Coronal magnetic flux rope equilibria and magnetic helicity

Using a 2.5-dimensional (2.5-D) ideal MHD model, this paper analyzes the equilibrium properties of coronal magnetic flux ropes in a bipolar ambient magnetic field. It is found that the geometrical features of the magnetic flux rope, including the height of the rope axis, the half-width of the rope, and the length of the vertical current sheet below the rope, are determined by a single magnetic parameter, the magnetic helicity, which is the sum of the self-helicity of the rope and the mutual helicity between the rope field and the ambient magnetic field. All the geometrical parameters increase monotonically with increasing magnetic helicity. The implication of this result in solar active phenomena is briefly discussed.