FORMATION OF ELECTRIC-CURRENT SHEETS IN THE MAGNETOSTATIC ATMOSPHERE

This paper presents an analytical illustration of the theorem due to Parker that a magnetic field with an arbitrarily prescribed topology in an electrically, perfectly conducting medium would, in general, seek equilibrium states with embedded electric current sheets, or magnetic tangential discontinuities. Low & Wolfson had previously shown that current sheets must form in certain magnetic fields driven to evolve quasi-statically through force-free states by the continuous displacements of the magnetic footpoints at the boundary. In particular, this process can take place in the absence of magnetic neutral points. This paper extends their result to the case of an isothermal atmosphere in which the Lorentz force does not vanish but balances pressure and gravitational forces in static equilibrium. Using the analytic magnetostatic solutions of Zweibel & Hundhausen, it is shown that the quasi-static evolution of the atmosphere in response to a continuously changing distribution of the plasma pressure at the atmospheric base can bring an initially smooth state to one in which an electric current sheet forms. The sheet formation is unavoidable in the end state because the balance of force requires the expulsion of magnetized plasma from between two magnetic surfaces under the frozen-in condition. A discussion is given of the result to relate it to recent developments.