Toroidal Contributions to the Shear and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>∥</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Kink Instability in the Tokamak and Screw Pinch

Ware, A. A.

doi:10.1103/physrevlett.26.1304

Cited by 13 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2n + 1 so that the necessary criterion for stability is (28) The complete necessary criterion for stability of surface modes is obtained by combining criteria ( 27) and (28) to give 0 + y _ yi/a > 0 Using the expressions (23) to (25) for a, 0 and 7 this becomes > 0 (29) Two results which can be immediately derived from criterion ( 29) are (i) if f = 0 on the plasma surface then, since p' = j^/R, marginal stability occurs for j ^a = 0 and (ii) if p' = 0 on the plasma surface then, since f -j^/B^, marginal stability again occurs for…”

Section: Localized Criteriamentioning

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

Section: Localized Criteriamentioning

confidence: 99%

Hydromagnetic stability of tokamaks

1978

View full text Add to dashboard Cite

show abstract

“…Here the mode is unstable for all p> 0. For p -0, it is a current-driven internal kink mode that is destabilized by toroidal effects 14 for q > 1. Note that this mode has no counterpart in cylindrical geometry, where q 0 < 1 is required for a / r driven internal kink mode.…”

mentioning

confidence: 99%

Mechanism for rapid sawtooth crashes in tokamaks

Aydemir

1987

Phys. Rev. Lett.

View full text Add to dashboard Cite

The standard picture of the Kadomtsev reconnection process predicts sawtooth crash times that are longer than those observed in present-day large tokamaks. Ideal kink modes are investigated as a possible mechanism for these fast crashes, by use of fully toroidal, compressible, full magnetohydrodynamic equations. In systems with low shear, parallel-current and pressure-driven modes are identified well below the previously accepted poloidal-/? limits. Linear and nonlinear calculations show good agreement with experiments and indicate that such modes may explain fast collapse times reported in the recent literature.PACS numbers: 52.55.FaThe sawtooth oscillations in the soft x-ray signals observed in tokamaks are associated with periodic changes in the central electron temperature, T e . l Typically, a slow phase during which the central temperature slowly rises is followed by a fast drop in T e , associated with flattening of the central temperature. The time scale of the slow phase is determined by various transport processes such as Ohmic heating. The resistive internal kink mode was invoked by Kadomtsev 2 to explain the crash phase of the oscillations. In this model, anm = l island (m is the poloidal mode number), associated with a safety factor q less than unity on axis, grows, forming a helical deformation of the internal plasma column. This kink structure subsequently relaxes to a symmetric state through complete reconnection of the helical flux inside the q = 1 surface with the flux from outside. The Kadomtsev model has been generally believed to explain the sawtooth oscillations in earlier tokamaks.Recent observations, however, indicate that tokamaks exhibit various types of sawtooth oscillations that cannot be fully explained by the Kadomtsev model. In addition to the simple sawtooth associated with this model, there are double or compound sawteeth 3 ' 4 thought to be caused by the presence of two or more q = 1 surfaces in the plasma. Moreover, both TFTR and JET tokamaks report crash times that cannot be easily reconciled with the Kadomtsev reconnection process. 5 Previous numerical studies of the sawtooth oscillations have concentrated on the m = 1 resistive tearing mode. Waddell et al. 6 performed the first nonlinear studies and found the current-flattening times to be in agreement with the internal disruption times reported in the ST tokamak. Sykes and Wesson 7 included self-consistent evolution of the temperature and resistivity in order to follow periodic sawtooth oscillations. However, in their simulations, sawteeth decayed away after a few periods. Denton et al., by including parallel thermal conductivity, have produced repeating sawtooth oscillations. 8 They were able to reproduce qualitatively many of the experimentally observed features of sawtooth oscillations, in-cluding compound sawteeth, by adjusting the transport coefficients. However, their studies did not adequately address the quantitative features of sawteeth, in particular anomalously fast crash times observed in the present-day large to...

show abstract

“…This can happen only when the minimum value of q satisfies q min > m/n, which means that the perturbation creating the buckets exists in the absence of resonant flux surfaces. As was mentioned above, such perturbations are known to occur in experiment [5,6].…”

Section: Resonance Islands (Buckets)mentioning

confidence: 91%

“…[3,4]), also has zero frequency in the plasma frame. On the other hand, when the q-profile slightly exceeds the resonant magnitude q = m/n, quasi-static deformations of flux surfaces occur; in particular, the infernal mode [5] with (m, n) = (1, 1) takes place when the q-profile is flat and slightly exceeds unity; a (1, 1)-mode may also occur in reversed-shear discharges with q min slightly exceeding unity [6]. Low-n static magnetic perturbations can also be produced by external coils with the aim to suppress or mitigate ELMs (edge-localized modes) [7].…”

Section: Introductionmentioning

confidence: 97%