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