Research Note

Tube waves: Exact and approximate

Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany

Corresponding author: stix@kis.uni-freiburg.de

Received: 8 December 2003
Accepted: 15 December 2003

Abstract

This note deals with magnetohydrodynamic body waves in a magnetic cylinder. It is shown that the solution obtained by the thin-tube expansion is, term by term, identical to the Taylor expansion of the exact solution. Each level of approximation adds a pair of modes, a slow and a fast one, and corrects the frequencies and eigenfunctions of the previous approximation. All eigenfrequencies, approximate and exact, can be read off from a single graph. All slow modes have phase velocities between the tube speed c_T and , all fast modes have phase velocities above .