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dc.contributor.authorElsden, T.
dc.contributor.authorWright, A. N.
dc.identifier.citationElsden , T & Wright , A N 2017 , ' The theoretical foundation of 3-D Alfvén resonances : time-dependent solutions ' , Journal of Geophysical Research: Space Physics , vol. 122 , no. 3 , pp. 3247-3261 .
dc.identifier.otherPURE: 249253058
dc.identifier.otherPURE UUID: adcaccb6-98dd-42b7-887d-753a86817f72
dc.identifier.otherScopus: 85017342102
dc.identifier.otherORCID: /0000-0002-9877-1457/work/58055399
dc.identifier.otherORCID: /0000-0002-1910-2010/work/60196738
dc.identifier.otherWOS: 000399710900029
dc.descriptionBoth authors were funded in part by STFC (through Consolidated Grant ST/N000609/1) and The Leverhulme Trust (through Research Grant RPG-2016-071).en
dc.description.abstractWe 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 1D and 2D. 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.
dc.relation.ispartofJournal of Geophysical Research: Space Physicsen
dc.rights© 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:
dc.subjectULF wavesen
dc.subjectAlfvén wavesen
dc.subjectQA Mathematicsen
dc.subjectQB Astronomyen
dc.subjectQC Physicsen
dc.titleThe theoretical foundation of 3-D Alfvén resonances : time-dependent solutionsen
dc.typeJournal articleen
dc.contributor.sponsorScience & Technology Facilities Councilen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.description.statusPeer revieweden

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