LAUSR

Axially symmetric constant-alpha force-free magnetic fields in toroidal flux ropes with elliptical cross sections are constructed in order to investigate how their alphas and magnetic helicities depend on parameters of the flux ropes. Magnetic configurations are found numerically using a general solution of a constant-alpha force-free field with an axial symmetry in cylindrical coordinates for a wide range of oblatenesses and aspect ratios. Resulting alphas and magnetic helicities are approximated by polynomial expansions in parameters related to oblateness and aspect ratio. These approximations hold for toroidal as well as cylindrical flux ropes with an accuracy better than or of about 1%. Using these formulae, we calculate relative helicities per unit length of two (probably very oblate) magnetic clouds and show that they are very sensitive to the assumed magnetic cloud shapes (circular versus elliptical cross sections).