S." "Ohdachi

"Ohdachi,  S."

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Core Density Collapse and high-nBallooning modesOHDACHI, SatoshiCore density collapse (CDC) is a large-scale relax-ation event observed in internal diﬀusion barrier (IDB)plasmas. The increase of the central beta is limited bythe CDC; the central beta is decreased up to 50%. In or-der to extend operational regime, understanding of theCDC is required. Steep pressure gradient with peakedproﬁle of IDB plasma is a candidate for the events. How-ever, the greater part of the plasma including the steepgradient region is within the magnetic well due to thelarge Shafranov-shift. CDC thus cannot be explained bythe interchange mode by the pressure gradient. Fromthe stability analysis, low–n MHD mode is stable in thecenter1). Another pressure–driven mode, high–n bal-looning mode 2, 3) is an instability destabilized in themagnetic hill region. It is a candidate to explain CDCphenomena since it is unstable in the edge region in theLHD. It is consistent with the experimental observationthat the collapse starts form the edge region4).The growth rate of ideal high–n ballooning modeis calculated using Hn-bal code. The pressure proﬁle isassumed to be p = p0(1−ρ2)2 where p and ρ is the pres-sure and normalized minor radius, respectively. In orderto ﬁll the parameter space of the experiments shown byFig. 1 (A), the preset–magnetic axis Rax0 and the cen-tral pressure p0 is scanned. The growth rates in the edgeregion (ρ ∼ 0.8) are shown in Fig. 1(B) with the samerange of x axis and y axis of Fig. 1(A). The growth ratedrastically increases at the experimental boundary forthe appearance of the CDC (shown by the dotted line inFig. 1(B)). It is thus likely the origin of the initial edgeactivity is high–n ballooning modes.The scale of the collapse is reduced with the de-crease of the magnetic ﬁeld. When the Bt is lower than1.0 T, no CDC is observed. Large amplitude m = 1modes localized in the core region are observed instead.The beta proﬁle during the m = 1 modes are almostidentical to the beta proﬁle just before the CDC in highBt cases. When 1T < Bt < 1.5T, we sometimes observem = 1 oscillation evolves and shift to a small CDC–like collapse. Therefore, those pre–cursor oscillations areconsidered to be direct cause of that CDC. Two-step sce-nario for CDC is being considered from the results. Atthe ﬁrst the step, the edge density proﬁle is ﬂatten fromthe enhancement of the transport due to the edge insta-bilities (possibly, high–n ballooning mode). That makesthe pressure gradient in the central region steeper. An m= 1 mode is destabilized in the core then and the mag-netic axis is moved radially. In the collisional plasmas(Bt > 1.5 T), the movement causes a magnetic recon-nection, i.e. CDC. In less collisional condition (Bt < 1.5T), continuous m = 1 mode are activated.There remain several points to be cleared for theconﬁrmation of this scenario. One is the determination ofthe unstable region of the high–n ballooning modes. Cal-culation of the spatial structure of the high–n ballooningmodes with realistic pressure proﬁle is in progress usingCAS3D code. The location where the initial small crashtakes place will be compared with the eigen function ofthe high–n ballooning modes in detail. Identiﬁcation ofthe m = 1 kink–type oscillation is also required for un-derstanding of the whole CDC process.3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.20.01.02.03.04.05.06.07.0DI = 0Growth Rate (log)ρ = 0.8β 0 [%]R [m](A)(B) γ/ωA=0.5γ/ωA=0.25γ/ωA=0.13β 0 [%]R [m]3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.20.01.02.03.04.05.06.07.04.00m3.90m3.85m3.70m3.75m3.80mFig. 1: Operational space of the IDB type dischargesis shown in (A). Each color corresponds to the vacuummagnetic axis position. CDCs are observed with theplasma parameters shown as the closed triangles. Fig.(B) shows the growth rate of the ballooning modes of badcurvature magnetic ﬁeld line on ρ = 0.8. Yellow dottedline is a rough marking where CDCs are activated withthose plasma parameters.1) Y. Narushima, et.al., J. Plasma Fusion Res. SERIES,8, 1070 (2009).2) N. Nakajima, Physics of Plasmas 3(12), 4545 (1996).3) N. Nakajima, Physics of Plasmas 3(12), 4556 (1996).4) S. Ohdachi, et. al, “Density Collapse events observedin the Large Helical Device:”, Contrib. Plasma Phys.accepted20§15. Core Density Collapse and High-n Ballooning ModesOhdachi, S.

Core Density Collapse and High-n Ballooning Modes

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