A singular finite element technique for calculating continuum damping of Alfv\'en eigenmodes
Abstract
Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics (MHD) provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfv\'en waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency are calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfv\'en eigenmode (TAE) in a large aspect ratio circular tokamak and are shown to agree closely with a complex contour technique.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.