Theoretical models of magnetic field line merging

TLDR

Models of magnetic field line merging in a limited region around the magnetic X line with roughly uniform, antiparallel external fields are reviewed. The authors review hydromagnetic models of magnetic merging, including Sweet–Parker’s diffusion‑dominated core, Petschek’s uniform‑field boundary formulation, and Sonnerup–Yeh–Axford’s nonsingular slow‑mode expansion fan models, and discuss extensions to collisionless plasmas and boundary‑condition effects. The reviewed models are fundamentally consistent, representing different aspects of the same problem, and the maximum merging rate equals the local Alfvén speed into the diffusion region, which can be increased arbitrarily by slow‑mode MHD expansion under suitable boundary conditions.

Abstract

Models of magnetic field line merging that consider processes in a limited region around the magnetic X line, within which the external magnetic fields are roughly uniform and antiparallel, are reviewed. Part 1 describes the concept of magnetic merging and then considers the models based on a hydromagnetic approach. The models developed by Sweet and Parker, by Petschek, and by Sonnerup and Yeh and Axford are shown to be fundamentally consistent, representing different aspects of the same problem. The model of Sweet and Parker describes the small region around the neutral line where magnetic field diffusion is the dominant process. The inclusion of inertial as well as finite resistivity effects allows an extension of their model to collisionless plasmas. Petschek's model represents a system with a boundary condition of uniform field at the sides; it has been extended and formulated in a mathematically precise manner. The nonsingular model of Sonnerup and of Yeh and Axford has special boundary conditions at the sides producing localized slow mode MHD expansion fans in the external flow; the singular models and the compressible similarity models are physically unrealizable. The maximum merging rate corresponds to flow into the diffusion region at the local Alfvén speed, which, however, can be made arbitrarily large by slow mode MHD expansion if suitable boundary conditions are present.