S-P1-3
Application of resonant magnetic perturbations to tokamak plasmas
トカマクプラズマへの外部共鳴摂動磁場印加実験
Yusuke Kikuchi
菊池 祐介
Graduate School of Engineering, University of Hyogo
2167 Shosha, Himeji, Hyogo 671-2280, Japan
兵庫県立大学 工学研究科 〒671-2280 兵庫県姫路市書写2167
Externally applied resonant magnetic perturbations (RMPs) are used for control of tokamak plasmas. TheRMP field penetration processes into tokamak plasmas are investigated by the dynamic ergodic divertor inTEXTOR. Measurements of the plasma response to the RMP field are performed and the observed data areinterpreted by theoretical models. It is observed that the growth of the magnetic island by the RMP field
penetration is accompanied by a change of the toroidal plasma fluid rotation. The relative rotation
frequency between the RMP field and the plasma plays an important role in the process of the RMP field
penetration.

1. Introduction
Externallyappliedresonant
magneticperturbations (RMPs) are used in order toinvestigate a lot of applications in tokamak
devices such as ergodic divertors [1], the controlof MHD instabilities [2], and the suppression ofedge localized modes (ELMs) [3]. In particular,
the application of RMPs by in-vessel coils is oneof the methods of foreseen to control ELMs inITER. The ergodisation of the edge magnetic
field is generally evaluated by adding theequilibrium magnetic field to the perturbation
field produced by the RMP coils, where the RMP
field propagates in vacuum. However, the plasma
response to the RMP strongly modifies the levelof edge ergodisation. It could affect the plasmatransport and the stability of ELMs. As
summarized in Fig. 1, the effect of plasmaresponse on the expected heat and particle fluxes
to plasma facing components between ELMs andduring ELMs mitigated with the application ofRMP has to be investigated.
The Dynamic Ergodic Divertor (DED) [4] inthe TEXTOR tokamak has been installed to study
a lot of applications connected to the interactionof RMP with tokamak plasmas. In this talk, bothexperimental and theoretical studies related to theRMP penetration in TEXTOR will be shown.
2. RMP coils in TEXTOR
The RMP coils in TEXTOR consist of 16
external perturbation coils at the high field side
inside the vacuum vessel. The DED system canproduce static or rotating RMP fields up to amaximum frequency of 10 kHz which covers thefrequency range of the typical plasma diamagnetic

Key physics: Plasma responses to RMPs
(1) Shielding current flow at the resonance surface(2) Field amplification, and growth of magnetic island(3) Alfven resonance

Structure of edge magnetic field,
Level of ergodisation

Power and particle fluxes on plasma facing
components between ELMs and during ELMs

Fig. 1 Relation between plasma response to RMPsand PWI issues

drift in the TEXTOR tokamak. The base mode
numbers of the RMP coils can be selected by theconnections of the power supplies to the coils
between m/n = 12/4, 6/2, and 3/1, where m, n refers
to the poloidal and toroidal mode number. The m/n= 12/4 mode decays rather quickly, so that it affects
mainly the plasma edge. On the other hand, the m/n= 3/1 mode penetrates deeply into the plasma. The
strong sideband component of m/n = 2/1 isproduced, so an m/n = 2/1 tearing mode is wellreproduced [5].
3. RMP penetration into tokamak plasmas
The DED with m/n = 3/1 mode is mainly used inthis study. The plasma response to the RMP ismeasured by a Hall probe. The Hall probe is locatedoutside the plasma (r/a = 1.04). It reveals that twostages in the time development of the plasmaresponse to the RMP field can be distinguished,
where the RMP coils current is linearly increased intime during the discharge [6]. In the first phase, theinduced plasma current at the resonant magnetic
surface (q = m/n) is phased such that it shields thepenetrating perturbation field. After passing thethreshold of the RMP field amplitude, a phase jumpof the plasma response to the RMP is observed andthe current at the resonant surface amplifies theexternal magnetic perturbation.
The observed RMP field penetration in theexperiment is compared with theoretical models asfollows. Firstly, it is also observed that the RMP
field penetration is accompanied by a change of thetoroidal plasma fluid rotation in the experiment.
The bifurcation of the RMP field penetration fromthe suppressed to the excited state is confirmed by aquasi-linear MHD simulation in cylindricalgeometry [7]. Secondary, the threshold of RMP
field amplitude for the bifurcation of the RMP field
penetration depends on the rotation direction of therotating RMP field in the experiment. A linear twofluid model is also performed in order to include theeffects of electron diamagnetic drift on the RMP
penetration [6, 8]. It is concluded that the relativerotation frequency between the mode and theapplied RMP field is important in determining thethreshold for the bifurcation. This feature is also
confirmed in a non-linear two-fluid model [9].
On the other hand, the RMP penetration is also
affected by the Alfven resonance (ωRMP2 = k||2vA2, k||is the wave number parallel to the equilibrium
magnetic field, and vA is the Alfven velocity).
When the distance between the two Alfven
resonances is wide enough compared with that of
the resistive layer at the resonant magnetic surface(k|| = 0), two current sheets are formed there [7, 10].
However, it is considered that the Alfvenresonances locate inside the resistive layer in theTEXTOR plasma. On the other hand, an rf currentof ~ 5 A with frequencies swept from 100 kHz to 1
MHz is applied on the RMP coil in TEXTOR [11].
Minov coil signals indicate that Alfven eigenmodeis excited by the RMP field. This experiment isconducted under the IEA-TEXTOR collaboration
program.
Finally, it should be noted that pioneering studies
related to RMP penetration processes into tokamak
plasmas have been performed on small tokamaks,
CSTN-IV [12] and HYBTOK-II [13] in Nagoya
University. It is confirmed that the theoreticalmodel can explain the observed radial profiles ofthe RMP field inside the plasma by inserting small
magnetic pick-up coils in HYBTOK-II [14]. It isconsidered that these fundamental studies play animportant role for understandings of the RMP
penetration in TEXTOR.
Acknowledgments
This work was conducted during my stay in IPP
Juelich from 2004 to 2006 supported by the Japan
Society for the Promotion of Science (JSPS)
Postdoctoral Fellowships for Research Abroad.
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