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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.

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