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

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McLaughlin, J. A.

Hood, A. W.

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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. The nature of fast and slow magnetoacoustic waves is investigated in a
finite $\beta$ plasma in the neighbourhood of a two-dimensional null point. 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. 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 \emph{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 Alfv\'en speed) and the contribution
from the non-zero sound speed. These experiments illustrate the importance of
the magnetic topology and of the location of the $\beta \approx 1$ layer in the
system.

Comment: 14 pages, 12 figures, 1 table

Comment: 14 pages, 12 figures, 1 table

##### Keywords

Astrophysics