Force-free field inside a toroidal magnetic cloud

[1] An analytical solution of force-free magnetic fields inside a toroid with an arbitrary aspect ratio was found. A scalar equation was derived which when solved gives the heart of the solution of the vector field in toroidal coordinates, in closed form in terms of hypergeometric functions. The solution can be used for interpretation of magnetic cloud measurements in the interplanetary space. If it is assumed that a magnetic cloud is a large loop with roots at the Sun, then its part can be locally treated as a part of a toroid. The former solution by Miller and Turner [ 1981] was limited only to larger aspect ratios. The presented solution coincides with the Lundquist [ 1950] one for cylindrical clouds in case of a very large aspect ratio torus.