Current-Direction-Dependent Evolution of a Vertical Current Sheet in the Hall Plasma of the Solar Chromosphere

The consequences of the entry of a weak magnetic field into the upper chromosphere of the Sun are theoretically studied. It is assumed that the plasma at the initial moment is immobile and has everywhere a temperature of 50 000 K and that the field consists of two identical opposite-polarity magnetic regions adjacent to each other with a vertical contact zone. A completely self-consistent, two-dimensional system of nonlinear collisional equations of single-fluid, resistive magnetohydrodynamics is numerically solved with allowance for the Hall effect and thermal conductivity. It has been found that, during the coevolution of the field and plasma, the upward-directed boundary current more often takes the form of a thin current sheet and exists in this form longer than the boundary current directed downwards. However, with a downward current, the conversion of the magnetic field energy into the energy of regular flows of the chromospheric plasma proceeds more efficiently. Upon the assumption of a slow change in the values along the vertical, a range of parameter values is analytically found where, regardless of the general form of magnetic inhomogeneities, the downward currents degrade (are blurred), while a density of upward currents sharply increases. A fundamental difference in the behavior of currents arises when ohmic dissipation and the drift of field lines, due to their partial freezing-in, have a lesser effect on changes in the magnetic field than the Hall effect in the presence of a plasma density gradient created by the gravity. It is shown that the minimum height where such pure gradient-Hall evolution of the magnetic field occurs corresponds to the base of the corona. It is suggested that the ohmic dissipation of spontaneously formed concentrated currents contributes to the corona heating.