Flute instability in a Tokamak of arbitrary cross-section

Yavlinskij, Yu.N.

doi:10.1088/0029-5515/13/6/023

Cited by 9 publications

(5 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Doublet shares those potential advantages of the ellipse that result from elongation (i.e. increased values of j3, J and ^p ) , and can introduce MHDstabilizing effects similar to those of the D-shape in respect to the preservation of moderate q-values [28]: the "active ingredient" in both configurations is the tear-drop shape of Fig. 4.…”

Section: 1 1 Equilibriummentioning

confidence: 93%

See 1 more Smart Citation

Tokamak research

Furth

1975

Nucl. Fusion

178

View full text Add to dashboard Cite

Progress in tokamak research is reviewed for the period 1971–74. The theories of MHD-stability, classical transport and anomalous transport have been refined. The tokamak device population has increased by about an order of magnitude. Non-Ohmic heating methods have been developed successfully. The severity of the problem of plasma impurity has been recognized, and technological countermeasures are being developed. The experimental results on energy confinement are not yet well understood theoretically and cannot be fitted by any simple empirical transport coefficient; the general empirical trend, however, is favourable to the achievement of reactor plasma conditions in large future tokamak devices.

show abstract

Section: 1 1 Equilibriummentioning

confidence: 93%

“…In the cases of the D-shape and Doublet (Fig. 4) this permits modest advantages in /3-value and current to be attained for moderate elongations [ 21,28,63].…”

Section: Mhd-stabilitymentioning

confidence: 99%

Tokamak research

Furth

1975

Nucl. Fusion

178

View full text Add to dashboard Cite

show abstract

“…An analytical treatment of this problem was given by Mikhajlovskij and Shafranov [48] who gave the stability requirement For the specific case of a parabolic pressure distribution P = $ 0p (r/R) 2 and the overall criterion for stability is where 7 is the ellipticity parameter of the plasma boundary, r measures its triangularity and e is the aspect ratio. For a circular cross-section the condition for stability becomes q * > Further investigations of the effect of shaped flux surfaces have been carried out by Grelot and Weisse [49], Yavlinskij [50] and Aymar and Jacquinot [51]. Galvab [52] has investigated the effect of the current profile on the stability criterion for localized modes around the magnetic axis.…”

Section: + Ementioning

confidence: 99%

Hydromagnetic stability of tokamaks

1978

View full text Add to dashboard Cite

A summary is given of the linear theory of the ideal and resistive hydromagnetic stability of tokamaks. The first section provides an introductory account of the various aspects of the stability problem, and the subsequent sections provide a survey of the subject and a review of the literature. For aperfectly conducting plasma the modes of instability are of three types: kink, internal, and axisymmetric. When resistivity is introduced the kink and internal modes have significantly modified forms. The analysis of the standard tokamak, having a large aspect ratio, circular cross-section and low β, is almost complete but the study of small aspect ratio, high-β configurations and the optimization of such configurations are at an early stage.

show abstract

“…To determine stability near the magnetic axis, a polynomial-trigonometric fit to the equilibrium is used. Then stability is examined by means identical to those used by Yavlinskij [19] . It must be remarked that not all configurations studied are least stable on axis.…”

Section: 732mentioning

confidence: 99%

Tokamak equilibria with arbitrary cross-section

Dobrott

Helton

1976

Nucl. Fusion

View full text Add to dashboard Cite

Magnetohydrodynamic equilibria are obtained by semi-analytic means for large-aspect-ratio tokamaks with fixed, non-circular boundaries and slightly non-uniform currents. The method uses the fact that there is a conformal map of any simple closed region onto the unit circle. Solutions are expressed as quadratures which involve the conformal maps. These quadratures are evaluated numerically for specific examples. Results for equilibria with circular, elliptical, dee-shaped and doublet-shaped cross-sections are presented and compared. Toroidal and finite-beta effects are noted and stability against flutes is examined by Mercier's criterion for the various configurations.

show abstract

Flute instability in a Tokamak of arbitrary cross-section

Cited by 9 publications

References 4 publications

Tokamak research

Tokamak research

Hydromagnetic stability of tokamaks

Tokamak equilibria with arbitrary cross-section

Contact Info

Product

Resources

About