GENERATION OF ELECTRIC CURRENTS IN 2-DIMENSIONAL MAGNETIC NULLS

We present detailed calculations and results for a model case of two-d imensional small distortions of static, current-free equilibrium aroun d a null-line magnetic configuration. This setup has been studied for fast energy release in flares, but has not been studied before in the context of the magnetic energy buildup that precedes the flare. Our an alytical results are new because they include gas pressure and provide explicit formulae for the expressions of all quantities (and especial ly the electric current) and energy storage as functions of the values of boundary conditions. A general solution is shown as a combination of eigenfunctions, with coefficients resulting from the boundary condi tions. These boundary conditions are given in terms of any arbitrary p lasma acceleration at a boundary enclosing the domain we study. The ap proach used here studies the MHD evolution of the electric current and plasma density variations driven by external forces. We find that bot h pressure and Lorentz forces are important, and that their boundary v alues select between a wide range of solutions, many of which have bee n found previously in numerical simulations. Most of the modes we find display strong current sheets, velocities, and pressure variations at the separatrices. Also we find that Joule and other dissipative terms are not important for typical cases, except at an extremely narrow in ner core, and near the separatrices. We discuss our results and their relationship to numerical MHD simulations.