On the dynamics of vortex modes within magnetic islands

TL;DR

This paper investigates the oscillatory vortex modes within magnetic islands, linking their dynamics to the Geodesic Acoustic Mode (GAM) through derivation and analysis of equations in a modified MHD geometry.

Contribution

It derives a GAM equation in a magnetic island geometry and analyzes the dynamics of vortex modes using numerical eigenvalues and eigenfunctions.

Findings

Vortex modes are related to GAM oscillations.

Eigenvalues and eigenfunctions characterize vortex dynamics.

Simulations confirm the GAM connection to vortex oscillations.

Abstract

Recent work investigating the interaction of magnetic islands with micro-turbulence has uncovered the striking observation of large scale vortex modes forming within the island structure [W.A. Hornsby {\it et al.}, Phys. Plasmas {\bf 17} 092301 (2010)]. These electrostatic vortices are found to be the size of the island and are oscillatory. It is this oscillatory behaviour and the presence of turbulence that leads us to believe that the dynamics are related to the Geodesic Acoustic Mode (GAM), and it is this link that is investigated in this paper. Here we derive an equation for the GAM in the MHD limit, in the presence of a magnetic island modified three-dimensional axisymmetric geometry. The eigenvalues and eigenfunctions are calculated numerically and then utilised to analyse the dynamics of oscillatory large-scale electrostatic potential structures seen in both linear and non-linear gyro-kinetic simulations.