Theoretical foundation of 3D Alfvén resonances : normal modes
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We consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (∝ exp(−iωt)) 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.
Wright , A N & Elsden , T W 2016 , ' Theoretical foundation of 3D Alfvén resonances : normal modes ' , Astrophysical Journal , vol. 833 , no. 2 , 230 , pp. 1-10 . https://doi.org/10.3847/1538-4357/833/2/230
© 2016, American Astronomical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at http://dx.doi.org/10.3847/1538-4357/833/2/230