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Journal Articles

Analysis of an aspect ratio effect on the stability of external MHD modes in tokamaks with the Newcomb equation

Aiba, Nobuyuki; Tokuda, Shinji; Ishizawa, Tomoko*

Journal of Plasma Physics, 72(6), p.1127 - 1131, 2006/12

https://doi.org/10.1017/S0022377806005782

Times Cited Count：1 Percentile：3.54(Physics, Fluids & Plasmas)

We develop the method for the stability analysis of a ideal external magnetohydrodynamic (MHD) mode by solving the eigenvalue problem associated with the two-dimensional Newcomb equation, the inertia free linear ideal MHD equation. This eigenvalue problem can be expected to provide a powerful tool for not only a low-n external MHD mode but also a high-n mode, where n is a toroidal mode number. With this method, we analyze an effect of the aspect ratio on the stability of middle-n (1n10) external MHD modes in tokamaks; this gets attention for the design research of a high performance tokamak. As the result of this work, we study that external MHD modes become stable as the aspect ratio decreases, and also find that the stability of middle-n external modes becomes important because an effect of a conducting wall is enhanced by reducing the aspect ratio.

Journal Articles

Application of the two-dimensional Newcomb problem to compute the stability matrix of external MHD modes in a tokamak

Aiba, Nobuyuki*; Tokuda, Shinji; Ishizawa, Tomoko*; Okamoto, Masao*

Plasma Physics and Controlled Fusion, 46(11), p.1699 - 1721, 2004/11

https://doi.org/10.1088/0741-3335/46/11/003

Times Cited Count：3 Percentile：9.99(Physics, Fluids & Plasmas)

The theory of the Newcomb equation has been applied to low-n external modes in a tokamak and a method has been developed to compute the stability matrix that gives the change of plasma potential energy due to external modes in terms of the surface values of the perturbations. By using this method, the spectral properties of the ideal external modes has been elucidated, such as coupling between external modes and internal modes, and the difference of the stability properties between a normal shear tokamak and a reversed shear tokamak. These results will be also useful in the stability analysis of resistive wall modes.

Journal Articles

Theory of the Newcomb equation and applications to MHD stability analysis of a tokamak

Tokuda, Shinji; Aiba, Nobuyuki*

Journal of Plasma and Fusion Research SERIES, Vol.6, p.207 - 209, 2004/00

Recent progress in the theory of the Newcomb equation is reported. Emphasis is put on the analysis of external modes including peeling modes (high kink modes), where is the toroidal mode number. A theory for low external modes is developed so that it is also useful for the analysis of resistive wall modes.

Journal Articles

Inner layer problem for ideal MHD modes in a toroidal system

Tokuda, Shinji

Proceedings of 30th EPS Conference on Controlled Fusion and Plasma Physics (CD-ROM), 4 Pages, 2003/00

When we solve the eigenvalue problem associated with the two-dimensional Newcomb equation, we can identify the stability of a tokamak plasma against ideal MHD perturbations. The eigenvalue problem does not give the physical growth rate when the plasma is unstable. However, we can determine the growth rate by constructing a dispersion relation that gives the relation between the growth rate and the eigenvalue. It is expected that the dispersion relation provides an effective and fast method of stability analysis of MHD modes close to the marginal stability against ideal MHD perturbations, and the relation can be extended for non-ideal MHD modes close to the marginal stability.

Journal Articles

Singular point analysis

Tokuda, Shinji

Purazuma, Kaku Yugo Gakkai-Shi, 78(9), p.913 - 924, 2002/09

https://doi.org/10.1585/jspf.78.913

An introductory review is given on recent developments in the methods for stability analysis of a toroidally confined plasma. Emphasis is put on the perturbation analysis of a magnetohydrodynamic system that has the marginally stable state as a terminal point of continuous spectra. We address ourselves to the asymptotic matching method pertinent to such a problem. The Newcomb equation and inner-layer equations are essential ingredients in the methods and the numerical methods for solving them are discussed.

Journal Articles

Tokamak MHD stability; Newcomb equation and boundary layer equations

Tokuda, Shinji

Theory of Fusion Plasmas, p.87 - 102, 2002/00

We report on recent development of solution methods of the Newcomb equation and boundary layer equations, which play important roles in MHD stability analysis of a tokamak. Especially, the two-dimensional Newcomb equation is applied to external modes and the method is desctribed for computing the stability matrix of the external modes.

Journal Articles