Abstract
The spatial and temporal evolution of the electric and magnetic fields in a current-carrying plasma is investigated in the nonlinear regime. Using the magnetohydrodynamic equations, a nonlinear diffusion equation for the magnetic field in the plasma is obtained. This nonlinear equation is numerically solved and the spatiotemporal evolution of the electric and magnetic fields and the electron density distribution are plotted. It is shown that as the time passes, the profile of the electric and magnetic fields changes from a sinusoidal shape to a saw-tooth one and the electron density distribution becomes very steepened. Also, the mechanism of the filament formation is then discussed. Furthermore, the effects of the thermal motion, collisions, and ion mass on growth rate of filaments as well as the saturation time are argued. Finally, it is found that the energy dissipation is associated with the aforementioned effects and strong plasma density gradient.
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