THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. I. SPONTANEOUS CURRENT SHEETS IN THREE-DIMENSIONAL FIELDS

We present mathematical models to demonstrate the inevitability of current-sheet formation in a cylindrical magnetic field governed by the ideal hydromagnetic induction equation, as described by the Parker theory. This process, central to the heating of the solar corona, is radically different in fully three-dimensional fields as compared with two-dimensional fields. Magnetic neutral points or separatrix flux surfaces are necessary for sheet formation in two-dimensional fields. In fully three-dimensional fields, current sheets form readily even in the complete absence of neutral points and separatrix surfaces, and these sheets can form densely throughout the field in response to changes in the magnetic volume. This general result is established for cylindrical fields that are topologically untwisted, including the first direct demonstration of sheet formation in the absence of any magnetic neutral point. We discuss simple implications of this basic result for solar flares and coronal heating. In subsequent papers, we apply our result to coronal mass ejections and solar flares.