Behaviour of Magnetoacoustic Waves in the Neighbourhood of a Two-Dimensional Null Point: Initially Cylindrically Symmetric Perturbations

Journal of astrophysics and astronomy

J. A. McLaughlin1¹ 

[1] Department of Mathematics and Information Sciences, Northumbria University, Newcastle-upon-Tyne, NE1 8ST, United Kingdom.$$

关键词: Magnetohydrodynamics (MHD);    waves;    magnetic fields;    Sun: atmosphere;    corona.;   

DOI  :  

学科分类：天文学(综合)

来源: Indian Academy of Sciences

【 摘 要 】

The propagation of magnetoacoustic waves in the neighbourhood of a 2D null point is investigated for both $eta =$ 0 and $eta$ $eq$ 0 plasmas. Previous work has shown that the Alfvén speed, here $u_A propto r$, plays a vital role in such systems and so a natural choice is to switch to polar coordinates. For $eta =$ 0 plasma, we derive an analytical solution for the behaviour of the fast magnetoacoustic wave in terms of the Klein–Gordone equation. We also solve the system with a semi-analytical WKB approximation which shows that the $eta =$ 0 wave focuses on the null and contracts around it but, due to exponential decay, never reaches the null in a finite time. For the $eta$ $eq$ 0 plasma, we solve the system numerically and find the behaviour to be similar to that of the $eta =$ 0 system at large radii, but completely different close to the null. We show that for an initially cylindrically-symmetric fast magnetoacoustic wave perturbation, there is a decrease in wave speed along the separatrices and so the perturbation starts to take on a quasi-diamond shape; with the corners located along the separatrices. This is due to the growth in pressure gradients that reach a maximum along the separatrices, which in turn reduces the acceleration of the fast wave along the separatrices leading to a deformation of the wave morphology.

【 授权许可】

Unknown