## Current sheets in two-dimensional potential magnetic fields## III. Formation in complex topology configurations and application to coronal heating
^{1} CEA/DSM/DAPNIA, Service d'Astrophysique (CNRS/URA 2052),
C.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France^{2} Observatoire de Paris, DASOP (CNRS/URA 326), F-92195
Meudon Principal Cedex, France
We study the spontaneous formation of a We compute analytically and its free-energy
contents as functionals of
(this boundary value depending on and
), and also, when there is a CS, of the unknown
heights and of its
bottom and top, respectively. We derive equations satisfied by the
latter quantities, and use them to show that: (i) When the initial
field is of the U- or I-type, a CS - and a vertical one indeed - is
actually present at time As an application, we consider a plasma heating process in which a field evolving through a sequence of singular equilibria as described above, relaxes at each time () to a new potential equilibrium, the vertical CS being destroyed by some reconnection process. We present an estimate of the resulting heating rate, which is found to depend on the ratio (assumed to be ) of a given phenomenological dissipation time to the ideal evolution time of the system. The relevance of this process for heating a stellar corona is briefly discussed.
## Contents- 1. Introduction
- 2. Quadrupolar potential magnetic fields
- 3. Evolution of a quadrupolar potential field
- 4. Magnetic evolution under the frozen-in constraint
- 5. Computation of a QPSE
- 6. Formation of a CS when is a X-field
- 7. Formation of a CS when is either a U- or a I-field
- 8. Free magnetic energy
- 9. Plasma heating by a relaxation mechanism
- 10. Conclusions
- Acknowledgements
- Appendix
- Appendix A: existence of a neutral point of on the z-axis
- A.1. Two elementary lemmas
- A.2. Existence of a neutral point of on the
*z*-axis - A.3. An example of quadrupolar potential configuration
- A.4. A second example of quadrupolar potential configuration
- Appendix B: computation of the field of a QPSE on the
*y*- and*z*-axis - Appendix C: conditions of appearance of a vertical CS
- Appendix D: reduction formulas for , and
*I* - Appendix E: computation of a QPSE when
- References
© European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |