Evolution of Coronal Magnetic Fields Consisting of Flux Ropes and Overlying Fields

A series of numerical MHD simulations are performed to investigate the evolution of coronal magnetic fields consisting of two flux ropes and an overlying field. Depending on the directions of the axial current and the axial field, two co-helicity cases and two counter-helicity cases are addressed. In Case 1, in which both the axial currents and the axial fields are parallel, flux rope merging bears a huge flux rope with a large winding number. This flux rope naturally erupts, but the whole evolutionary process is rather slow. In Case 2, in which the axial currents are parallel while the axial fields are antiparallel, a self-closed structure is formed and it drives eruption. In Case 3, in which the axial currents are antiparallel and the axial fields are parallel, each flux rope erupts independently and the presence of the other flux rope does not affect the eruption of one flux rope. In Case 4, in which both the axial currents and the axial fields are antiparallel, interaction of the flux ropes and the overlying field effects a breakout reconnection creating an apple-like CME configuration. Our study tells what kind of eruption mechanisms are involved for different eruption features observed.