Magnetic reconnection in electron magnetohydrodynamics

The magnetic field dynamics and reconnection processes in a highly conducting plasma are investigated in the regimes where Ohm’s law is dominated by the Hall term, using a single (electron) fluid description (electron magnetohydrodynamics). In these regimes, which correspond to the frequency range of the so-called whistler (helicon) mode, the electromagnetic field is nearly force free: (j×B)/c+eneE=0. The evolution of the magnetic field in the vicinity of an X line is discussed in the linear and nonlinear regimes. The propagation of whistler waves results in the steepening of their wave front and in the increase of the electric current density in the neighborhood of the magnetic separatrix surfaces. Small-scale magnetic reconnection occurs near surfaces where k⋅B=0, with k the mode wave number, and tearing-type modes can be unstable due to the effect of electron inertia. A class of exact self-similar solutions is obtained. These describe, within the scope of a local approximation, the nonlinear time development (magnetic collapse) of the singularities that occur in three-dimensional magnetic configurations. Flat electric current sheets are formed during this collapse. Finally, the rate of reconnection in the electron-magnetohydrodynamic frequency range is estimated in the framework of a steady-state approximation.