Magnetic coordinates for equilibria with a continuous symmetry

Dewar, R. L.; Monticello, D.; Sy, W. N. C.

doi:10.1063/1.864828

Cited by 40 publications

(40 citation statements)

References 23 publications

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“…Specifically, the magnetic field line curvature is κ = (b · ∇)b, where b = B/B is the unit vector along the magnetic field lines, while the local magnetic shear is defined as S = −h · ∇ × h with h = B × ∇s/|∇s| 2 (Greene & Johnson 1968;Dewar et al 1984;Hegna 2000). The parallel current density factor is σ ≡ j · B/B 2 and ξ is the perturbed displacement vector.…”

Section: Analysis Of the Linear 3-d Ideal Mhd Analysismentioning

confidence: 99%

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A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

et al. 2015

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Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma-vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number n = 1 distortions when the edge bootstrap current is large and higher n corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch-Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch-Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

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Section: Analysis Of the Linear 3-d Ideal Mhd Analysismentioning

confidence: 99%

“…The internal plasma potential energy is written in the form (Dewar, Monticello & Sy 1984;Greene 1996;Cooper 1997) …”

Section: Ideal Mhd Stability Of Axisymmetric Tcv Equilibriamentioning

confidence: 99%

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

et al. 2015

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“…The local integrated shear is given by R + θ ∂ ψ q = −∇α·∇ψ/|∇ψ| 2 , and the normal and geodesic components of the magnetic curvature vector κ ≡ e || ·∇e || (where e || ≡ B/B) are given by κ n ≡ κ·∇s/|∇s| and κ g ≡ κ·∇s×B/|B∇s|, respectively [4]. The parameter θ k is related to the direction of the mode wave vector.…”

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confidence: 99%

Anderson-localized ballooning modes in general toroidal plasmas

Cuthbert¹,

Dewar²

2000

Physics of Plasmas

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Ballooning instabilities are investigated in three-dimensional magnetic toroidal plasma confinement systems with low global magnetic shear. The lack of any continuous symmetry in the plasma equilibrium can lead to these modes being localized along the field lines by a process similar to Anderson localization. This produces a multibranched local eigenvalue dependence, where each branch corresponds to a different unit cell of the extended covering space in which the eigenfunction peak resides. These phenomena are illustrated numerically for the three-field-period heliac H-1, and contrasted with an axisymmetric s-α tokamak model. The localization allows a perturbative expansion about zero shear, enabling the effects of shear to be investigated. Ballooning instabilities are pressure-driven ideal magnetohydrodynamic (MHD) instabilities which limit the maximum β (plasma pressure/magnetic pressure) that can be obtained in a plasma. They are localized about regions where the field lines are concave to the plasma, which are known as unfavourable regions of curvature. Another localizing influence is the magnetic shear, which measures the rate at which neighboring field lines at different minor radii separate as they wind their way around the torus. Large shear helps stabilize these modes, thereby playing an important role in the MHD stability. In this paper however we consider the effects of very small or zero shear, such as occurs in the heliac class of stellarators or in the shear-reversal layers of an advanced tokamak.We begin by making the usual assumption that the magnetic field lines map out nested flux surfaces, or magnetic surfaces. These are labeled using a normalizedtoroidal-flux variable s, which varies between zero at the center of the plasma and unity at the plasma edge. Within each surface the straight-field-line poloidal θ and toroidal ζ angle variables are defined such that the field lines appear as straight lines in the (θ, ζ) plane. The magnetic field may then be written B = ∇ζ×∇ψ − q∇θ×∇ψ ≡ ∇α×∇ψ, where the field-line label α ≡ ζ − qθ. Here, 2πψ represents the poloidal magnetic flux, while q = q(s) is the safety factor (inverse of rotational transform), which is equal to the average number of toroidal circuits traversed by a field line per poloidal circuit traversed around the torus.Ballooning modes can be characterized as having a long parallel and short perpendicular wavelength with respect to the field lines. By ordering the perpendicular wavelength to be small and expanding to lowest order in an asymptotic series the local mode behavior can be expressed by a one-dimensional equation along a field line [1]. Taking the plasma to be incompressible, the ballooning equation may be written [2]where the eigenfunction ξ is related to the mode displacement while the eigenvalue λ is equal to the mode growth rate squared. This represents the local stability, local to a field line. In forming global modes, ray tracing must be performed in the three-dimensional λ phase space to determine which of these local sol...

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“…In the associated perturbed energy, one of the stabilising terms involves the perturbed component of the magnetic field (Greene and Johnson 1968) which, in turn, contains the local magnetic shear. Following Dewar et al (1984), the LMS can be written:…”

Section: Q Armentioning

confidence: 99%

“…The global magnetic shear is a surface averaged quantity and, at least for localised modes, the local magnetic shear (Greene and Johnson 1968;Ware 1965) and the integrated shear (Dewar et al 1984) are more fundamental quantities. Pressure driven modes in particular are often in the region of unfavourable curvature (Greene and Chance 1981), emphasising the importance of a local measure of the magnetic shear.…”

Section: Introductionmentioning

confidence: 99%