Wave propagation in steady stratified one-dimensional cylindrical waveguides

Solar Physics & Space Plasma Research Center, SPRC, Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH Sheffield, UK e-mail: [robertus;j.hargreaves]@sheffield.ac.uk

Received: 6 November 2007
Accepted: 13 February 2008

Abstract

Aims. This paper studies the propagation of longitudinal magnetic tube waves in a stratified isothermal flux tube with an internal equilibrium background flow.

Methods. The governing differential equation is solved by means of Laplace transforms and temporal and spatial solutions are developed, with boundary conditions given by various footpoint drivers, namely a monochromatic source, a delta function pulse, and a sinusoidal pulse. The effect of the background flow is to introduce an increase in amplitude of the wave perturbation and changes in phase shift when compared with the corresponding static case.

Results. Results are presented and applied to conditions in the solar atmosphere. When the source is driven continuously, the forced atmospheric oscillations are shown to have large percentage differences when compared to the corresponding static case. For the free atmospheric oscillations, percentage increases in amplitude merely a few percent are found and vary greatly in height but are practically unaltered in time. Phase shifts up to a radian are introduced and weakly depend on both height and time.

Conclusions. The results presented in this paper may have interesting observational consequences, especially when using the tools of magnetic seismology of solar atmospheric wave guides (i.e. flux tubes from photosphere to corona) in light of the present and near-future high spatial and temporal resolution space missions, e.g. Hinode, Solar Dynamics Observatory, or Solar Orbiter.