The theoretical foundation of 3-D Alfvén resonances: time-dependent solutions

Elsden, T. and Wright, A. N. (2017) The theoretical foundation of 3-D Alfvén resonances: time-dependent solutions. Journal of Geophysical Research: Space Physics, 122(3), pp. 3247-3261. (doi: 10.1002/2016JA023811)

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Abstract

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 ( urn:x-wiley:jgra:media:jgra53379:jgra53379-math-0001) 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.

Item Type:Articles
Additional Information:Both authors were funded in partby STFC (through consolidatedgrant ST/N000609/1) and theLeverhulme Trust (through researchgrant RPG-2016-071).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Elsden, Dr Thomas
Authors: Elsden, T., and Wright, A. N.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Geophysical Research: Space Physics
Publisher:Wiley
ISSN:2169-9402
ISSN (Online):2169-9402
Published Online:09 March 2017

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