Dynamics of a toroidal magnetic cloud in the solar wind

Knowledge about the behavior of compact toroidal magnetic force-free objects in ambient magnetic field may help to better understand dynamical processes in association with coronal mass ejections and their interplanetary counterparts. The problem to find the diamagnetic force acting on a toroidal object in an inhomogeneous magnetic field is solved analytically. At first the drapery of the inhomogeneous magnetic field caused by an insertion of a toroid was found, and then the force acting on the toroid by this disturbed magnetic field was obtained. The problem is considered in purely toroidal coordinates. The obtained solution can be used for calculations of the repulsing diamagnetic force acting on isolated objects in the solar corona such as magnetic clouds of a toroidal shape and for the determination of their velocity profiles, Deformations of toroidal transients due to this melon seed force are not investigated here. Only the force acting on the toroid as a whole is taken in consideration.