We investigate two successive flux rope (FR1 and FR2) eruptions resulting in two coronal mass ejections (CMEs) on 2012 January 23. Both FRs appeared as an EUV channel structure in the images of high temperature passbands of the Atmospheric Imaging Assembly prior to the CME eruption. Through fitting their height evolution with a function consisting of linear and exponential components, we determine the onset time of the FR impulsive acceleration with high temporal accuracy for the first time. Using this onset time, we divide the evolution of the FRs in the low corona into two phases: a slow rise phase and an impulsive acceleration phase. In the slow rise phase of the FR1, the appearance of sporadic EUV and UV brightening and the strong shearing along the polarity inverse line indicates that the quasi-separatrix-layer reconnection likely initiates the slow rise. On the other hand for the FR2, we mainly contribute its slow rise to the FR1 eruption, which partially opened the overlying field and thus decreased the magnetic restriction. At the onset of the impulsive acceleration phase, the FR1 (FR2) reaches the critical height of 84.4$pm$11.2 Mm (86.2$pm$13.0 Mm) where the decline of the overlying field with height is fast enough to trigger the torus instability. After a very short interval ($sim$2 minutes), the flare emission began to enhance. These results reveal the compound activity involving multiple magnetic FRs and further suggest that the ideal torus instability probably plays the essential role of initiating the impulsive acceleration of CMEs.
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