# Quasi-Potential-Singular-Equilibria and Evolution of the Coronal Magnetic Field Due to Photospheric Boundary Motions

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

Published Online: 21 MAR 2013

DOI: 10.1029/GM058p0245

Copyright 1990 by the American Geophysical Union.

Book Title

## Physics of Magnetic Flux Ropes

Additional Information

#### How to Cite

Amari, T. and Aly, J. J. (1990) Quasi-Potential-Singular-Equilibria and Evolution of the Coronal Magnetic Field Due to Photospheric Boundary Motions, 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/GM058p0245

#### 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

We consider the structure of a particular class of 2D-x-invariant magnetostatic equilibria (in which the magnetic field is potential everywhere in some domain of space but on some singular surfaces-current sheets-carrying a non-zero x-current) for which only particular examples were selected in all the previous models. We present some new general properties of configurations of this type. We prove in particular that the general condition of equilibrium at the extremities of the Current Sheet which has never been analysed before implies a new constraint on the magnetic field. We also present a variational principle and results of existence and stability of such singular equilibria when they arise in a physical context. We consider in detail the situation in which such singular states are obtained asymptotically by an arcade like x-invariant force free field in {z > 0} when indefinitely sheared. We present a method which allows us to compute analytically these asymptotic states as the solutions of well set boundary value problems even in the slightly non-symmetric case for which no analytical model has ever been proposed before.