Rapid Reconnection and Field Line Topology
Rapid reconnection of magnetic fields arises where the magnetic stresses push the plasma and field so as to increase the field gradient without limit. The intent of the present writing is to show the larger topological context in which this commonly occurs. Consider an interlaced field line topology as commonly occurs in the bipolar magnetic regions on the Sun. A simple model is constructed starting with a strong uniform magnetic field B0 in the z-direction through an infinitely conducting fluid from the end plate z = 0 to z = L with the field lines tied at both end plates. Field line interlacing is introduced by smooth continuous random turbulent mixing of the footpoints at the end plates. This configuration is well suited to be modeled with the reduced magnetohydrodynamic (MHD) equations, with the equilibria given by the solutions of the 2D vorticity equation in this case. The set of continuous solutions to the “vorticity” equation have greatly restricted topologies, so almost all interlaced field topologies do not have continuous solutions. That infinite set represents the “weak” solutions of the vorticity equation, wherein there are surfaces of tangential discontinuity (current sheets) in the field dividing regions of smooth continuous field. It follows then that current sheets are to be found throughout interlaced fields, providing potential sites for rapid reconnection. That is to say, rapid reconnection and nanoflaring are expected throughout the bipolar magnetic fields in the solar corona, providing substantial heating to the ambient gas. Numerical simulations provide a direct illustration of the process, showing that current sheets thin on fast ideal Alfvén timescales down to the smallest numerically resolved scales. The asymmetric structure of the equilibria and the interlacing threshold for the onset of singularities are discussed. Current sheet formation and dynamics are further analyzed with dissipative and ideal numerical simulations.
KeywordsCoronal heating Field line topologies Flares Interlaced field lines Magnetic equilibrium equation Numerical simulations Rapid reconnection Rate of reconnection Singular flux surfaces
It is a pleasure to thank the organizers of the “Parker Workshop on Magnetic Reconnection” for their work and invitations. This research has been supported in part by NASA through a subcontract with the Jet Propulsion Laboratory, California Institute of Technology, and NASA LWS grants number NNX15AB89G and NNX15AB88G. Computational resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center.
- A. Bhattacharjee, Y.-M. Huang, H. Yang, B. Rogers, Phys. Fluids 16, 112102 (2009)Google Scholar
- S.V. Bulanov, S.I. Syrovatskii, J. Sakai, J. Exp. Theor. Phys. Lett. 28, 177 (1978)Google Scholar
- R. Courant, D. Hilbert, Methods of Mathematical Physics, vol. 2 (Interscience, New York, 1980), pp. 635–636Google Scholar
- U. Frisch, Turbulence. The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995)Google Scholar
- N.F. Loureiro, A.A. Schekochihin, S.C. Cowley, Phys. Fluids 14, 100703 (2007)Google Scholar
- E.N. Parker, Cosmical Magnetic Fields: Their Origin and Their Activity (Oxford University Press, New York, 1979)Google Scholar
- E.N. Parker, Spontaneous Current Sheets in Magnetic Fields (Oxford University Press, New York, 1994)Google Scholar
- E.N. Parker, Conversations on Electric and Magnetic Fields in the Cosmos (Princeton University Press, Princeton, 2007)Google Scholar
- E.N. Parker, Field Line Topology and Rapid Reconnection. Astrophysics and Space Science Proceedings, vol. 33 (Springer Berlin Heidelberg, 2012a), pp. 3–9Google Scholar
- P.A. Sweet, in Electromagnetic Phenomena in Cosmical Physics, ed. by B. Lehnert. IAU Symposium, vol. 6 (1958a), p. 123Google Scholar
- T. Tao (2015). arXiv:1402.0290 [math.AP]Google Scholar