Theoretical Analysis of Driven Magnetic Reconnection Experiments
Authors: D. Uzdensky, R. Kulsrud, and M. Yamada
In this paper we develop a theoretical framework for the Magnetic Reconnection Experiment (MRX) 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. In order to simplify the problem we reduce it to a 1-D MHD model. Also, we define a special class of holonomic boundary conditions under which a unique sequence of global equilibria can be obtained, independent of the rate of reconnection. This enables us to break the whole problem into two parts: a global problem for the ideal region, and a local problem for the resistive reconnection layer. We carry out 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, we tackle the problem of the rate of reconnection region. This rate tells us how fast we proceed through the sequence of global equilibria but does not affect the sequence itself. Assuming the Sweet-Parker model for the reconnection layer, we calculate the reconnection rate, and demonstrate the difference between the co and counterhelicity cases, as well as the role of the external forces. We find our results to be in a reasonable agreement with the experiment.
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