Rapid Change of Field Line Connectivity and Reconnection in Stochastic Magnetic Fields

Abstract:

Magnetic fields depending on three spatial coordinates generally have the feature that neighboring field lines exponentiate away from each other and become stochastic. Such a generic condition usually occurs in space and astrophysical plasmas, such as coronal magnetic field entangled by photospheric footpoint shuffling, as well as in fusion plasmas in the presence of multiple tearing modes. Under the condition of large exponentiation, the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law, which may potentially lead to rapid magnetic reconnection. This idea of breaking field line connectivity by stochasticity is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are identified in the process of resistive relaxation. During the quasi-static phase, it is found that regions of high field line exponentiation (akin to quasi-separatrix-layers) are associated with rapid change of field line connectivity and strong induced flow. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of footpoint mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, it is found that resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold. Onset of the instability leads to formation of intense current filaments, followed by rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity may be more appropriately designated as magnetic reconnection. Our results reveal and address the difficulty in distinguishing magnetic reconnection from enhanced diffusion in the presence of field line stochasticity. Rapid change of field line connectivity appears to be a necessary, but may not be sufficient, condition for fast reconnection.