Pulsed Dissipation of Spontaneous Current Sheets in the Solar Corona

A simple one-dimensional model of the pulsed dissipation of a spontaneous current sheet is presented. Parker has demonstrated that spontaneous current sheets, or magnetic tangential discontinuities, must inevitably form and dissipate in the electrically near-perfectly conducting solar corona. Under the simplifying assumption that the effects of magnetic diffusion and near-ideal MHD relaxation to equilibrium may be idealized to occur separately in time, exact analytical one-dimensional isothermal solutions for successive alternate equilibrium and diffused states are obtained showing explicitly the gradual removal of the magnetic discontinuity. For discontinuities between both parallel and antiparallel fields, this removal results in the liberation of energy stored in the field. Energy losses in the antiparallel cases are found to be larger than for the parallel cases, and this difference increases as the plasma β decreases. Diffusions of parallel fields are found to result in magnetic flux transfer across the current sheet during the evolution while discontinuities between parallel fields cause flux annihilation, the creation of magnetic neutral points, inflows, and localized plasma accumulations. Numerical solutions obtained using the Versatile Advection Code reproduce these basic properties under isothermal, nonisothermal adiabatic, and nonadiabatic conditions and with magnetic diffusion and MHD relaxation occurring simultaneously. The relevance of these models to more complicated systems is discussed.