Numerical simulation of fundamental trapped sausage modes

TL;DR

This study uses high-resolution numerical simulations to analyze the behavior, coupling, and damping mechanisms of fundamental trapped sausage modes in magnetic loops, revealing complex interactions and energy transfer processes.

Contribution

It provides the first detailed numerical analysis of sausage mode coupling, damping, and leaky regimes in dense, thick magnetic loops using advanced shock-capturing methods.

Findings

Pure sausage modes are coupled with slow modes due to non-linearities.

Resonant coupling leads to non-dissipative damping of sausage modes.

Discontinuities induce a leaky regime with external Alfvén wave energy transfer.

Abstract

Context: We integrate the 2D MHD ideal equations of a straight slab to simulate observational results associated with fundamental sausage trapped modes. Aims: Starting from a non-equilibrium state with a dense chromospheric layer, we analyse the evolution of the internal plasma dynamics of magnetic loops, subject to line-tying boundary conditions, and with the coronal parameters described in Asai et al. (2001) and Melnikov et al. (2002) to investigate the onset and damping of sausage modes. Methods: To integrate the equations we used a high resolution shock-capturing (HRSC) method specially designed to deal appropriately with flow discontinuities. Results: Due to non-linearities and inhomogeneities, pure modes are difficult to sustain and always occur coupled among them so as to satisfy, e.g., the line-tying constraint. We found that, in one case, the resonant coupling of the sausage fundamental mode with a slow one results in a non-dissipative damping of the former. Conclusions: In scenarios of thick and dense loops, where the analytical theory predicts the existence of fundamental trapped sausage modes, the coupling of fast and slow quasi-periodic modes -with a node at the center of the longitudinal speed- occur contributing to the damping of the fast mode. If a discontinuity in the total pressure between the loop and the corona is assumed, a fundamental fast sausage transitory leaky regime is spontaneously produced and an external compressional Alfv\'en wave takes away the magnetic energy.