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 beta waves across the beta approximate to 1 layer. The work here contributes specifically to what happens when a low beta fast wave crosses the beta approximate to 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-Wendro. 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 approximate to 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 Alfven 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 approximate to 1 layer in the system.