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The theoretical foundation of 3-D Alfven resonances: Time-dependent solutions

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journal contribution
posted on 08.04.2020, 11:43 by T Elsden, AN Wright
We present results from a 3-D 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 (2016) and provides a theoretical basis for understanding 3-D Alfvén resonances. Wright and Elsden (2016) show that these are fundamentally different to resonances in 1-D and 2-D. We demonstrate the temporal behavior 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 3-D resonant sheet in the steady state. We show that the width of the 3-D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1-D theory. We further provide an analytical estimate for the resonance amplitude in 3-D, based upon extending 2-D theory.

Funding

Funding Information STFC. Grant Number: ST/N000609/1 Leverhulme Trust. Grant Number: RPG-2016-071

History

Citation

Elsden, T., and Wright, A. N. ( 2017), The theoretical foundation of 3‐D Alfvén resonances: Time‐dependent solutions, J. Geophys. Res. Space Physics, 122, 3247– 3261, doi:10.1002/2016JA023811.

Version

VoR (Version of Record)

Published in

JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS

Volume

122

Issue

3

Pagination

3247 - 3261 (15)

Publisher

AMER GEOPHYSICAL UNION

issn

2169-9380

eissn

2169-9402

Acceptance date

28/02/2017

Copyright date

2017

Available date

09/03/2017

Publisher version

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2016JA023811

Language

English