# On the Thin Magnetic Flux Tube Approximation

- C. T. Russell,
- E. R. Priest and
- L. C. Lee

Published Online: 21 MAR 2013

DOI: 10.1029/GM058p0141

Copyright 1990 by the American Geophysical Union.

Book Title

## Physics of Magnetic Flux Ropes

Additional Information

#### How to Cite

Ferriz-Mas, A. and Schüssler, M. (1990) On the Thin Magnetic Flux Tube Approximation, in Physics of Magnetic Flux Ropes (eds C. T. Russell, E. R. Priest and L. C. Lee), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM058p0141

#### Publication History

- Published Online: 21 MAR 2013
- Published Print: 1 JAN 1990

#### Book Series:

#### ISBN Information

Print ISBN: 9780875900261

Online ISBN: 9781118663868

- Summary
- Chapter
- References

### Keywords:

- Solar photosphere;
- Magnetic flux;
- Astrophysics

### Summary

A large number of theoretical studies on the structure and dynamics of magnetic flux tubes make use of the “thin flux tube approximation”, based on an expansion approach about the axis of the tube, which permits the reduction of the full magnetohydrodynamic (MHD) problem to a mathematically more tractable set of equations. In this paper the assumptions underlying this approximation are analyzed.

For a vertical, axisymmetric magnetic flux tube the pertaining physical quantities are expanded in the radial coordinate about the axis of symmetry and the power series are introduced into the MHD equations written in cylindrical coordinates. The assumption of axial symmetry significantly reduces the number of unknowns and equations. The closure of the system is provided by appropriate boundary conditions. By retaining only the zeroth- and first-order terms, the equations of the conventional thin flux tube approximation (Defouw, 1976; Roberts and Webb, 1978) are obtained. To include twisted magnetic fields and azimuthal flows, the expansion has to be extended at least to second order. As an application, the axisymmetric wave modes of a uniform magnetic cylinder are studied. The above formalism is also applied to derive the magnetostatic equations governing the equilibrium structure of an axisymmetric, vertical flux tube embedded in a stratified atmosphere. Key words: magnetic flux tubes - magnetohydrodynamics - solar and stellar magnetic fields