Three‐dimensional Solutions for Fan and Spine Magnetic Reconnection in Partially Ionized Plasmas

Abstract

Under the approximation of incompressible flow, we solve both momentum equations (for neutrals and ions) and magnetic induction equation at three-dimensional level, obtaining solutions for steady spine and fan magnetic reconnection in partially ionized plasmas. In the case of weak coupling between the two species, sharp structures can form not only for the magnetic field but also for the ions' velocity, while for the neutrals the level of sharpness falls off by an order of ionization degree. In the strong coupling case when both species move together sharp structures appear only for magnetic field. The results could be used to understand the phenomena which are observed in the solar lower atmosphere, e.g., Ellerman bombs, type II white light flares, and photospheric magnetic flux cancellation which may be caused by magnetic reconnection. In an ideal approximation, the sharp structures have a power-law distribution: in the fan reconnection the field and both flows go up according to z(-\kappa\), while in the spine reconnection they obey the inverse square law r(-2). However, due to the existence of finite resistivity, the enhancements of currents, field, and flows should saturate at some level in the diffusion layer. When the ionization degree goes up (corresponds to epsilon --> 0 in this paper), our solutions recover previous formulation for wholly ionized case. Since the Ohmic resistivity is very small (similar to 10(-10)), the induced current becomes so large that, as we estimate, it will cause plasma micro-instability which could speed up the reconnection process significantly. So near the current sheet which is provided here usual MHD description must fail, we need another theory to join in, such as kinematic description, to account for violent phenomena (e.g., Ellerman bombs and type II white light flares) which occur in the Sun's lower atmosphere.