MHD mode coupling in the neighbourhood of a 2D null point

Free access article

Issue		A&A Volume 459, Number 2, November IV 2006


Page(s)		641 - 649
Section		The Sun
DOI		http://dx.doi.org/10.1051/0004-6361:20065558

A&A 459, 641-649 (2006)
DOI: 10.1051/0004-6361:20065558

MHD mode coupling in the neighbourhood of a 2D null point

J. A. McLaughlin and A. W. Hood

School of Mathematics and Statistics, University of St Andrews, KY16 9SS, UK
e-mail: james@mcs.st-and.ac.uk

(Received 5 May 2006 / Accepted 4 August 2006)

Abstract
Context.At this time there does not exist a robust set of rules connecting low and high $\beta$ waves across the $\beta \approx 1$ layer. The work here contributes specifically to what happens when a low $\beta$ fast wave crosses the $\beta \approx 1$ layer and transforms into high $\beta$ fast and slow waves.
Aims.The nature of fast and slow magnetoacoustic waves is investigated in a finite $\beta$ plasma in the neighbourhood of a two-dimensional null point.
Methods.The linearised equations are solved in both polar and cartesian forms with a two-step Lax-Wendroff numerical scheme. Analytical work (e.g. small $\beta$ expansion and WKB approximation) also complement the work.
Results.It is found that when a finite gas pressure is included in magnetic equilibrium containing an X-type null point, a fast wave is attracted towards the null by a refraction effect and that a slow wave is generated as the wave crosses the $\beta \approx 1$ layer. Current accumulation occurs close to the null and along nearby separatrices. The fast wave can now pass through the origin due to the non-zero sound speed, an effect not previously seen in related papers but clear seen for larger values of $\beta$ . Some of the energy can now leave the region of the null point and there is again generation of a slow wave component (we find that the fraction of the incident wave converted to a slow wave is proportional to $\beta$ ). We conclude that there are two competing phenomena; the refraction effect (due to the variable Alfvén speed) and the contribution from the non-zero sound speed.
Conclusions.These experiments illustrate the importance of the magnetic topology and of the location of the $\beta \approx 1$ layer in the system.

Key words: magnetohydrodynamics (MHD) -- waves -- Sun: corona -- Sun: magnetic fields -- Sun: oscillations

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