Thermodynamic Phase Transition in Magnetic Reconnection

By examining the entropy production in fully kinetic simulations of collisional plasmas, it is shown that the transition from collisional Sweet-Parker reconnection to collisionless Hall reconnection may be viewed as a thermodynamic phase transition. The phase transition occurs when the reconnection electric field satisfies E=E_{D}sqrt[m_{e}/m_{i}], where m_{e}/m_{i} is the electron-to-ion mass ratio and E_{D} is the Dreicer electric field. This condition applies for all m_{i}/m_{e}, including m_{i}/m_{e}=1, where the Hall regime vanishes and a direct phase transition from the collisional to the kinetic regime occurs. In the limit m_{e}/m_{i}→0, this condition is equivalent to there being a critical electron temperature T_{e}≈m_{i}Ω_{i}^{2}δ^{2}, where Ω_{i} is the ion cyclotron frequency and δ is the current sheet half-thickness. The heat capacity of the current sheet changes discontinuously across the phase transition, and a critical power law is identified in an effective heat capacity. A model for the time-dependent evolution of an isolated current sheet in the collisional regime is derived.