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

Context: At this time there does not exist a robust set of rules connecting low and high β waves across the β ≈ 1 layer. The work here contributes specifically to what happens when a low β fast wave crosses the β ≈ 1 layer and transforms into high β fast and slow waves. Aims: The nature of fast and slow magnetoacoustic waves is investigated in a finite β 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 β 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 β ≈ 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 β. 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 β). 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 β ≈ 1 layer in the system.