  We mode Solar coronal mass ejections (CMEs) as expanding force-fee magnetic
structures and find the self-similar dynamics of configurations with spatially
constant \alpha, where {\bf J} =\alpha {\bf B}, in spherical and cylindrical
geometries, expanding spheromaks and expanding Lundquist fields
correspondingly. The field structures remain force-free, under the conventional
non-relativistic assumption that the dynamical effects of the inductive
electric fields can be neglected. While keeping the internal magnetic field
structure of the stationary solutions, expansion leads to complicated internal
velocities and rotation, induced by inductive electric field. The structures
depends only on overall radius R(t) and rate of expansion \dot{R}(t) measured
at a given moment, and thus are applicable to arbitrary expansion laws. In case
of cylindrical Lundquist fields, the flux conservation requires that both axial
and radial expansion proceed with equal rates. In accordance with observations,
the model predicts that the maximum magnetic field is reached before the
spacecraft reaches the geometric center of a CME.
