Theoretical analysis of driven magnetic reconnection experiments

Abstract

In this paper the authors 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 they reduce it to a 1-D resistive MHD model. Also, they 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 them 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 authors carry out the calculations and obtain the global solution for the ideal region 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, they tackle the problem of the rate of reconnection in the resistive reconnection region. This rate tells how fast they proceed through the sequence of global equilibria but does not affects the sequence itself. Assuming the Sweet-Parker model for the reconnection layer, they calculate the reconnection rate, and demonstrate the difference between the co and counterhelicity cases, as well as the role of the external forces. The authors find their results to be in reasonable agreement with the experiment. Magnetic reconnection is important both in laboratory experiments and in astrophysics.