  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.
