FORMATION OF CURRENT LAYERS IN 3-DIMENSIONAL, INHOMOGENEOUS CORONAL MAGNETIC-FIELDS BY PHOTOSPHERIC MOTIONS

We present a method for calculating analytical expressions for the vel ocity, magnetic field, electric field, and current density arising fro m the quasistatic stressing of an initially potential, inhomogeneous c oronal magnetic field by photospheric flows. Four exact solutions that are produced by a wide variety of driving flows are examined. We have found that large gradients in the vorticity can lead to the generatio n of strong current layers, across which the magnetic field is continu ous. In two of the exact solutions these appear as logarithmic singula rities in the current density and first spatial derivatives of the vor ticity. Two other solutions, on the other hand, driven by continuous a nd differentiable photospheric flows lacking large gradients in the vo rticity, exhibit little intensification of the current density. When c urrent layers appear, they are located at the quasi-separatrix layers (QSL) of the magnetic configuration, where small displacements of the magnetic field footpoints at one part of the photosphere lead to large displacements of the footpoints at the other end of the field line. T his extends previous QSL work by providing an additional constraint on the driving flow in order that strong currents are generated at such layers in the course of a quasi-static evolution of the magnetic field .