A force-free field with constant alpha in an oblate cylinder: A generalization of the Lundquist solution

A force-free magnetic field with constant alpha for a circular cylindrical flux rope (Lundquist solution) is widely used to describe the magnetic field configuration in interplanetary flux ropes. Observations as well as MHD simulations indicate that interplanetary flux ropes are not circular but have an oblate shape. Here we present an analytical solution for a force-free magnetic field with constant alpha in an elliptic flux rope which may be regarded as a direct generalization of the Lundquist solution. An alternative simpler solution for a force-free magnetic field with constant alpha in an oblate flux rope is discussed.