Using a 2.5-dimensional MHD simulation, we investigate the role played by the inner coronal null point in the formation and evolution of solar quiescent prominences. The flux rope is characterized by its magnetic fluxes, the toroidal magnetic flux Φ p and the poloidal flux Φ. It is found that for a given Φ p , the catastrophe does not occur in the flux rope system until Φ increases to a critical point. Moreover, the magnetic flux of the null point is the maximum value of the magnetic flux in the quadrupole background magnetic field, and represented by ψ N . The results show that the bigger ψ N usually corresponds to the smaller catastrophic point, the lower magnetic energy of the flux rope system, and the lesser magnetic energy inside the flux rope. Our results confirm that catastrophic disruption of the prominence occurs more easily when there is a bigger ψ N . However, ψ N has little influence on the maximum speed of the coronal mass ejections (CMEs) with an erupted prominence. Thus we argue that a topological configuration with the inner coronal null point is a necessary structure for the formation and evolution of solar quiescent prominences. In conclusion, it is easier for the prominences to form and to erupt as a core part of the CMEs in the magnetic structure with a greater ψ N .
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