Effects of net toroidal current on the Mercier criterion in the Large Helical Device

Ichiguchi, K.; Nakajima, N.; Okamoto, Masayuki; Nakamura, Yukio; Wakatani, Masahiro

doi:10.1088/0029-5515/33/3/i10

Cited by 57 publications

(60 citation statements)

References 21 publications

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“…Equations (1), (2), and (3) are the Ohm's law, the vorticity equation, and the equation of state, respectively. The equations are normalized in the following way.…”

Section: Nonlinear Calculation With Norm Codementioning

confidence: 99%

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Mercier Stability Improvement in Nonlinear Development of LHD Plasma

Ichiguchi

Carreras²

2008

Plasma and Fusion Research

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A stable path to high-beta plasmas is investigated for an inward-shifted LHD configuration. An improvement of Mercier stability is observed due to the nonlinear saturation of the resistive interchange modes. For this study, a multi-scale numerical scheme is used. In this scheme, the beta value is increased by adding a small pressure increment to the background pressure. We focus on the dependence of the Mercier stability on the profile of the pressure increment. It is found that the total pressure profile approaches a profile marginally stable to the Mercier criterion when the pressure increment has a fixed profile.

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“…Equations (1), (2), and (3) are the Ohm's law, the vorticity equation, and the equation of state, respectively. The equations are normalized in the following way.…”

Section: Nonlinear Calculation With Norm Codementioning

confidence: 99%

“…However, linear ideal interchange modes (Mercier modes) were predicted to be unstable in this configuration [2]. In order to investigate the stabilizing mechanism of the modes, we developed a nonlinear MHD code, NORM, based on the reduced MHD equations [3,4].…”

Section: Introductionmentioning

confidence: 99%

Mercier Stability Improvement in Nonlinear Development of LHD Plasma

Ichiguchi

Carreras²

2008

Plasma and Fusion Research

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“…In stellarators, the magnetic well is always 'shallow' [14][15][16][17][18][19][20][21][22][28][29][30], just several percent. Since A ∝ β and β is small,…”

Section: General Relations and Assumptionsmentioning

confidence: 99%

Theory of Diamagnetic Signal in Current-Free Stellarators

Pustovitov

2010

Plasma and Fusion Research

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The toroidal magnetic flux through the plasma column is calculated analytically for current-free stellarators of arbitrary geometry without assumptions on the plasma shape, aspect ratio, etc. This is done with accuracy sufficient for extracting the contribution due to the finite plasma pressure from this flux. The final result is a formula relating the measured diamagnetic signal with β, the ratio of the plasma pressure to the magnetic pressure. This formula is obtained assuming small β and the relative depth of the magnetic well. These are natural conditions for stellarators, therefore the final result can be recommended for magnetic diagnostics without practical limitations. Keywords: stellarator, magnetic diagnostics, diamagnetic signal, plasma equilibrium, current-free plasma DOI: 10.1585/pfr.5.S2054 InroductionDiamagnetic measurements are a traditional diagnostics used for determining the plasma energy content in tokamaks and stellarators [1][2][3][4][5]. Interpretation of the measurements are based on a simple formula originally derived for a circular plasma cylinder [6] 2 δΦwhere the measured diamagnetic signal is defined asB is the magnetic field, B v is the vacuum magnetic field, Φ 0 = B 0 S ⊥ with S ⊥ = πb 2 being the transverse crosssection of the plasma column, b is its minor radius, B 0 is the toroidal field, B J is the poloidal field at the plasma boundary due to the net toroidal current,β ≡ 2p/B 2 0 is the ratio of the volume-averaged plasma pressure p to the magnetic field pressure B 2 0 /2. It is known that Eq. (1) can be applied to large-aspectratio tokamaks with a circular plasma [7]. The same or slightly modified formula has been used for conventional stellarators [8][9][10], though the validity of Eq. (1) has been proved for straight stellarators only [11,12]. Strictly speaking, for stellarators with current-carrying plasma (B J 0) Eq. (1) should contain an additional term [11,12]. Here we consider the case when this contribution can be disregarded.The diamagnetic signal for arbitrary shape and aspect ratio current-free plasma in a toroidal conventional stellarator was calculated analytically in [13]. In analytical author's e-mail: pustovit@nfi.kiae.ru * permanent address: Russian Research Centre 'Kurchatov Institute', Pl. Kurchatova, Moscow, 123182, Russia theory, when a cylindrical result is generalized for account of the toroidal effects, this is usually done by large-aspectratio expansion. It was unexpected that the problem considered in [13] turned out to be solvable without this 'natural' simplification and even without any assumption on the plasma shape. The obtained result [13] was ready for practical use. Similar to (1), it directly relates the measured diamagnetic signal δΦ to the value of interest, the integral on the right hand side over the plasma volume. Here the constant F b = 2πrB t describes the vacuum toroidal field B t , r is the radius from the main vertical axis, and δ SH is a small correction related to the Shafranov shift and helical field. Later, numerical calculation...

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“…Here a set of parameters aϭ1 and bϭ2 is adopted. The choice of parameters is the same as those of Ichiguchi et al 22 who studied the Mercier stability of the LHD system by using the VMEC code. 23 We study a case where the major radius of the vacuum magnetic axis R ax is located at R ax ϭ3.7 m in the real dimension.…”

Section: B An Initial Equilibrium Obtained By Using the Hint Codementioning

confidence: 99%

“…͑The center of the helical coil for LHD is located at 3.9 m in the major radius.͒ In this paper, we restrict ourselves to an initial equilibrium whose central beta ␤ 0 is 4%. According to a previous study, 22 a part of magnetic surfaces for an equilibrium with R ax ϭ3.7 m and ␤ 0 ϭ4% is analyzed to be unstable for the Mercier criterion. In Figs.…”

Section: B An Initial Equilibrium Obtained By Using the Hint Codementioning

confidence: 99%

Nonlinear simulation of resistive ballooning modes in the Large Helical Device

2001

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Nonlinear simulations of a magnetohydrodynamic ͑MHD͒ plasma in full three-dimensional geometry of the Large Helical Device ͑LHD͒ ͓O. Motojima et al., Phys. Plasmas 6, 1843 ͑1999͔͒ are conducted. A series of simulations shows growth of resistive ballooning instability, for which the growth rate is seen to be proportional to the one-third power of the resistivity. Nonlinear saturation of the excited mode and its slow decay are observed. Distinct ridge/valley structures in the pressure are formed in the course of the nonlinear evolution. The compressibility and the viscous heating, as well as the thermal conduction, are shown to be crucial to suppress the pressure deformations. Indication of a pressure-driven relaxation phenomenon that leads to an equilibrium with broader pressure profile is observed.

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Effects of net toroidal current on the Mercier criterion in the Large Helical Device

Cited by 57 publications

References 21 publications

Mercier Stability Improvement in Nonlinear Development of LHD Plasma

Mercier Stability Improvement in Nonlinear Development of LHD Plasma

Theory of Diamagnetic Signal in Current-Free Stellarators

Nonlinear simulation of resistive ballooning modes in the Large Helical Device

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