Quasi-linear evolution of tearing modes

Pellat, R.; Frey, Michael; Tagger, M.

doi:10.1051/jphys:0198400450100161500

Cited by 8 publications

(9 citation statements)

References 5 publications

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“…where rl/go is the resistive diffusion rate, k 1 and k 2 are positive constants of order unity and DR is the resistive interchange parameter as defined in Ref. 26.…”

Section: The Eigenfunctionmentioning

confidence: 99%

Stability of tearing modes in tokamak plasmas

1994

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The stability properties of m > 2 tearing instabilities in tokamak plasmas are analyzed. A boundary layer theory is used to find asymptotic solutions to the ideal external kink equation which are used to obtain a simple analytic expression for the tearing instability parameter A'. This calculation generalizes previous work on this topic by considering more general toroidal equilibria q (however, toroidal coupling effects are ignored.) Constructions of A" are " obtained for plasmas with finite beta and for islands that have nonzero wiLdth. A simple heuristic estimate is given for the value of the saturated island width when the instability criterion is violated. A connection is made between the calculation of the asymptotic matching parameter in the finite beta and island width case to the nonlinear analog of the Glasser effect [A. H. Glasser, et al, Phys. Fluids 18, 875 (1975)].

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“…where rl/go is the resistive diffusion rate, k 1 and k 2 are positive constants of order unity and DR is the resistive interchange parameter as defined in Ref. 26.…”

Section: The Eigenfunctionmentioning

confidence: 99%

Stability of tearing modes in tokamak plasmas

1994

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“…3 for stationary islands and in Ref. 4 for the time dependent problem. It was revisited more recently in series of papers, [5][6][7][8] where the expressions for magnetic island width at saturation were derived for generic current profiles.…”

Section: Introductionmentioning

confidence: 99%

Higher order and asymmetry effects on saturation of magnetic islands

et al. 2013

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Higher order asymptotic matching procedure is developed to derive the nonlinear equation for saturated magnetic island with the symmetric profile of the equilibrium current. The theory extends the previous results to include higher order effects such as nonlinear modification of the equilibrium current and asymmetry in the boundary conditions in the outer region. It is shown that due to a finite width of the nonlinear region, the magnitude of the magnetic flux at the rational surface is different from the asymptotic value found from the outer solution, resulting in the suppression of the island growth for higher values of D 0 parameter. V C 2013 AIP Publishing LLC.

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“…Within this setting, the magnetic island growth was studied in pioneering work by Rutherford [1]. Subsequently, the saturation of magnetic islands was investigated with different variations of the asymptotic matching techniques [2][3][4][5][6][7][8][9][10][11]. This approach results in the Rutherford type equation with additional terms due to the gradients of the equilibrium current profile.…”

Section: Introductionmentioning

confidence: 99%

Saturation of magnetic islands in equilibria with a finite current gradient. Part I: asymptotic theory

Smolyakov

Poyé

Agullo

et al. 2014

Plasma Phys. Control. Fusion

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The problem of saturation of magnetic islands for the case of a finite current gradient at the rational surface has been revisited. The asymptotic procedure is presented giving the explicit expressions for the perturbed magnetic flux function at saturation. The resulting nonlinear equation for the island width has been obtained in the form similar to the previous work but with fully analytical expressions for the asymptotic series.

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Quasi-linear evolution of tearing modes

Cited by 8 publications

References 5 publications

Stability of tearing modes in tokamak plasmas

Stability of tearing modes in tokamak plasmas

Higher order and asymmetry effects on saturation of magnetic islands

Saturation of magnetic islands in equilibria with a finite current gradient. Part I: asymptotic theory

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