3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory

McLaughlin, James, Ferguson, J. S. L. and Hood, Alan William (2008) 3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory. Solar Physics, 251 (1-2). pp. 563-587. ISSN 0038-0938

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Official URL: http://dx.doi.org/10.1007/s11207-007-9107-2

Abstract

This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[ x, ɛ y,-( ɛ+1) z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ɛ. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ɛ determines where the wave accumulation will occur: fan plane ( ɛ=1), along the x-axis (0< ɛ<1) or along the y-axis ( ɛ>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.

Item Type: Article
Subjects: F300 Physics
F500 Astronomy
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Related URLs:
Depositing User: James McLaughlin
Date Deposited: 05 Apr 2012 08:11
Last Modified: 10 Aug 2015 11:29
URI: http://nrl.northumbria.ac.uk/id/eprint/6025

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