Non-ideal stability: variational method for the determination of the outer-region matching data

Pletzer, A.; Dewar, R. L.

doi:10.1017/s0022377800015828

Cited by 46 publications

(44 citation statements)

References 16 publications

(28 reference statements)

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“…A general form for the magnetohydrodynamic ͑MHD͒ stability equation has been derived for finite ␤ equilibria with arbitrary geometry, 11 and implemented in the PEST-III numerical method. 12 This code determines ⌬Ј from the ratio of the Frobenius expansion coefficients of the small and large solutions to the stability problem, which are matched from each side of the rational surface. This numerical approach is accurate for shaped equilibria with finite ␤, and with low poloidal and toroidal mode numbers.…”

Section: Tearing Stability and The Ideal Limitmentioning

confidence: 99%

A mechanism for tearing onset near ideal stability boundaries

et al. 2003

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The prevention of neoclassical tearing modes (NTMs) in tokamak plasmas is a major challenge for fusion. Ideal modes can seed NTMs through forced reconnection, yet in sawtoothing discharges it is not well understood why a particular sawtooth crash seeds a NTM after several preceding sawteeth did not. Also, tearing modes sometimes appear and grow without an obvious ideal mode causing a seed island. Based on theoretical and experimental results a new mechanism for tearing mode onset is proposed and tested which explains these puzzling observations. Tearing stability calculations based on experimental equilibria from the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] indicate that tearing modes can be driven unstable by a rapid increase in the linear tearing stability index Δ′ just before onset. Near the ideal kink limit in βN≡β/(I/aBT), Δ′ becomes large and positive as it approaches a pole discontinuity. The relative time scales of the change in Δ′ vs the effects of finite island width will determine the evolution of the island, and the eventual nonlinear state. Theoretical predictions of the onset point, the βN at a specified small island width, and the early evolution characteristics are compared with results from new DIII-D experiments designed specifically to test this hypothesis. Time integration of the island evolution equation shows that these predictions are consistent with the experimental observations. The nonlinear 3D resistive magnetohydrodynamic code NIMROD [A. H. Glasser et al., Plasma Phys. Control. Fusion 41, A747 (1999)] is used to evolve equilibria reconstructed from these experiments in time to provide a more comprehensive prediction of the island evolution during the early nonlinear phase. The simulations are also consistent with the proposed mechanism.

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Section: Tearing Stability and The Ideal Limitmentioning

confidence: 99%

A mechanism for tearing onset near ideal stability boundaries

et al. 2003

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“…The final approach is to solve the linearized, marginally stable, ideal-MHD equations throughout the bulk of the plasma and asymptotically match the solutions thus obtained to nonideal layer (or magnetic island) solutions at the rational surfaces. [19][20][21][22][23][24] This approach, which is much more efficient than the first, and is able to capture the non-ideal effects neglected in the second, is the one adopted in this paper.…”

Section: -11mentioning

confidence: 99%

“…Finally, simultaneous asymptotic matching of the layer solutions in the inner region to the ideal-MHD solution in the outer region yields a matrix tearing/twisting dispersion relation. [19][20][21][22][23][24]27,28 Let the m j , for j ¼ 1; J, be the coupled poloidal harmonics included in the stability calculation. The linearized, marginally stable, ideal-MHD equations that govern the perturbation in the outer region become singular at the various rational surfaces lying within the plasma.…”

Section: Homogeneous Tearing/twisting Dispersion Relationmentioning

confidence: 99%

Determination of the non-ideal response of a high temperature tokamak plasma to a static external magnetic perturbation via asymptotic matching

Fitzpatrick

2017

Physics of Plasmas

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Asymptotic matching techniques are used to calculate the response of a high temperature tokamak plasma with a realistic equilibrium to an externally generated, non-axisymmetric, static, magnetic perturbation. The plasma is divided into two regions. In the outer region, which comprises most of the plasma, the response is governed by the linearized equations of marginally stable, ideal-magnetohydrodynamics (MHD). In the inner region, which is strongly localized around the various rational surfaces within the plasma (where the marginally stable, ideal-MHD equations become singular), the response is governed by Glasser-Greene-Johnson linear layer physics. For the sake of simplicity, the paper focuses on the situation where the plasma at one of the internal rational surfaces is locked to the external perturbation, whereas that at the other surfaces is rotating.

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“…The reason why we adopt a finite-width inner region is because it can remove difficulties inherent in numerical applications of the matched asymptotic expansion. For example, it is not easy to precisely compute the ratio of the diverging big to small solutions around the resonant surface numerically, which is required for the matched asymptotic expansion, although sophisticated theories have been developed [9][10][11][12]. By using the inner region with a finite width, we do not need to compute the ratio of the author's e-mail: furukawa@damp.tottori-u.ac.jp big to small solutions for the matching.…”

Section: Introductionmentioning

confidence: 99%

Extension of Numerical Matching Method to Weakly Nonlinear Evolution of Resistive MHD Modes

Furukawa

Tokuda

2017

Plasma and Fusion Research

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We have extended "numerical matching method" to weakly nonlinear regime, which is relevant for the Rutherford regime of magnetic island evolution in normal magnetic shear plasmas as well as for reversed magnetic shear plasmas to which the Rutherford theory does not apply. The numerical matching method was developed for linear stability analyses of resistive magnetohydrodynamics (MHD) modes by utilizing an inner region with a finite width, that removes difficulties inherent in its numerical applications of the traditional matched asymptotic expansion. The extended method is applied to low-beta reduced MHD simulations of magnetic island evolution in cylindrical plasmas with normal and reversed magnetic shear profiles. The numerical results agree well with fully nonlinear simulation without using the matching method from the linear to weakly nonlinear regimes continuously. Since the nonlinear equation is solved only in the inner region of a finite width, the computational cost is reduced, which enables us to include more detailed physics effects. Our extended method therefore makes a significant contribution in the MHD analysis of magnetic island evolution beyond the restriction in the conventional Rutherford theory.

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Non-ideal stability: variational method for the determination of the outer-region matching data

Cited by 46 publications

References 16 publications

A mechanism for tearing onset near ideal stability boundaries

A mechanism for tearing onset near ideal stability boundaries

Determination of the non-ideal response of a high temperature tokamak plasma to a static external magnetic perturbation via asymptotic matching

Extension of Numerical Matching Method to Weakly Nonlinear Evolution of Resistive MHD Modes

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