A self-similar magnetohydrodynamic model of magnetic clouds

Interplanetary magnetic clouds disconnected from the solar corona are modelled by magnetohydrodynamic (MHD) equations in two-dimensional spherical geometry. The structures of these clouds are described by self-similar solutions with axisymmetric force-free magnetic field and spherically symmetric plasma pressure and mass density. These force-free magnetic solutions show that inside the magnetic cloud, which is termed as the primary plasmoid, secondary plasmoids with closed magnetic field lines could be embedded if the azimuthal magnetic field is sufficiently strong. This magnetic cloud with embedded secondary structures could allow a calm encounter with Earth's magnetosphere. The polytropic index γ is determined self-consistently by the plasma parameters. With exponential plasma pressure profiles, γ would be unity. Should the pressure gradient be negative, the magnetic cloud would increase indefinitely in radius with an ever increasing velocity. On the other hand, should the pressure gradient be positive, the magnetic cloud would expand asymptotically to a finite stationary radius, and could be followed by a final collapse.