Nonlinear Interaction of a 3D Kinetic Alfvén Wave with a Null Point and Turbulence Generation in the Solar Corona

Abstract

In the present paper, we have studied nonlinear kinetic Alfvén waves (KAWs) in the vicinity of a null point. We have considered the nonlinearity due to ponderomotive effects associated with KAWs in the solar corona. A 3D model equation representing the dynamics of KAWs is developed in this null point scenario. Using numerical methods, we have solved the model equation for solar coronal parameters. The pseudospectral method and the finite difference method have been applied to tackle spatial integration and temporal evaluation, respectively. The outcome of the simulation demonstrates the formation of localized structures. With the evolution of time, these localized structures become more chaotic. Chaotic (turbulent) structures can efficiently transfer energy. The power spectrum of these turbulent structures shows the Kolmogorov spectral index of nearly $-5/3$ in the inertial range followed by a steeper spectrum of nearly −3.3 (in the range of −2 to −4). These structures also lead to the generation of a current sheet. To understand the physics of our model, we have also done a semi-analytical study for our model equation. Semi-analytical calculations reveal that the current sheet structures have scale sizes of the order of the ion gyro-radius. The relevance of this investigation to the current observations by Parker Solar Probe has also been discussed.