  We investigate the magnetic reconnection in an MHD simulation of a coronal
magnetic flux rope (MFR) confined by a helmet streamer, where a
prominence-cavity system forms. This system includes a hot cavity surrounding a
prominence with prominence horns and a central hot core above the prominence.
The evolution of the system from quasi-equilibrium to eruption can be divided
into four phases: quasi-static, slow rise, fast rise, and propagation phases.
The emerged MFR initially stays quasi-static and magnetic reconnection occurs
at the overlying high-Q (squashing factor) apex region, which gradually evolves
into a hyperbolic flux tube (HFT). The decrease of the integrated magnetic
tension force (above the location of the overlying reconnection) is due to the
removal of overlying confinement by the enhanced overlying reconnection between
the MFR and the overlying fields at the apex HFT, thus engines the slow rise of
the MFR with a nearly constant velocity. Once the MFR reaches the regime of
torus instability, another HFT immediately forms at the dip region under the
MFR, followed by the explosive flare reconnection. The integrated resultant
force (above the location of the flare reconnection) exponentially increases,
which drives the exponential fast rise of the MFR. The system enters the
propagation phase, once its apex reaches the height of about one solar radius
above the photosphere. The simulation reproduces the main processes of one
group of prominence eruptions especially those occurring on the quiet Sun.
