  Magnetic clouds (MCs) are "magnetized plasma clouds" moving in the solar
wind. MCs transport magnetic flux and helicity away from the Sun. These
structures are not stationary but feature temporal evolution. Commonly,
simplified MC models are considered. The goal of the present study is to
investigate the dynamics of more general, radially expanding MCs. They are
considered as cylindrically symmetric magnetic structures with low plasma
{\beta}. In order to study MC`evolution the self-similar approach method and a
numerical approach are used. It is shown that the forces are balanced in the
considered self-similarly evolving, cylindrically symmetric magnetic
structures. Explicit analytical expressions for magnetic field, plasma
velocity, density and pressure within MCs are derived. These solutions are
characterized by conserved values of magnetic flux and helicity. We also
investigate the dynamics of self-similarly evolving MCs by means of the
numerical code "Graale". In addition, their expansion in a medium with higher
density and higher plasma {\beta} is studied. It is shown that the physical
parameters of the MCs maintain their self-similar character throughout their
evolution. Conclusions. A comparison of the different self-similar and
numerical solutions allows us to conclude that the evolving MCs are quite
adequately described by our self-similar solutions - they retain their
self-similar, coherent nature for quite a long time and over large distances
from the Sun.
