Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

In an ideal magnetohydrodynamic (MHD) plasma, shear Alfven eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfven continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfven eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite eleme...