Theoretical analysis of driven magnetic reconnection experiments

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Abstract
In this paper we present a theoretical framework for the Magnetic Reconnection Experiment (MRX) [M. Yamada et al., Bull. Am. Phys. Soc. 40, 1877 (1995)] in order to understand the basic physics of the experiment, including the effect of the external driving force, and the difference between co‐ and counterhelicity cases of the experiment. The problem is reduced to a one‐dimensional (1‐D) resistive magnetohydrodynamic (MHD) model. A special class of holonomic boundary conditions is defined, under which a unique sequence of global equilibria can be obtained, independent of the rate of reconnection. This enables one to break the whole problem into two parts: a global problem for the ideal region, and a local problem for the resistive reconnection layer. The calculations are then carried out and the global solution for the ideal region is obtained in one particular case of holonomic constraints, the so called ‘‘constant force’’ regime, for both the co‐ and counterhelicity cases. After the sequence of equilibria in the ideal region is found, the problem of the rate of reconnection in the resistive reconnection region is considered. This rate tells how fast the plasma proceeds through the sequence of global equilibria but does not affect the sequence itself. Based on a modified Sweet–Parker model for the reconnection layer, the reconnection rate is calculated, and the difference between the co‐ and counterhelicity cases, as well as the role of the external forces is demonstrated. The results from the present analysis are qualitatively consistent with the experimental data, predicting faster reconnection rate for the counterhelicity merging and yielding a positive correlation with external forcing.