Incompressible MHD modes in the thin magnetically twisted flux tube

TL;DR

This study analytically investigates incompressible MHD wave modes in twisted magnetic flux tubes, revealing that twist influences fluting modes and introduces a frequency cutoff, while kink modes remain unaffected in the long wavelength limit.

Contribution

It provides an analytical derivation of the dispersion relation for incompressible MHD modes in twisted flux tubes, highlighting the effects of magnetic twist on different wave modes.

Findings

Kink mode frequency and velocity are unaffected by twist in long wavelengths.

Fluting modes are sensitive to magnetic twist and have a low frequency cutoff.

Magnetic twist influences wave propagation depending on wave direction and twist sign.

Abstract

Context. Observations have shown that twisted magnetic fields naturally occur, and indeed are omnipresent in the Sun's atmosphere. It is therefore of great theoretical interest in solar atmospheric waves research to investigate the types of magnetohydrodynamic (MHD) wave modes that can propagate along twisted magnetic flux tubes. Aims. Within the framework of ideal MHD, the main aim of this work is to investigate small amplitude incompressible wave modes of twisted magnetic flux tubes with m more or equal 1. The axial magnetic field strength inside and outside the tube will be allowed to vary, to ensure the results will not be restricted to only cold plasma equilibria conditions. Methods. The dispersion equation for these incompressible linear MHD wave modes was derived analytically by implementing the long wavelength approximation. Results. It is shown, in the long wavelength limit, that both the frequency and radial velocity profile of the m = 1 kink mode are completely unaffected by the choice of internal background magnetic twist. However, fluting modes with m more or equal 2 are sensitive to the particular radial profile of magnetic twist chosen. Furthermore, due to background twist, a low frequency cut-off is introduced for fluting modes that is not present for kink modes. From an observational point of view, although magnetic twist does not affect the propagation of long wavelength kink modes, for fluting modes it will either work for or against the propagation, depending on the direction of wave travel relative to the sign of the background twist.