1 EX/P4-9
Characteristics of Magnetic Braking Depending on 3D Field Configuration
in KSTAR
Kimin Kim1,2*, W. Choe1,2, Y. In3, W.H. Ko3, J.G. Bak3, M.J. Choi3, H.S. Kim3, H.Y. Lee1,2,
J.-K. Park4, Y.M. Jeon3, J.G. Kwak3, S.W. Yoon3, and Y.K. Oh3
1
Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea
2
Impurity and Edge plasma Research Center, KAIST, Daejeon, Republic of Korea
3
National Fusion Research Institute, Daejeon, Republic of Korea
4
Princeton Plasma Physics Laboratory, Princeton, NJ, USA
*
E-mail contact: [email protected]
Abstract. Toroidal rotation braking by neoclassical toroidal viscosity driven by non-axisymmetric (3D)
magnetic fields, called magnetic braking, has great potential to control rotation profile, and thereby improve
tokamak stability and performance. In order to characterize magnetic braking in various 3D field configurations,
dedicated experiments have been carried out in KSTAR, applying a variety of static n=1 3D fields of different
phasing of -90, 0, and +90. Resonant-type magnetic braking was achieved by the -90 phasing fields, which is
identified by strong density pump-out and confinement degradation, and explained by excitation of kink
response captured by ideal plasma response calculation. Strong resonant plasma response was also observed
under the +90 phasing at q95~6.0, leading to severe confinement degradation and eventual disruption by locked
modes. Such a strong resonant transport was substantially modified to non-resonant-type transport at higher
q95~7.2, as the resonant particle transport was significantly reduced and global rotation braking was changed to
localized braking. This is well explained by ideal perturbed equilibrium calculations indicating the strong kink
coupling at lower q95 is substantially shielded by ideal plasma response for higher q95 discharge. The 0 phasing
fields achieved quiescent magnetic braking without density pump-out and confinement degradation, which is
consistent with vacuum and ideal plasma response analysis predicting deeply penetrating 3D fields without
significant plasma response.
1. Introduction
Understanding the physics of plasma response to non-axisymmetric (3D) magnetic fields in
tokamaks is important since a small amount of 3D fields can significantly influence global
confinement and stability [1]. Among a number of 3D field applications, toroidal rotation
braking by neoclassical toroidal viscosity (NTV) driven by 3D fields [2], called magnetic
braking, has great potential to control the profile of toroidal plasma rotation and thereby
change tokamak stability and performance. The NTV in tokamaks with toroidal nonaxisymmetry has been of great interest in the fusion research community due to its
importance to understand the physics of kinetic plasma response to the applied 3D fields and
to effectively utilize the 3D fields as a control method of tokamak performance. As such
efforts, a number of experiments have been conducted in the various tokamak devices along
with significant theoretical and numerical progresses [3, 4]. A common observation in the 3D
tokamak experiments is the alteration of toroidal plasma rotation toward neoclassical offset,
of which characteristics depend on the operational conditions.
NTV theories, simulations, and experiments have confirmed strong quadratic proportionality
of the NTV to the magnitude of perturbed 3D fields [5, 6]. Other parameters such as plasma
2 EX/P4-9
collisionality, ExB and bounce frequencies of plasma particles also determine the amplitude
of NTV torque [7], however their relationship is much more complicated as pronounced by
the existence of complicated resonance physics such as bounce-harmonic resonance [8] and
the transport regimes by collisionality dependency such as ν, 1/ν, superbanana plateau [2].
Therefore, it is not straightforward to control the NTV torque profile in an explicit manner
using the operational plasma parameters such as temperature, density, and rotation. One may
imply that a relatively simple method for the control the NTV and thereby magnetic braking
performance can be achievable by control of the applied 3D field structure, since the NTV
profile will directly follow the shape of applied 3D fields with other parameters fixed.
Plasma response is also of great importance, since it reestablishes the perturbed 3D
equilibrium by generating toroidal plasma currents that shield or amplify the applied 3D fields
[9]. In practice, the 3D field structure determined by the perturbed equilibrium obeys the
characteristics of the magnetic braking. However, the perturbed 3D field structure is not
solely determined by the applied 3D field configuration but by complicated interactions
between the field and the plasma response. This is another critical element that significantly
changes and thereby determines the resonance characteristics of plasmas as well as the
magnetic braking. Among a number of plasma parameters, q-profile will play a key role to
determine the plasma responses and the perturbed 3D field structure, due to its significant
impact on the pitch-alignment with the applied 3D fields. One can imply the control of 3D
field spectrum produced by the applied field configuration along with q95 determined by
axisymmetric equilibrium can be a simple but powerful knob for control of global plasma
response and transport in the magnetic braking experiments.
2. 3D field configurations in KSTAR
Dedicated experiments have been carried out in KSTAR in order to characterize magnetic
braking depending on the 3D field configuration, where a variety of static n=1 3D fields were
applied to the H-mode plasmas. The KSTAR device is a good machine to demonstrate and
characterize the kinetic plasma response and magnetic braking physics associated with the 3D
field configurations, since it creates a wide range of poloidal field spectra using a variety of
the 3D coil phasing. The 3D field coils in KSTAR, called in-vessel control coils (IVCCs), are
composed of poloidally 3 and toroidally 4 sets of internal coils. They can generate the static
3D fields of toroidal mode numbers n=1 and n=2, and the 3D field structure is defined by
relative phase difference between the 3 rows, called the phasing. Then, a number of 3D fields
depending on the phasing can be produced, which include standard n=1 configurations such
as -90, 0, and +90 phasing, as shown in Fig. 1.
Figure 1. IVCC configurations of KSTAR for n=1, (a) -90 phasing, (b) 0 phasing, and (c) +90 phasing
Using this capability of IVCCs, we carried out magnetic braking experiments to demonstrate
various types of magnetic braking. Three kinds of static n=1 3D fields of different phasing of
-90, 0, and +90 were applied to investigate the plasma response to the applied field
3 EX/P4-9
configuration. The IVCC phasing is a key knob in this experiment to control and determine
the resonant and/or non-resonant features of the plasma response. The q-profile was another
control element varied in a series of H-mode discharges with ~2.7MW of neutral beam
heating, where the axisymmetric toroidal magnetic field was changed (2.0T, 2.2T, 2.4T) with
fixed plasma current (0.5MA) to vary q95 from ~6 to ~7.2 and investigate q95 effects on the
magnetic braking characteristics. All other parameters were kept fixed in a single discharge,
thus the phasing was the main parameter that characterizes the plasma behavior for each
axisymmetric equilibrium.
3. Observations of magnetic braking discharges
3.1. Resonant braking by -90 phasing
Strong resonant-type magnetic braking was achieved by the -90 phasing fields. The resonant
plasma response was identified by substantial density pump-out and confinement degradation
along with ELM mitigations. Time traces of these discharges are presented in Fig. 2, which
shows time evolution of toroidal plasma rotation, ion temperature, averaged electron density,
and Dα signal for three discharges with different q95. Figure 2. Time trace of magnetic braking discharges by -90 phasing for (a) q95~6, (b) q95~6.5, and (c)
q95~7.2. Shaded indicates the period of 3D field application.
One can notice that the toroidal rotation was instantly decelerated by the 3D fields and the
braking occurred globally in the whole plasma volume. Strong reductions of density due to an
enhanced particle transport by the 3D fields were observed, implying the resonant plasma
response in the discharge. Mitigation of the ELMs was achieved by -90 phasing as presented
by reduction of Dα signal during the 3D field phase. Fig 3. presents the toroidal rotation
profiles before and after the application of -90 phasing fields, which shows that toroidal
rotation braking occurred globally for all three q95 values. This braking appeared the strongest
for the lowest q95 discharge and became weak as q95 was increased, which is consistent to the
strongest resonant plasma response at q95~6.2.
4 EX/P4-9
Figure 3. Comparison of toroidal
rotation before and after
application of -90 phasing fields
Such observations of resonant plasma transport are opposite to vacuum field spectrum
calculation that predicts highly non-resonant feature of the -90 phasing as shown in Fig. 4(a).
However, excitation of kink-coupling captured by ideal perturbed equilibrium calculation
using IPEC, shown in Fig. 4(b), explains the observed resonant plasma response consistently.
These features were similarly found in the higher q95 discharges. These observations are
opposite to the previous experiments that achieved highly non-resonant magnetic braking in
the validation experiments of rotational resonances of NTV transport [5], where there were no
severe density pump-out and confinement degradations.
Figure 4. Poloidal field spectrum of -90 phasing for (a) vacuum field and (b) ideal plasma response
3.2. Change of braking characteristics by q95 in the +90 phasing
The +90 phasing configuration of the n=1 fields in KSTAR has been known as the most
resonant n=1 configuration, as reported by the ELM suppression and the mode-locking
phenomena using this configuration [10]. Due to strong pitch-alignment in this phasing, we
applied reduced IVCC currents of 2kA to avoid too strong resonant plasma response and
locked modes, however very strong resonant plasma response was unavoidable in the
relatively low discharge at q95~6. The +90 phasing produced the strongest torodial torque
among the experiments described in this paper, along with significant density pump-out and
confinement degradation. This strong magnetic braking at low q95 eventually disrupted the
discharge by locked modes, as shown in Fig. 5(a). One can also notice that distinctive braking
characteristics were observed under +90 phasing depending on q95. As presented in Fig. 5(b)
and (c), one can find the strongest resonant plasma response and toroidal rotation braking
became weaker as q95 was increased. Even though the resonant plasma response and global
magnetic braking were retained at q95~6.5, the reduction of plasma density and rotation was
5 EX/P4-9
weakened, as shown in Fig. 5(b). The toroidal rotation braking still appeared globally, and
slight increase of the ion temperature was observed due to the reduced density. ELMs were
not suppressed but slightly mitigated in this condition.
Figure 5. Time trace of magnetic braking discharges by +90 phasing for (a) q95~6, (b) q95~6.5, and (c)
q95~7.2. Shaded indicates the period of 3D field application.
Figure 6. Poloidal field spectrum of +90 phasing using ideal plasma response for (a) q95~6 and (b)
q95~7.2
Interestingly, the resonant type plasma transport at q95~6.0 and 6.5 was substantially modified
to non-resonant-type transport as q95 was increased up to ~7.2 as shown in Fig. 5(c). At this
q95 discharge, strong particle transport driven by resonant plasma response was significantly
reduced, thus the plasma density was almost maintained without the pump-out. The global
rotation braking observed at lower q95 was changed to localized braking at the plasma edge,
and the significant core rotation braking at lower q95 was weakened. The transition to nonresonant-type plasma response and transport under the +90 phasing can be explained by
perturbed equilibrium calculations with IPEC in Fig. 6. The poloidal spectrum at q95~6.0
indicate the strong kink coupling due to significant pitch-alignment responsible for the
strongest resonant response, however such a strong kink response is substantially reduced by
6 EX/P4-9
shielding of ideal plasma response at higher q95~7.2, which is consistent to the experimental
observations of non-resonant-type plasma transport.
Figure 7. Vacuum Chirikov parameter
profiles for +90 phasing as a function of
normalized flux
The role of plasma response in the higher q95 discharge changing the resonant features to the
non-resonant braking is also can be found in the calculation of vacuum Chirikov parameter,
which is a measure of overlapping of magnetic islands due to resonant field components. Fig.
7 indicates that magnetic islands are significantly overlapped at the edge pedestal region for
all three q95 cases. Even though radial position where the Chirikov value is greater than unity
is outward-shifted from ~0.8 to ~0.88 as q95 is increased, the vacuum field calculation still
indicate the island overlapping will be significant even for high q95 case and plasma response
will be highly resonant. However, as discussed previously with the result of ideal plasma
response calculation in Fig. 6, plasma response at high q95 causes non-resonant-type response
through the strong shielding of kink-coupling, which implies the important role of plasma
response for determining the characteristics of magnetic braking.
3.3. Quiescent braking by 0 phasing
A quiescent magnetic braking was achieved by the 0 phasing fields. Fig. 8 shows that the
toroidal rotation in the whole volume was damped by the 0 phasing fields, while the plasma
density was sustained without pump-out. A slight increases of ion temperature and total
stored energy were observed, which may be correlated with modification of ion thermal
transport during the 0 phasing period. ELMs were slightly mitigated, as ECEI measurements
indicate transition of large-size ELMs without 3D to intermediate size ELMs during the 0
phasing period. Similar quiescent non-resonant momentum transport without density pumpout was retained at higher q95 discharges. These experimental results confirm that the 0
phasing is the most non-resonant configuration between the static n=1 field configurations,
thus it has a great potential for toroidal rotation control by the quiescent magnetic braking
without disturbing other operational parameters.
The poloidal field spectrum calculations with the vacuum field and the ideal plasma response
indicate the 0 phasing is highly non-resonant, as shown in Fig. 9. One can find that window of
poloidal harmonics for resonant pitch-alignment for the 0 phasing is very narrow compared to
the -90 and +90 phasing and any significant kink-type resonant responses are not excited by
the ideal plasma response. These calculation results are consistent with the achievement of
quiescent magnetic braking in the experiments.
7 EX/P4-9
Important and potentially beneficial features of such a quiescent magnetic braking achieved
using the 0 phasing is that particle transport and density pump-out was not enhanced by this
phasing even though strong rotation braking was achieved. Therefore, increase of core ion
temperature about 0.4-0.6keV observed during the 0 phasing period lead to slight increase of
stored energy along with the absence of density reduction. Interestingly, the increased ion
temperature was sustained after turning-off of the 3D fields without turning back to the
temperature level prior to 3D field application. Instead, large fluctuations of ion thermal
transport were generated, implying the changes in equilibrium plasma state and/or excitement
of fast ion transport by the 3D fields. Underlying mechanism is not clear yet. One can imply
that the quiescent magnetic braking may be a potential ingredient to improve ion thermal
transport via toroidal rotation profile control, however further investigations are required to
clarify the associated plasma transport mechanism. Future experiments will explore potential
utilization of the quiescent magnetic braking to improve global confinement and performance
through toroidal rotation profile control.
Figure 8. Time trace of magnetic braking discharges by 0 phasing for (a) q95~6, (b) q95~6.5, and (c)
q95~7.2. Shaded indicates the period of 3D field application.
Figure 9. Poloidal field spectrum of 0 phasing using (a) vacuum field and (b) ideal plasma response
for q95
8 EX/P4-9
4. Summary
Magnetic braking using various n=1 3D field configurations has been demonstrated in
KSTAR and characterized experimentally and numerically based on measurements and
modeling of plasma response. Clear dependency of resonant and non-resonant plasma
response on the applied 3D field configuration and q95 was revealed from the observations,
such as enhanced density pump-out and change of ELM behavior as well as global and local
deceleration of toroidal rotation. Numerical modeling with the perturbed 3D equilibrium
considering vacuum and ideal plasma response consistently explains the experimental
observations, indicating the important role of plasma response in determining the
characteristics of magnetic braking discharges. The analysis results on the n=1 braking
discharges have consistencies with the n=2 magnetic braking discharges that produced a
significant variation in the NTV torque profile depending on the phasing of n=2 field coils.
Non-resonant magnetic braking can be produced by avoiding the pitch-alignment even using
the generally resonant 3D field configurations such as n=1, +90 phasing and n=2, +90
phasing. Production of quiescent magnetic braking can be possible using highly non-resonant
0 phasing 3D fields both in the n=1 and n=2 configurations.
Acknowledgements
This work was supported by National Research Foundation of Korea (NRF) funded by the
Ministry of Science, ICT and Future Planning (NRF-2014M1A7A1A03045092), and the
Korean Ministry of Science, ICT and Future Planning under the KSTAR project contract
(NFRI).
References
[1] CALLEN, J.D., “Effects of 3D magnetic perturbations on toroidal plasmas”, Nucl. Fusion
51 (2011) 094026.
[2] SHAING, K.C., et al., “Neoclassical plasma viscosity and transport processes in nonaxisymmetric tori”, Nucl. Fusion 55 (2015) 125001.
[3] GAROFALO, A.M., et al., “Observation of plasma rotation driven by static
nonaxisymmetric magnetic fields in a tokamak”, Phys. Rev. Lett. 101 (2008) 195005.
[4] PARK, J.-K., et al., “Importance of plasma response to nonaxisymmetric perturbations in
tokamaks”, Phys. Plasmas 16 (2009) 056115.
[5] PARK, J.-K., et al., “Rotational resonance of nonaxisymmetric magnetic braking in the
KSTAR tokamak”, Phys. Rev. Lett. 111 (2013) 095002.
[6] KIM, K., et al., “δf Monte Carlo calculation of neoclassical transport in perturbed
tokamaks”, Phys. Plasmas 19 (2012) 082503.
[7] KIM, K., et al., “Calculation of neoclassical toroidal viscosity with a particle simulation in
the tokamak magnetic braking experiments”, Nucl. Fusion 54 (2014) 073014.
[8] KIM, K., et al., “Numerical verification of bounce-harmonic resonances in neoclassical
toroidal viscosity for tokamaks”, Phys. Rev. Lett. 110 (2013) 185004.
[9] TURNBULL, A.D., et al., “Comparisons of linear and nonlinear plasma response models
for nonaxisymmetric perturbations”, Phys. Plasmas 20 (2013) 056114.
[10] JEON, Y.M., et al., “Suppression of edge localized modes in high-confinement KSTAR
plasmas by nonaxisymmetric magnetic perturbations”, Phys. Rev. Lett. 109 (2012) 035004.