Catastrophe of coronal magnetic flux ropes in partially open magnetic fields

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, a n umerical study is carried out to find equilibrium solutions associated with a magnetic flux rope in the corona. The ambient magnetic field is partiall y open, consisting of a closed arcade in the center and an open field at th e flank. The coronal magnetic flux rope is characterized by its magnetic pr operties, including the axial and annular magnetic fluxes and the magnetic helicity, and its geometrical features, including the height of the rope ax is, the halfwidth of the rope and the length of the vertical current sheet below the rope. It is shown that for a given partially open ambient magneti c field, the dependence of the geometrical features on the magnetic propert ies displays a catastrophic behavior, namely, there exists a certain critic al point, across which an infinitesimal enhancement of the magnetic paramet ers causes a finite jump of the geometrical parameters for the rope. The am plitude of the jump depends on the extent to which the ambient magnetic fie ld in open, and approaches to zero when the ambient magnetic field becomes completely closed. The implication of such a catastrophe in solar active ph enomena is briefly discussed.