24A01
Physics of Resonant Magnetic Perturbations in Toroidal Plasmas
トロイダルプラズマにおける共鳴磁場摂動の物理
Todd Evans,1 Jeffrey Harris,2 Katsumi Ida,3 Satoshi Ohdachi,3 Morgan Shafer,2 Yasuhiro Suzuki,3Kenji Tanaka,3 Ezekiel Unterberg2 and the LHD Experiment Group3
トッド・エバンス、ジェフリー・ハリス、居田克巳、大館暁、モーガン・シェファー、鈴木康浩、田中謙治、エゼキール・ウンターベルグ、LHD 実験グループ
1General Atomics, San Diego, California 92186 USA
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 USA
3National Institute for Fusion Sciences, Toki, Gifu 509-5292, Japan

2Recent experiments on a variety of tokamaks and stellarators/heliotrons have demonstrated that 3D,resonant magnetic perturbation (RMP), fields can be beneficial for controlling the properties of hightemperature plasmas. These results are of significant scientific interest for understanding the basic physics
that defines the confinement and stability properties of toroidal plasmas. In tokamaks, applied RMPs havebeen used to suppress edge MHD instabilities while maintaining H-mode transport barriers. Instellarators/heliotrons intrinsic RMPs produce islands and an edge stochastic layers that are associated withimproved confinement. Here, we discuss common features of RMP physics found in the DIII-D tokamak
and the LHD heliotron.

1. Introduction
An interesting aspect of Resonant MagneticPerturbations (RMP) in tokamaks is that the RMP
fields act primarily on particle confinement withminor effects on energy confinement [1]. This isinconsistent with a straightforward application ofquasi-linear transport theory, which predicts thatheat flux along open field lines should be dominant.
This suggests that either the global magnetic
topology induced by the RMP fields in a tokamak
H-mode pedestal is different from that observedwith RMP fields in Ohmic plasmas [2] or that otherphysics effects are competing with parallel heat
conduction along open stochastic field lines inplasmas with edge transport barriers. Instellarators/heliotrons, stochastic boundaries havebeen associated with the formation of edgetransport barriers that have properties similar toH-modes in tokamaks [3].
Here, we discuss comparisons of edge stochastic
layers in tokamaks and stellarators/heliotrons withthe goal of developing a common physics basis forbetter understanding the general properties of theconfinement and stability in these two devices.
2. Magnetic Topology Measurements
In low  tokamaks, with relatively small plasma
flows, vacuum calculations of the magnetic
topology match experimentally observed magnetic
islands very well [2]. On the other hand in H-modes,
with high edge temperatures, imaging magnetic
islands with visible spectral lines is not possible so
we must rely on new techniques for measuring theproperties of the magnetic topology. Several newtechniques developed in the LHD heliotron are now
in use on the DIII-D tokamak. These include soft
x-ray imaging [4,5], heat pulse propagation studies[6] and 3D equilibrium reconstructions [7]. These
are needed to better understand the plasma response
to RMP fields and changes in the field topology thataffect the plasma performance.
3. Topological Effects on Plasma Performance
A working assumption is that the structure of theedge magnetic topology plays an essential role in
the plasma performance. For example, when RMP
fields from perturbation coils are applied to DIII-D
tokamak H-modes the toroidal and poloidal rotationis strongly altered while the radial electric field (Er)across the pedestal plasma at the edge goes frombeing entirely negative (radially inward) to mostly
positive (radially outward) as shown in Fig. 1.

Fig.1. Change in the (a) toroidal (), (b) poloidal
ExB (ExB), (c) poloidal diamagnetic (dia)rotation and (d) radial electric field (Er) with (dashed)
and without (solid) the RMP in DIII-D shot 123306.

These data are consistent with an increase in theplasma potential due to a loss of thermal electrons
from the pedestal region along open magnetic fieldlines that connect to divertor target plates. Numerical studies have shown that vacuum RMP fields
create magnetic structures known as homoclinic
tangles in the separatrix of a diverted tokamak
plasma [8]. The lobes of these tangles can intersect
the divertor target plates allowing field lines frominside the separatrix to escape and hit divertor surfaces. Experimental data has verified the existenceof homoclinic tangles due to RMP fields [8,9].
Similar effects are seen in the poloidal flow (vpol)
profile of the LHD heliotron near the edge of theplasma where the vacuum magnetic field is
intrinsically stochastic due to the finite geometry of
the helical coils. As shown in Fig. 2, charge
exchange spectroscopy (CXS) measurements of vpol
going from the good flux surface region through theedge stochastic region show a sharp reversal of theflow starting at the edge of the stochastic fieldregion. Here, positive Er field measurements
indicate open field lines but do not directly indicate
a stochastic field. It is not clear whether themagnetic field is stochastic as predicted by vacuum
calculation or healed by the plasma.

the plasma response to the RMP field in DIII-D. Onthe other hand, there is typically a significant
change in the toroidal rotation of the DIII-D plasma
when the RMP field is applied and this has an
impact on Er through radial force balance.
Comparisons of the magnetic structure in DIII-D
and LHD, based on heat pulse propagation studies[6], soft x-ray imaging [4,5] and HINT2 3D
equilibrium reconstructions [7], are expected toprovide key information on the extent of thestochastic region and the existence of islands versus
good flux surfaces. HINT2 results for LHD indicatethat the width of the stochastic region increases
with  and edge localized mode suppression inDIII-D with RMP fields is known to improve withincreasing normalized . These results imply that
there should be a clear dependence on Er andplasma flows with increasing  in each machine.
4. Summary and Conclusions
Developing a better understanding of the plasma
response to externally applied RMP fields in highconfinement tokamaks and stellarators/heliotrons isimportant for improving the performance of thenext generation of toroidal magnetic devices. A keyelement needed for progressing along thisdevelopment path is the ability to diagnose theglobal magnetic topology of the plasma edge.
Methods such as heat pulse propagation studies,that have been used in the LHD to distinguishbetween good flux surfaces, magnetic islands andstochastic layers, have recently been applied in
DIII-D and the result are being used to determine
whether variations in the thickness of the edge
stochastic layer with increasing  or RMP field
amplitude are correlated with changes in the radial
electric field, plasma flows and turbulence.

Fig. 2. (a) Closed flux surfaces bounded by a stochastic
magnetic field region on the horizontal midplane whereCXS measurements are made (x’s and +’s), (b) vpol
profile from CXS measurements showing a sharp
reversal from negative flows in the closed surface region
to positive in the open field region.

Acknowledgments
This work was supported in part by the US
Department of Energy under DE-FC02-04ER54698
and DE-AC05-00OR22725, and the NIFS budget
code NIFS11ULHH021.

Note that there is a strong similarity between vpol
in LHD and ExB in DIII-D [dashed curve,Fig. 1(b)]. In LHD the radial position where vpolchanges from negative to positive is thought toindicate the location of the last closed flux surface.
Outside this point the field is open and Er is positive(radially outward). Inside this position Er isnegative (radially inward). Applying thisobservation to the DIII-D data suggests that the lastclosed flux surface in DIII-D could be significantly
closer to the separatrix than indicated by vacuum
field calculations, which may be a consequence ofReferences[1] T. E.Evans, et al., Nature Physics 2 (2006) 419.
[2] T. E. Evans, R. A. Moyer and P. Monat: Phys.
Plasmas 9 (2002) 4957.
[3] K. Toi, et al., Fusion Sci. Technol. 58 (2009) 61.
[4] S. Ohdachi, et al., Fusion Sci. Technol. 58 (2010) 418[5] M. Shafer, et al., Plasma and Fusion Research 6(2011) 2402041.
[6] K. Ida, et al., Phys. Rev. Lett. 100 (2008) 045003[7] Y. Suzuki, et al., Nucl. Fusion 46 (2006) L19[8] T. E. Evans, et al., J. Phys. Conf. Ser. 7 (2005) 174[9] T. E. Evans, et al., J. Nucl. Mater. 363-365 (2007)
570.