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10 - Thin Flux Tubes: The Sausage Mode

Published online by Cambridge University Press:  15 July 2019

Bernard Roberts
Bernard Roberts
Affiliation:
University of St Andrews, Scotland
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Summary

The thin tube theory for a sausage wave is developed from first principles and shown to lead to the Klein-Gordon equation. The equations that hold when gravity is negligible are explored and the dispersion relation obtained and compared with earlier results. The effects of stratification are explored in detail, with contributing terms to the cutoff frequency explored for various cases ranging from a rigid and straight tube to a diverging elastic tube of the shape expected for a thin flux tube. The cutoff frequency is illustrated for a range of conditions likely to arise in the solar atmosphere. The role of cutoff for coronal loops is explored.

Keywords

thin tubessausage modethin tube equationsKlein-Gordon equationcutoffdispersion relations
Type
Chapter
Information
MHD Waves in the Solar Atmosphere , pp. 281 - 310
Publisher: Cambridge University Press
Print publication year: 2019

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