The Power Output of Spine and Fan Magnetic Reconnection Solutions

Abstract

The ability of three-dimensional magnetic "" spine ÏÏ and "" fan ÏÏ reconnection solutions to provide Ñarelike energy release is discussed. It is pointed out, on the basis of exact analytic solutions, that fast dissipation is possible only if the hydromagnetic pressure in the reconnection region becomes unbounded in the limit of small plasma resistivities. The implication is that some "" saturation ÏÏ of the power output is inevitable for realistic coronal plasmas. Estimates of the saturated power, based on limiting the Ñux pileup in the Ðeld, suggest that the geometry of the spine reconnection mechanism precludes signiÐcant Ñare energy release. However, the current sheet structures involved in fan reconnection seem able to release sufficient magnetic energy fast enough to account for modest Ñares, even under the conservative assumption of classical plasma resistivities.

Dynamic magnetic reconnection in three space dimensions: Fan current solutions

“…The fact that the pressure must be bounded in any realistic plasma shows that the flux pile-up solutions eventually saturate ͑at some sufficiently small resistivity͒ in any viable model of the reconnection process. 9 This point is discussed further in Sec. VI.…”

“…More physically, Craig et al 9 working in the context of steady-state, solar flare reconnection, consider the ''saturated energy dissipation rate'' obtained by bounding the plasma pressure to levels available in the solar atmosphere. Realistic pressures require that the amplitude of the disturbance field washed into the reconnection region be suitably limited.…”

“…Although the spine formulation leads to richer current structures, the magnetic energy in the disturbance field is typically many orders of magnitude weaker than the fan model. 9 A brief discussion of spine current reconnection is given in Appendix B.…”

“…We dismissed this solution earlier on the grounds that the scalings were bound to be unfavorable given the steady-state analysis of Craig et al 9 Since the spine current solution is close to the threshold of being able to provide sufficient energy to describe a small flare ͑when we take into account the possible local enhancement of ͒, this form of reconnection should not be completely ignored.…”

“…The spine model provides extremely rich, tubular current structures, but it seems doubtful whether these can contain sufficient magnetic energy for many applications-for instance, for explaining the huge, explosive release of the solar flare. 9 The purpose of the present paper is to explore timedependent, fan reconnection models. In particular, we are interested in the question of whether fan solutions can produce fast ohmic dissipation, that is, whether they can release magnetic energy at a rate independent of the plasma resistivity .…”