Flux Ropes Embedded In A Radial Magnetic Field: Analytic Solutions For The External Magnetic Field

We present a new exact solution of the magnetostatic equations, describing a flux rope embedded in a radial magnetic field. Its axis is perpendicular to the radial direction and parallel to the ecliptic plane and it has a radius r0 and an arbitrary angular distance θ0 to the polar axis of the Sun. We outline the general method of how one can gain a new solution of the magnetostatic equations by rotating the vector potential of a known solution by an angle θ0 in the r−θ plane. Using the flux-rope solution, a construction procedure for an approximate solution which describes a torus around the polar axis and which is embedded in a radial magnetic field is given. The method has considerable potential as a tool for initializing numerical simulations.