Calculation of toroidal Alfv\'en eigenmode mode structure in general axisymmetric toroidal geometry

A workflow is developed based on the ideal MHD model to investigate the linear physics of various Alfv\'en eigenmodes in general axisymmetric toroidal geometry, by solving the coupled shear Alfv\'en wave (SAW) and ion sound wave (ISW) equations in ballooning space. The model equations are solved by the FALCON code in the singular layer, and the corresponding solutions are then taken as the boundary conditions for calculating parallel mode structures in the whole ballooning space. As an application of the code, the frequencies and mode structures of toroidal Alfv\'en eigenmode (TAE) are calculated in the reference equilibria of the Divertor Tokamak Test facility (DTT) with positive and negative triangularities, respectively. By properly handling the boundary conditions, we demonstrate finite TAE damping due to coupling with the local acoustic continuum, and find that the damping rate is small for typical plasma parameters.