A 2.5-dimensional ideal magnetohydrodynamic model for coronal magnetic flux ropes

Coronal magnetic flux ropes are closely related to various solar active phenomena such as prominences, flares, and coronal mass ejections. Using a 2.5-dimensional (2.5-D), time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find the equilibrium solution associated with a magnetic flux rope in the corona, which is assumed to emerge as a whole from the photosphere. The rope in equilibrium is characterized by its geometrical features such as the height of the axis, the half-width of the rope, and the length of the vertical current sheet below the rope, and its magnetic properties such as the axial and annular magnetic fluxes and the magnetic helicity as well, which are conserved quantities of the rope in the frame of ideal MHD. It is shown that, for a given bipolar ambient magnetic field, the magnetic flux rope is detached from the photosphere, leaving a vertical current sheet below, when its axial magnetic flux, annular magnetic flux, or magnetic helicity exceeds a certain critical value. The magnetic field is nearly force free in the rope but not in the prominence region, where the Lorentz force takes an important role in supporting the prominence appearing below the rope axis. The geometrical features of the rope vary smoothly with its magnetic properties, and no catastrophe occurs, a similar conclusion to that reached by Forbes & Isenberg for magnetic flux ropes of large radius.