A necessary condition for hydromagnetic stability of plasma with axial symmetry

Mercier, C.

doi:10.1088/0029-5515/1/1/004

Cited by 250 publications

(141 citation statements)

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“…6 Finally we stress that, because of their finite perpendicular wavelength, our global interchange modes are not affected by finite-Larmor-radius stabilization provided the ion Larmor radius is much smaller than r 0 . This is in marked contrast with the original, large-n Mercier interchanges, 7 and provides the first opportunity for the Mercier stability criterion to have an observable, macroscopic effect on the behavior of tokamak plasmas. In summary, under rather general conditions we have obtained a robust, large scale instability which is likely to play an important role in elongated tokamaks if the prevalent transport processes produce flat central q-profiles.…”

Section: Fo(r)mentioning

confidence: 83%

Theory of global interchange modes in shaped tokamaks with small central shear

Ramos

1988

Phys. Rev. Lett.

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Section: Fo(r)mentioning

confidence: 83%

Theory of global interchange modes in shaped tokamaks with small central shear

Ramos

1988

Phys. Rev. Lett.

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“…where the Mercier stability criterion [17] (for the unperturbed equilibrium) takes the form 1 4 + D M ∞ > 0. We will assume that this equilibrium is Mercier stable.…”

Section: The Localised Tearing Mode Equation With Pressure Flatteningmentioning

confidence: 99%

The role of pressure flattening in calculating tearing mode stability

Ham

Connor

Cowley

et al. 2013

Plasma Phys. Control. Fusion

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Abstract. Calculations of tearing mode stability in tokamaks split conveniently into an external region, where marginally stable ideal MHD is applicable, and a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter ∆ ′ . Pressure and current perturbations localized around the rational surface alter the stability of tearing modes. Equations governing the changes in the external solution and ∆ ′ are derived for arbitrary perturbations in axisymmetric toroidal geometry. The relationship of ∆ ′ with and without pressure flattening is obtained analytically for four pressure flattening functions. Resistive MHD codes do not contain the appropriate layer physics and therefore cannot predict stability directly. They can, however, be used to calculate ∆ ′ . Existing methods (Ham et al. 2012 Plasma Phys. Control. Fusion 54 025009) for extracting ∆ ′ from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface and favourable average curvature because of the Glasser stabilizing effect. To overcome this difficulty we introduce a specific pressure flattening function that allows the earlier approach to be used. The technique is first tested numerically in cylindrical geometry with an artificial favourable curvature. Its application to toroidal geometry is then demonstrated using the toroidal tokamak tearing mode stability code T7 (Fitzpatrick et al. 1993 Nucl. Fusion 33 1533) which uses an approximate analytic equilibrium. The prospects for applying this approach to resistive MHD codes such as MARS-F (Liu et al. 2000 Phys. Plasmas 7 3681) which utilize a fully toroidal equilibrium are discussed.

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“…For the loops under consideration, the typical value is q -0.2, remaining less than unity inside the loop. The condition for stability against local perturbation is given by the Suydam condition (Suydam, 1958) appropriately modified for the toroidal geometry (Mercier, 1960) 19 q 2 /1 .0 q r2…”

Section: Mhd Stability Propertiesmentioning

confidence: 99%

MHD equilibrium and stability properties of a bipolar current loop

Xue

Chen

1983

Sol Phys

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A study is made of equilibrium and stability properties of a semi-toroidal current loop imbedded in a high temperature plasma. The loop has a toroidal current density and poloidal current density. By explicitly including the global curvature of the loop, the net Lorentz and pressure forces acting along the major radius are calculated. Requirement of equilibrium force-balance gives rise to conditions that must be satisfied by physical parameters such as current, pressure, magnetic field and geometry. On the basis of these conditions, we deduce a class of equilibrium semi-toroidal current loops satisfying c~ 1 JxB -p = 0. Furthermore, this class of equilibria is shown to be stable to a number of destructive MHD modes.Application of the theoretical results to solar bipolar current loops is discussed.

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A necessary condition for hydromagnetic stability of plasma with axial symmetry

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Cited by 250 publications

References 1 publication

Theory of global interchange modes in shaped tokamaks with small central shear

Theory of global interchange modes in shaped tokamaks with small central shear

The role of pressure flattening in calculating tearing mode stability

MHD equilibrium and stability properties of a bipolar current loop

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