2024-10-13T19:10:06Z
https://ir.soken.ac.jp/oai
oai:ir.soken.ac.jp:00000516
2023-06-20T16:12:55Z
2:427:12
Theory and Computational Method for the Stability Analysis of External MHD Modes in Toroidal Plasmas
Theory and Computational Method for the Stability Analysis of External MHD Modes in Toroidal Plasmas
相羽, 信行
アイバ, ノブユキ
AIBA, Nobuyuki
The theory and analytical model for the stability analysis of magnetohydrodynamic (MHD) modes based on the two-dimensional Newcomb equation are extended for the analysis of external MHD modes both with low-n and with high-n toroidal mode numbers. In this model, since the appropriate weight function and the boundary conditions at rational surfaces are introduced to solve the eigenvalue problem associated with the Newcomb equation, the spectrum of this eigenvalue problem contains only discrete eigenvalues. This feature enables us to reveal explicitly whether plasma is stable or unstable.<br /> In this dissertation, the analytical model is first applied to the development of a new method that analyzes the stability of a low-n external MHD mode in a matrix form, and hence this new method is called the stability matrix method. A numerical code (MARG2D-SM) is developed according to the stability matrix method, and the validity of the code is confirmed by several benchmark tests. The code clarifies the spectral structure of n=1 ideal external kink modes, which are stable or unstable. The spectral gaps induced by the poloidal coupling are also investigated. The stability matrix method reveals the effect of stable ideal internal modes (fixed boundary modes) on the stability of ideal external modes (free boundary modes). With this effect, the mode structure of an ideal external mode changes from a surface mode structure to a global mode structure as a beta value increases, and an external mode destabilizes when an internal mode approaches to their marginal stability; a beta value is a ratio of the plasma pressure to the magnetic pressure. This effect explains how a safety factor profile in the core region of high beta tokamak plasma affects the stability of an ideal external mode. <br /> The model based on the Newcomb equation has an advantage that the marginal stability can be identified only with a short computation time. Such an advantage is demonstrated to be powerful in the study on the aspect ratio dependence of the n=1 ideal external MHD mode stability.<br /> For high-n external MHD modes, the analytical method based on the Newcomb equation is extended in the vacuum region; the vacuum energy integral is calculated by using the vector potential method. The MARG2D code, which solves numerically the eigenvalue problem associated with the two-dimensional Newcomb equation, is adapted to this new model, and the validity of this extension is confirmed by benchmark tests. This extended MARG2D code is developed as a parallel computing code, and enables the fast stability analysis of high-n modes like a peeling mode, an edge ballooning mode, and a couple of them called a peeling-ballooning mode.
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総研大甲第842号
eng
thesis
https://ir.soken.ac.jp/records/516
博士（理学）
2005-03-24
総合研究大学院大学
https://ir.soken.ac.jp/record/516/files/甲842_要旨.pdf
application/pdf
232.7 kB
2016-02-17
https://ir.soken.ac.jp/record/516/files/甲842_本文.pdf
application/pdf
4.9 MB
2016-02-17