A numerical approach to the calculation of the Alfven continuum in the presence of magnetic islands

A numerical approach is devised to calculate the shear Alfven continuum inside and outside magnetic islands in cylindrical and stellarator plasmas. Equations for an appropriate set of coordinates and the arising equations for the continuum are derived and implemented in the CONTI code. An experiment-oriented representation of the results is chosen to allow a radial localization of the modes and a comparison of different magnetic configurations. Comparison is made with results of earlier analytic work for validation. Agreement is good but more details of the spectrum, such as the generation of island induced gaps inside and outside the separatrix, are found. While the code is easily usable and can be applied to any magnetic equilibrium accessible with VMEC, the calculations are plagued with convergence issues close to the separatrix. A calculation for a realistic W7-X equilibrium with islands is done where the island width is estimated with the HINT code. (C) 2022 Author(s)