Past studies of the structure of solar magnetic fields have used magnetograph data to compute selected field lines for comparison with the morphology of structures seen in various spectral wavelengths. While those analyses examine one of the integral properties of magnetic fields (field lines), they are not complete since they fail to determine the other important integral property: the boundaries of the flux of field lines of given connectivity. In the present analysis we determine such a system of boundaries, called separatrices, for the current free field of two p-f spot pairs so as to exhibit the line of self-intersection, called the separator. The analysis is compared with previous analytical work. These computer results, confirming earlier studies carried out using iron fillings, show that the separatrix has the form of two intersecting ovoids, defining four flux cells. New features which have emerged from this study include the observation that the projections of the separatrix in a plane perpendicular to the separator at its highest point do not intersect at 90 ~ as has been widely believed, but rather closer to 60 ~ in the case studied. The separator is very nearly circular over most of its length. The two neutral points (B = 0) which appear at the photospheric ends of the separator have the mixed radial-hyperbolic form as expected, a feature requiring every field line lying on the separatrix to connect with at least one of the two neutral points. The rotation of line direction with height (shear) is graphically illustrated in the potential field case studied here. We also exhibit a magnetic arcade.

We briefly review the results of a laboratory field-line reconnection experiment. In doing so the flux transfer rate is defined and contrasted with magnetic Mach numbers as measures of the reconnection rate. We examine the origin of the reconnection electric field to determine some of the requirements of nonsteady versus steady reconnection. The. dependence of various measures of the reconnection rate on electrical conductivity is discussed as well as some experimental features which may relate to previous theory. Finally, we present some approximate scaling between laboratory events and the geomagnetic substorm. We reach three major conclusions: (a) The flux transfer rate as a measure of the reconnection rate is different from a magnetic Mach number. (b) The early reconnection process is quasi-steady state or "Petschek-like" and we associate this phase with magnetic energy storage. A later rapid flux transfer event is more energetic and is associated with storm events. The flux transfer event is triggered by a change in resistivity. (c) The laboratory event scales reasonably well to the duration and energy of a substorm.

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A number of reconnexion concepts and experiments are briefly reviewed in order to re-examine the present interpretation of these experiments. In particular, we offer explanations as to why some experiments appear to develop Petschek modes, tearing modes, or netural current sheets. The explanations require an understanding of the proper role of magnetic Reynolds numbers, the limits of the frozen-in concept, and the importance of natural importance of natural boundary conditions. We find that netural current sheets usually from in experiments with highly symmetrical (and therefore unnatural) boundary conditions. The classical tearing mode develops from perturbations of a neutral current sheet. In less constrained geometries multiple neutral points may appear but the classical tearing mode theory needs modification to explain these cases rigorously. A Petschek mode develops in even less constrained systems although the theoretical description is highly idealized. We offer explanations as to why some experimenters appear to find neutral current sheets in quadrupole fields and examine the usefulness of concepts derived from neutral current sheet theory.

Time-resolved measurements of temperatures, density, and other parameters which describe the plasma at the X-type neutral point of the double inverse pinch laboratory discharge device are reported. Turbulent resistivity develops in this experiment without the usual application of an external electric field. The electric field is generated by field line reconnection or magnetic flux transfer. Various conductivity mechanisms are examined including binary collisions, space charge current limitation (Alfv́en-Carlqvist instability), and other current driven instabilities. The evidence suggests that the ion-acoustic instability is responsible for the observed current cutoff and turbulent conductivity. However, this instability must be driven well above its normal threshold. The competing effects of electron runaway and wave-particle interactions are discussed.