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Quasilinear perturbed equilibria of resistively unstable current carrying plasma

Part of: PLA Tribute to V D Shafranov: 1929-2014 Focus on Fusion

Published online by Cambridge University Press:  02 November 2015

Di Hu  and
Leonid E. Zakharov
Di Hu
Affiliation:
School of Physics, Peking University, No. 209 Chengfu Rd., Haidian District, Beijing 100871, China
Leonid E. Zakharov*
Affiliation:
LiWFusion, PO Box 2391, Princeton, NJ 08543, USA
*
†Email address for correspondence: lzakharov@comcast.net
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Abstract

A formalism for consideration of island formation is presented using a model of a cylindrical resistively unstable plasma. Both current and pressure driven island formation at resonant surfaces are considered. The proposed formalism of perturbed equilibria avoids problems typical for linear analysis of resistive magneto-hydrodynamic instabilities related to extraction of the so-called small solution near the resonant surfaces. The matching technique of this paper is not sensitive to configuration parameters near the resonant surfaces. The comparison of the perturbed equilibrium method with the frequently used quasilinear mode analysis based on a perturbed averaged current density profile shows that the latter is limited in its applicability and underestimates the stability. Presented here for a cylindrical case, the perturbed equilibrium technique can be used in toroidal perturbed equilibrium codes with minor modifications.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 515810602
Copyright
© Cambridge University Press 2015 

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References

Bodin, H. A. B. 1990 The reversed field pinch. Nucl. Fusion 30, 1717–1737.Google Scholar
Chang, Z. & Callen, J. D. 1990 Global energy confinement degradation due to macroscopic phenomena in tokamak. Nucl. Fusion 30, 219–233.Google Scholar
Chu, M. S., Dewar, R. L., Greene, J. M. & Pletzer, A. 1993 A new formulation of the resistive tearing mode stability criterion. Phys. Fluids B 5, 1593–1604.Google Scholar
Coppi, B., Greene, J. M. & Johnson, J. L. 1966 Resistive instabilities in a diffuse linear pinch. Nucl. Fusion 6, 101–117.Google Scholar
Escande, D. F. & Ottaviani, M. 2004 Simple and rigorous solution for the nonlinear tearing mode. Phys. Lett. A 323, 278–284.Google Scholar
Fitzpatrick, R. 1995 Helical temperature perturbations associated with tearing modes in tokamak plasmas. Phys. Plasmas 2, 825–838.CrossRefGoogle Scholar
Freidberg, J. P. 1987 Ideal Magnetohydrodynamics. Plenum.CrossRefGoogle Scholar
Furth, H. P., Rutherford, P. H. & Selberg, H. 1973 Tearing mode in the cylindrical tokamak. Phys. Fluids 16, 1054–1063.Google Scholar
Furukawa, M., Tokuda, S. & Zheng, L. J. 2010 A numerical matching technique for linear resistive magnetohydrodynamics modes. Phys. Plasmas 17, 052502.CrossRefGoogle Scholar
Gates, D. A. & Delgato-Aparicio, L. 2012 Origin of tokamak density limit scaling. Phys. Rev. Lett 108, 165004.Google Scholar
Glasser, A. H., Greene, J. M. & Johnson, J. L. 1975 Resistive instabilities in general toroidal plasma configuration. Phys. Fluids 18, 875–888.CrossRefGoogle Scholar
Hastie, R. J., Militello, F. & Procelli, F. 2005 Nonlinear saturation of tearing mode islands. Phys. Rev. Lett. 95, 065001.Google Scholar
Hegna, C. C. & Callen, J. D. 1994 Stability of tearing modes in tokamak plasmas. Phys. Plasmas 1, 2308–2318.Google Scholar
Hindmarsh, A. C. 1980 LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM Signum Newsletter 15.4, 10–11.Google Scholar
Iacono, R., Bhattacharjee, A., Ronchi, C., Greene, J. M. & Hughes, M. H. Stability of tearing modes in finite-beta plasmas. Phys. Plasmas 1, 2645–2652.Google Scholar
Jiang, M., Hu, D., Wang, X. G., Shi, Z. B., Xu, Y., Chen, W., Ding, X. T., Zhong, W. L., Dong, Y. B., Ji, X. Q. et al. 2015 Synchronous oscillation prior to disruption caused by kink modes in HL-2A tokamak plasmas. Nucl. Fusion 55, 083002.Google Scholar
Kotschenreuther, M., Hazeltine, R. D. & Morrison, P. J. 1985 Nonlinear dynamics of magnetic islands with curvature and pressure. Phys. Fluids 28, 294–302.Google Scholar
Mercier, C. 1962 Stability criterion of a hydromagnetic toroidal system with scalar pressure. Nucl. Fusion Suppl. Pt. 2, 801–808.Google Scholar
Newcomb, W. A. 1960 Hydromagnetic stability of a diffuse linear pinch. Ann. Phys. (NY) 10, 232–267.Google Scholar
Pletzer, A. & Dewar, R. L. 1991 Non-ideal stability: variational method for the determination of the outer region matching data. J. Plasma Phys. 45, 427–451.Google Scholar
Robinson, D. C. 1978 Tearing-mode-stable diffuse-pinch configurations. Nucl. Fusion 18, 335–953.CrossRefGoogle Scholar
Rutherford, P. H. 1973 Nonlinear growth of the tearing mode. Phys. Fluids 16, 1903–1908.Google Scholar
Suydam, B. R. 1958 Stability of a linear pinch. In Proceedings of the 2nd International Conference Peaceful Uses Atomic Energy, vol. 31, pp. 157–159. United Nations Publication.Google Scholar
Tokuda, S. & Watanabe, T. 1999 A new eigenvalue problem associated with the two-dimensional Newcomb equation without continuous spectra. Phys. Plasmas 6, 3012–3026.CrossRefGoogle Scholar
Waelbroeck, F. L., Fitzpatrick, R. & Grasso, D. 2007 Effect of sheared flow on magnetic islands. Phys. Plasmas 14, 022302.Google Scholar
Wang, X. G., Bhattacharjee, A., Ma, Z. W., Ren, C., Hegna, C. C. & Callen, J. D. 1998 Structure and dynamics of current sheets at Alfvén resonances in a differentially rotating plasma. Phys. Plasmas 5, 2291–2296.CrossRefGoogle Scholar
White, R. B. 1986 Resistive reconnection. Rev. Mod. Phys. 58, 183–207.CrossRefGoogle Scholar
White, R. B., Gates, D. A. & Brennan, D. P. 2015 Thermal island destabilization and Greenwald density limit. Phys. Plasmas 22, 022514.Google Scholar
White, R. B., Monticello, D. A., Rosenbluth, M. N. & Waddell, B. V. 1977 Saturation of tearing mode. Phys. Fluids 20, 800–805.Google Scholar
Yu, Q. 2006 Numerical modeling of diffusive heat transport across magnetic islands and local stochastic field. Phys. Plasmas 13, 062310.CrossRefGoogle Scholar
Zakharov, L. E. 1978 The theory of hydromagnetic stability of a tokamak plasma. Nucl. Fusion 18, 335–342.Google Scholar
Zakharov, L. E.1986 Stability conditions for helical MHD perturbations and disruptive instability in tokamaks. In 11th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Kyoto, Nucl. Fusion. Suppl., vol. 2, p. 75. IAEA.Google Scholar
Zakharov, L. E. & Shafranov, V. D. 1986 Equilibrium of current carrying plasmas in toroidal configurations. In Reviews of Plasma Physics, vol. II, p. 164. Plenum.Google Scholar