Self‐consistent Magnetohydrodynamic Modeling of Current Sheet Structure and Heating Using Realistic Descriptions of Transport Processes

Abstract

A magnetohydrodynamic (MHD) model of an electron-ion, collision-dominated plasma that includes the electrical conductivity and thermoelectric tensors in Ohm's law is used to generate current sheet solutions in parameter ranges that correspond to those of the solar transition region and lower corona. The model contains a prescribed sheared magnetic field with a characteristic length scale L. The characteristic sheet width is 2L, but it is found that the temperature has transition region or coronal values only within a diffusion region (DR) with a width several orders of magnitude smaller than 2L. The heating rate per unit mass and flow speed in the DR are orders of magnitude larger, and the density is orders of magnitude smaller than in the surrounding plasma. The heating rate per unit volume is a maximum in the DR and falls off steadily outside the DR. The Joule heating rate and current density each consist of a conduction component driven by the center-of-mass electric field and a thermoelectric component driven by the temperature gradient. It is found that these components largely cancel, leading to a total heating rate and current density orders of magnitude smaller than either of their components. This suggests that thermoelectric current drive is important in determining current sheet structure. The center-of-mass electric field that provides the energy to maintain the plasma in a steady state is almost entirely the convection electric field. The electron magnetization Me is the product of the electron cyclotron frequency and the electron-ion collision time. Nonzero values of Me cause the conductivity and thermoelectric tensors to be anisotropic. It is found that the large values of Me that occur in the DR increase the heating rates per unit volume and mass by several orders of magnitude and can change the sign of the heating rate per unit mass from negative to positive, corresponding to a change from a cooling process to a heating process. This suggests that electron magnetization, and hence anisotropic transport, is a major factor in current sheet heating.