Nonlinear steepening of a fast magnetoacoustic wave in the vicinity of a coronal magnetic null point

Abstract: The interaction of a fast magnetoacoustic wave with a magnetic null point is studied in the context of the sympathetic flare phenomenon. Attention is paid to steepening the wave caused by the finite-amplitude effects in a non-uniform plasma environment. The null point is modelled by a potential magnetic configuration without a guiding field. The equilibrium plasma density and temperature are taken to be constant. The fast wave is excited by an impulsive point source outside the distance at which the local Alfvén and sound speeds are equal to each other. The incoming fast wave approaches the null point along the bisector of the magnetic configuration, i.e., across the local field. The fast-speed non-uniformity around the null point causes the refraction of the incident fast wave. However, the segment of the incoming wave, which approaches the null point is locally plane. The decrease in the fast speed towards the null point amplifies the nonlinear deformation of the incoming wave. Hence, the fast wave can become subject to nonlinear dissipation at a distance from the null point and not reach it.