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 X-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 dis turbances 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.

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.

An exact three-dimensional solution is derived for the steady state magnetic reconnection of incompressible, resistive plasmas. The analysis provides a natural extension of the analytic, two-dimensional reconnection solution of Craig & Henton. The solution shows how advective motions through the separatrix ''spine-curve'' lead to global current sheets aligned to the separatrix ''fan.'' Subject headings: MHD-plasmas L198 CRAIG ET AL. Vol. 455

The problem of incompressible, nonlinear magnetic reconnection in three-dimensional ''open'' geometries is considered. An analytic treatment shows that dynamic ''fan current'' reconnection may be driven by superposing long wavelength, finite amplitude, plane wave disturbances onto three-dimensional magnetic X-points. The nonlinear reconnection of the field is preceded by an advection phase in which magnetic shear waves drive large currents as they localize in the vicinity of the magnetic null. Analytic arguments, reinforced by detailed simulations, show that the ohmic dissipation rate can be independent of the plasma resistivity if the merging is suitably driven.

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