The evolution of magnetic configurations with a current-carrying flux rope for modeling a prominence is investigated. The configurations evolve as a result of the interaction between two or more magnetic source regions. The background field of the system is produced by either two dipoles or four monopoles located on the boundary surface. Our purpose is to study the catastrophic behaviors of the systems' evolutions in response to the change in either the distance between source regions or the strength of background field, and to find the maximum heights that the flux rope can attain before it loses equilibrium and catastrophe occurs. We find that the domain in parameter space over which the flux rope remains in equilibrium is smaller than in the simpler configurations that have been previously investigated. Consequently, the equilibrium heights of the flux rope studied in this work are fairly low, such that the maximum values of these heights compared to the corresponding distances between the active regions vary from less than 3% to about 23%, with an average of about 13.2%, all of which are below 25%. This result has an important observational consequence, namely that a prominence appearing between different active regions will tend to be located in the low corona and will tend to become unstable if its height increases.
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