Stability conditions for kink and tearing modes in tokamaks

Богомолов, Л. М.; Zakharov, L.; Blekher, P. M.

doi:10.1088/0029-5515/27/2/005

Cited by 4 publications

(6 citation statements)

References 10 publications

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“…The predominantly m = 5 peeling mode has a maximum growth rate at q at the boundary of 4.93. The resistive peeling mode is unstable also when the q = 5 surface is just inside the plasma (in agreement with earlier results without a separatrix [17][18][19]). However, the peeling mode is stable for ψ b = 0.998 (CASTOR) and with the full separatrix (JOREK).…”

Section: External Kink (Peeling) Mode In X-point Geometrysupporting

confidence: 92%

MHD stability in X-point geometry: simulation of ELMs

2007

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A non-linear MHD code, named JOREK, is under development with the aim of studying the non-linear evolution of the MHD instabilities thought to be responsible for edge localized modes (ELMs): external kink (peeling) and medium-n ballooning modes. The full toroidal X-point geometry is taken into account including the separatrix, open and closed field lines. Analysis of the influence of the separatrix shows a strong stabilization of the ideal and resistive MHD external kink/peeling modes. One instability remains unstable in the presence of the X-point, characterized by a combination of a tearing and a peeling mode. The so-called peeling–tearing mode shows a much weaker dependence on the edge q. Non-linearly the n = 1 peeling–tearing mode saturates at a constant amplitude yielding a mostly kink-like perturbation of the boundary with an island-like structure close to the X-point. The non-linear evolution of a medium-n ballooning mode shows the formation of density filaments. The density filaments are sheared off from the main plasma by an n = 0 flow non-linearly induced by the Maxwell stress. The amplitude of the ballooning mode is limited by this n = 0 flow and multiple (in time) density filaments can develop to bring the plasma below the stability boundary.

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Section: External Kink (Peeling) Mode In X-point Geometrysupporting

confidence: 92%

MHD stability in X-point geometry: simulation of ELMs

2007

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“…This is consistent with Ref. 13 where it was shown that adding to the outer region current layers with j 0 eq ðxÞ > 0 degrades the magnetic island stability.…”

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confidence: 92%

Global current profile effects on the evolution and saturation of magnetic islands

et al. 2013

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The nonlinear evolution of magnetic islands is investigated by means of numerical simulations. The growth and saturation of the island are shown to depend not only on asymptotic tearing mode stability parameter D 0 but also on the initial global current profile. Presence of the external current sheets leads to the formation of different island state for the same value of D 0 . It is found that the flow vorticity generated by the interacting current sheets is an important feature of nonlocal interactions and nonlocal effects in magnetic islands dynamics. V C 2013 American Institute of Physics. [http://dx.Magnetic islands are ubiquitous in space and magnetic fusion plasmas. Magnetic islands associated with magnetic reconnection precede the destruction of flux ropes in solar corona and energy release in the Earth magnetotail. 1,2 In tokamaks, magnetic islands are a major cause of the degradation of plasma confinement and disruptions. 3 Within the boundary layer approach, the stability and growth of the tearing mode are determined by the stability parameter D 0 which characterizes the jump of the magnetic field function at the resonant surface. 4,5 This is a common paradigm of the analytical theory when all non-local effects such as the global current profile and boundary conditions are cast into the parameter D 0 and the predictions of the asymptotic island size require only the knowledge of D 0 and the current profile (current gradients) at the resonant surface. 6,7 This approach has also been adopted in numerical studies 8 including those for practical applications such as control and suppression of magnetic islands with external current drive and heating. 9 The asymptotic approach of the boundary layer is applicable in the regimes of small D 0 , typically D 0 L ? < 1, where L ? is the characteristic length scale of the outer linear region. In fact, in many applications to realistic current profiles, the value of D 0 is not small, rather D 0 L ? can easily be of the order of 10, 10 and even higher in case of the externally driven island. In this letter, the non-local effects of the current profile are investigated in high D 0 regimes. It is shown that the equilibrium current profile far from the resonance can strongly impact the nonlinear dynamics and saturation of magnetic islands and that this impact is not captured by the D 0 stability parameter. We perform a series of numerical experiments with different current profiles (but identical values of D 0 Þ to investigate the quantitative behavior and mechanisms of global effects beyond the D 0 parameterization.In the following, we use a 2D slab reduced MHD model in the low plasma pressure limit. 5,11 The coupled equations for electrostatic potential fluctuations / and the magnetic flux fluctuations w are

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“…Later on, using the principle of successive current layers [5,6] and the analytical criteria of stability for the case of homogeneous current density, we shall show that configurations with j = const for p < a, and with a current density decaying to zero for p > ai will be stable in relation to ideal modes even when condition (9) is fulfilled only at the boundary of the…”

Section: W Jomentioning

confidence: 96%

“…region of homogeneity of j(p). Note that fulfilment of condition (9) does not guarantee the stability of tearing modes.…”

Section: W Jomentioning

confidence: 99%

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Stable current profile in a stellarator with shear

Mikhajlov

Shafranov

1990

Nucl. Fusion

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The authors have studied the stability of helical modes in a current carrying stellarator, ignoring the curvature of the axis and plasma pressure. They show that it is possible to fully stabilize a current column with a given arbitrary current value against both ideal and tearing modes by superimposing an external stellarator rotational transform with a sufficiently large value of its difference along the radius, |Δth| = |th(a) − th(0)|, in configurations of two types, namely with the total rotational transform increasing or decreasing with the radius. The value of the difference |Δth| needed for stabilization increases with the value of the total current.

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Stability conditions for kink and tearing modes in tokamaks

Cited by 4 publications

References 10 publications

MHD stability in X-point geometry: simulation of ELMs

MHD stability in X-point geometry: simulation of ELMs

Global current profile effects on the evolution and saturation of magnetic islands

Stable current profile in a stellarator with shear

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