The magnetic flux rope (MFR) is believed to be the underlying magnetic structure of coronal mass ejections (CMEs). However, it remains unclear how an MFR evolves into and forms the multi-component structure of a CME. In this paper, we perform a comprehensive study of an extreme-ultraviolet (EUV) MFR eruption on 2013 May 22 by tracking its morphological evolution, studying its kinematics, and quantifying its thermal property. As EUV brightenings begin, the MFR starts to rise slowly and shows helical threads winding around an axis. Meanwhile, cool filamentary materials descend spirally down to the chromosphere. These features provide direct observational evidence of intrinsically helical structure of the MFR. Through detailed kinematical analysis, we find that the MFR evolution experiences two distinct phases: a slow rise phase and an impulsive acceleration phase. We attribute the first phase to the magnetic reconnection within the quasi-separatrix-layers surrounding the MFR, and the much more energetic second phase to the fast magnetic reconnection underneath the MFR. We suggest that the transition between these two phases be caused by the torus instability. Moreover, we identify that the MFR evolves smoothly into the outer corona and appears as a coherent structure within the white light CME volume. The MFR in the outer corona was enveloped by bright fronts that originated from plasma pile-up in front of the expanding MFR. The fronts are also associated with the preceding sheath region followed the outmost MFR-driven shock.
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