Abstract
Under conditions of very high electrical conductivity, such as in the fully ionized, million-degree solar corona, the magnetic field is essentially frozen into the plasma and, therefore, the magnetic field topology cannot change. The topology is described by where each thin flux tube enters and leaves the volume, and the twist and linkages of the magnetic flux tubes. The freezing of magnetic flux prevents the mixing of local fluid volumes that trap different flux systems. This can induce thin sheets of intense electric-current density to flow tangentially on the magnetic flux surfaces. The nonlinear thinning of these current sheets can reach the point where resistive dissipation becomes significant, producing heating and changes in field topology. I will describe Parker's theory of this hydromagnetic process with explicit demonstrations of how current sheets are inevitable in untwisted magnetic fields as a consequence of the frozen-in condition. I will also discuss the implications of these demonstrations for coronal heating and flares.