The theoretical foundation of 3D Alfvén resonances : time dependent solutions
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We present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden , and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden  show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.
Elsden , T & Wright , A N 2017 , ' The theoretical foundation of 3D Alfvén resonances : time dependent solutions ' Journal of Geophysical Research: Space Physics , vol Early View . DOI: 10.1002/2016JA023811
Journal of Geophysical Research: Space Physics
© 2017 American Geophysical Union. All Rights Reserved. This work is made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at: https://dx.doi.org/10.1002/2016JA023811
Both authors were funded in part by STFC (through Consolidated Grant ST/N000609/1) and The Leverhulme Trust (through Research Grant RPG-2016-071).
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