The power output of spine and fan magnetic reconnection solutions

The ability of three-dimensional magnetic “spine” and “fan” reconnection solutions to provide flarelike 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” of the power output is inevitable for realistic coronal plasmas. Estimates of the saturated power, based on limiting the flux pileup in the field, suggest that the geometry of the spine reconnection mechanism precludes significant flare energy release. However, the current sheet structures involved in fan reconnection seem able to release sufficient magnetic energy fast enough to account for modest flares, even under the conservative assumption of classical plasma resistivities

Magnetic reconnection solutions in the presence of multiple nulls

It is known that exact analytic solutions can be constructed for incompressible magnetic reconnection in three space dimensions. In the case of an isolated X-point null, there are two types of reconnection solutions, namely, “spine” and “fan” models, which depend on the form of the X-point disturbance. However, such models cannot describe multiple null “separator” reconnection, for which there is independent observational evidence. Here we show that the spine formalism naturally extends to the case of multiple null fields. Solutions showing the characteristics of fan, spine, and separator are described, and a discussion is given of their energy dissipation properties. We demonstrate a family of multiple null, fast reconnection solutions and point out that the classical Sweet-Parker dissipation rate is the slowest that can be achieved with the present models

Exact solutions for steady state, spine, and fan magnetic reconnection

The problem of steady state, incompressible magnetic reconnection in three dimensions is addressed. It is shown that exact reconnection solutions can be constructed by superposing nonlinear disturbances onto three-dimensional magnetic AT-points. There are two distinct families of reconnection solutions. These can be understood in terms of the eigenstructure of the null, that is, in terms of the "spine" curves and "fan" surfaces that define the separatrices of the field. One family of solutions is driven by disturbances in the fan and involves quasi-cylindrical current structures aligned to the axis of the spine; the other is associated with advection across the spine and a global current sheet aligned to the fan. Although both spine and fan solutions reduce to the two-dimensional analytic, shear-flow solutions of Craig & Henton, the three-dimensional spine current formulation allows far richer reconnective current structures. © 1996, The American Astronomical Society. All rights reserved