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Eigenvalue Method for the Outer-Region Matching Data in Resistive MHD Stability Analysis

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  • Eigenvalue Method for the Outer-Region

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A new method is presented to compute the outer-region matching data which play a crucial role in resistive MHD stability analysis in a tokamak plasma. The method also provides an alternative method for the ideal MHD stability analysis which can identify the marginally stable state. In the present method, an eigenvalue problem is posed for the Newcomb equation, one dimensional marginally stable ideal MHD equation. And then, the finite energy part of the solution for the Newcomb equation is divided into two components: the eigenfunction whose eigenvalue is the nearest to zero and the remainder which is orthogonal to the eigenfunction and satisfies a singular equation. An integral relation by Pletzer-Dewar [J. Plasma Phys. 45, 427 (1991)] is employed to abstract the matching data from the finite energy part of the solution. Numerical experiments are performed to demonstrate effectiveness of the new method for a model equation with analytical solutions and for the Newcomb equation in the m = 1 mode theory (m: poloidal mode number).


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