Free-boundary studies for the Large Helical Device

Ichiguchi, K.; Nakajima, N.; Gardner, Henry

doi:10.1088/0029-5515/36/9/i05

Cited by 15 publications

(27 citation statements)

References 19 publications

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“…But this is more of an excuse and is not the main reason for the present article, which is that with growing interest in magnetic diagnostics in stellarators [37][38][39][40][41][63][64][65][66][67] and with excessive orientation of the modern theory towards numerical simulation there arises a natural necessity for a general evaluation of the problem and for stating physically clear general criteria for evaluating any particular result. We would like to emphasize the simple idea that the measured magnetic signals are integral by their nature, and in interpreting experimental results we must take this into account.…”

Section: Discussionmentioning

confidence: 99%

Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems

Pustovitov

2001

Nucl. Fusion

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Restrictions on magnetic diagnostics are discussed. Being related to the integral nature of the measurable quantities, these follow from the fundamental laws of electromagnetism. A series of examples demonstrating the strength of these restrictions is analysed. The general rule is emphasized that information obtained from external magnetic measurements is insufficient for reliable evaluation of plasma current and pressure profiles in tokamaks and in stellarators. The underlying reason is that outside the plasma the self-field of the equilibrium plasma currents is determined by the boundary conditions on the plasma surface alone.

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Section: Discussionmentioning

confidence: 99%

Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems

Pustovitov

2001

Nucl. Fusion

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“…Although the resultant MHD equilibria indicate that a good agreement in the MHD stability is improved as β increases, Fourier modes observed by the magnetic probes do not correctly correspond to those predicted from the theoretical analyses, the discrepancy of which is considered to come from the remaining discrepancy of the MHD equilibria. On the other hand, as a convenient approach to determine the free boundary MHD equilibria corresponding to experimental observations, a virtual limiter [19] is introduced at the location of the vacuum LCFS in the horizontally elongated poloidal cross section, instead of prescribing the total toroidal flux inside of the LCFS [20,21]. The virtual limiter simulates the change of the plasma volume by the stochasticity of l = 2 separatrix and constrains the outer edge in the horizontally elongated cross section to a precribed point by reducing the total toridal flux inside of the LCFS.…”

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confidence: 99%

Development and application of HINT2 to helical system plasmas

et al. 2006

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“…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 calculations [14] for the Large Helical Device (LHD) have demonstrated astonishing accuracy of Eq. (3).…”

Section: Inroductionmentioning

confidence: 99%

“…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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Free-boundary studies for the Large Helical Device

Cited by 15 publications

References 19 publications

Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems

Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems

Development and application of HINT2 to helical system plasmas

Theory of Diamagnetic Signal in Current-Free Stellarators

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