Wright_Elsden_2016_ApJ.pdf (1.62 MB)
THE THEORETICAL FOUNDATION OF 3D ALFVEN RESONANCES: NORMAL MODES
journal contribution
posted on 2020-04-08, 11:46 authored by Andrew N Wright, Thomas ElsdenWe consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (μexp(-iwt)) are presented, along with a theoretical framework to interpret them. The solutions we find are fundamentally different from those in 1D and 2D. In 3D there exists an infinite number of possible resonant solutions within a Resonant Zone, and we show how boundary conditions and locally 2D regions can favor particular solutions. A unique feature of the resonance in 3D is switching between different permissible solutions when the boundary of the Resonant Zone is encountered. The theoretical foundation that we develop relies upon recognizing that, in 3D, the orientation of the resonant surface will not align in a simple fashion with an equilibrium coordinate. We present a method for generating the Alfvén wave natural frequencies for an arbitrarily oriented Alfvén wave, which requires a careful treatment of scale factors describing the background magnetic field geometry.
Funding
Both authors were funded in part by STFC (through Consolidated Grant ST/N000609/1) and The Leverhulme Trust (through Research Grant RPG-2016-071).
History
Citation
Andrew N. Wright and Thomas Elsden 2016 ApJ 833 230Version
- VoR (Version of Record)
Published in
ASTROPHYSICAL JOURNALVolume
833Issue
2Pagination
(10)Publisher
IOP PUBLISHING LTDissn
0004-637Xeissn
1538-4357Acceptance date
2016-11-17Copyright date
2016Available date
2016-12-20Publisher DOI
Publisher version
https://iopscience.iop.org/article/10.3847/1538-4357/833/2/230Language
EnglishUsage metrics
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