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We investigate equilibrium height of the flux rope, and its internalequilibrium in a realistic plasma environment by carrying out numericalsimulations of the evolution of systems including a current-carrying flux rope.We find that the equilibrium height of the flux rope is approximately apower-law function of the relative strength of the background field. Oursimulations indicate that the flux rope can escape more easily from a weakerbackground field. This further confirms the catastrophe in the magneticconfiguration of interest can be triggered by decrease of strength of thebackground field. Our results show that it takes some time to reach internalequilibrium depending on the initial state of the flux rope. The plasma flowinside the flux rope due to the adjustment for the internal equilibrium of theflux rope remains small and does not last very long when the initial state ofthe flux rope commences from the stable branch of the theoretical equilibriumcurve. This work also confirms the influence of the initial radius of flux ropeon its evolution, the results indicate that the flux rope with larger initialradius erupts more easily. In addition, by using the realistic plasmaenvironment and much higher resolution in our simulations, we notice somedifferent characters compared to previous studies in Forbes (1990).

Evolution of the Coronal Magnetic Configurations Including a Current-Carrying Flux Rope in Response to the Change in the Background Field