Theoretical models of magnetic field line merging

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.

The Acceleration and Propagation of Solar Flare Energetic Particles

“…The inclusion of other terms in equation (28) is discussed by Vasyliunas (1975). The resistive term is unimportant everywhere except in a small region near the x-type neutral point where 8 becomes small and J is large (because the gradients of B are large).…”

“…A detailed discussion of the fluid theory of steady state reconnection has been given by Vasyliunas (1975). Early descriptions of the reconnection process and its application to solar flares were given by Parker (1957Parker ( , 1963 and Sweet (1958).…”

Electromagnetic hybrid‐code simulation of magnetic reconnection: Velocity distribution functions of accelerated ions

“…The assumed resistivity corresponds to the anomalous resistivity that is due to some unstable wave or inertia resistivity of particles [Vasyliunas, 1975;Sonnerup, 1970]. Conductivity must depend to some extent on current density, but, we neglected that effect in this study, because it was the structures of the downstream plasma sheet and the PSBL that were our primary concern and not the detailed structure near the diffusion region.…”

“…The process was originally studied by means of analytical and numerical calculations with an assumption of a steady state [Petschek, 1964;$onnerup, 1970;and Vasyliunas, 1975]. Those studies were followed by magne- Now, a theoretical understanding of the structure of particle distribution functions in a •econnection topology that develops over time is necessary for making comparisons with these observational results.…”

Interactions of the heliospheric current and plasma sheets with the bow shock: Cluster and Polar observations in the magnetosheath

“…If d i,e ( 1 for ions and electrons, both are well described by guiding center theory, and the MHD approximation to the generalized Ohm's law applies. Conversely, a particle species is said to be demagnetized if d i,e >1 [MacMahon, 1965;Vasyliunas, 1975;Scudder et al, 2008]. The simultaneous demagnetization of both ions and electrons is a signature of electron diffusion regions near magnetic merging sites.…”