to the ELMs. Changing the pedestal current by
current drives can also mitigate the modes.
• We can trigger more small elms avoiding a large
type-1 elm, reduce the particle and heat roads to
the plasma facing materials.
Thanks for your attention !
• References
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2687(1998).
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EPS Conf. on Controlled Fusion and Plasma Physics (St.Petersburg,7–11
July,2003) vol. 27A (ECA) P-3.129.
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