A. "Sanpei

H. Himura

K. Oki

K." Ichiguchi

N. Mizuguchi

S. Masamune

National Institute for Fusion Science (NIFS-Repository)

Nonlinear three-dimensional MHD simulations havebeen executed for the low-aspect-ratio reversed-ﬁeld-pinch(RFP) plasma to reveal the physical mechanism ofthe formation processes of helical structures1). The sim-ulation results show a clear formation of n = 4 structureas a result of dominant growth of resistive modes. Theresultant relaxed helical state consists of a unique bean-shaped and hollow pressure proﬁle in the poloidal crosssection both for the cases of resonant and non-resonanttriggering instability modes. The results are partiallycomparable to the experimental observations.To avoid the degradation of conﬁnement due tothe chaotizing of the ﬁeld lines in the core region ofRFP, a unique control method making use of the self-concentrating nature of the plasma perturbations intoa small number of modes has been proposed both ex-perimentally and theoretically. Several types of suchstates have been observed, such as the quasi-single he-licity (QSH) and the single helical axis (SHAx) states.However, the physical mechanisms for the formation anddeformation of the structures have not been clariﬁed well.In this study, we apply the nonlinear 3-D MHD sim-ulations which have been well established for modelingthe tokamak or helical plasmas to the RFP system. Timedevelopment of plasma is calculated by using the MIPScode. A standard set of the nonlinear resistive compres-sive MHD equations is solved explicitly in a cylindricalfull-toroidal geometry with ﬁnite diﬀerence grids. Theinitial conditions are the reconstructed equilibria whichroughly follow the RELAX data obtained by the RE-LAXFit code. Two cases, where the q = 1/4 rationalsurface does(Case D) and does not(Case C) exist, areexamined.Under the condition of ﬁnite resistivity, the n = 4component dominates the growth compared to the othermodes for both cases. The system undergoes relaxationstwice before the dissipative phase of long duration. Sucha transient concentration to the n = 4 mode is also ob-served in the experiment. It should be noted that thedominant component is the n = 4 mode for both cases.The corresponding changes in the poloidal cross sec-tion are shown in Fig.1. The poloidal contour gradu-ally deforms into a bean-shaped structure for both ofthe cases, reﬂecting the linear eigenmode structure withthe m = 1 component. At the relaxed states (Fig.1(c)and (f)), each of the poloidal pressure proﬁles reachesto a highly hollow and deformed ring structure with alarge hole. Such a hollow bean-shaped helical structureappears for a wide range of parameters and proﬁles inthe simulation.The formation mechanism of the hollow structureis diﬀerent between the two cases. For Case D, the reso-nantm/n = 1/4 mode grows with a large single magneticisland (Fig.1(b)), showing a typical behavior of the tear-ing modes. The original magnetic axis shrinks gradually,whereas the created O-point of the island forms a newmagnetic axis. Such a mechanism has been convention-ally proposed for the model of the QSH or SHAx states.On the other hand, for Case D, a similar helical structureis still formed in the relaxation process. In this case, theoriginal nested surfaces are directly deformed into a he-lical one by the non-resonant mode (Fig.1(e)). Then, forboth of the cases, the core pressure ﬂows out along thedeformed magnetic ﬁeld lines, probably through a mag-netic reconnection between the core and the bean-shapedsurface region. The resultant pressure proﬁle forms abean-shaped bank. The investigation of the physicalproperties of the relaxed state and detailed comparisonwith the experiments are our ongoing research.Fig. 1: Time development of the magnetic con-ﬁguration. Puncture plots of the magnetic ﬁeld at(a)t=240, (b)250, (c)260τA for Case D, and (d)280,(e)290, (f)300τA for Case C are shown on the color con-tour of the n=4 component((a),(b),(d), and (e)) and thenet((c) and (f)) pressure.1) N. Mizuguchi, et al., “Modeling of Formation of He-lical Structure in Reversed-Field Pinch”, Plasma Fu-sion Res., (2012), in press.364§23. Modeling of Helical-Structure Formation in Reversed-Field PinchSanpei, A., Masamune, S., Oki, K., Himura, H. (Kyoto Inst. Tech.),  Mizuguchi, N., Ichiguchi, K.

Modeling of Helical-Structure Formation in Reversed-Field Pinch

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