Analysis of large scale MHD quantities in expanding magnetic clouds

Magnetic clouds (MCs) transport the magnetic flux and helicity released by the Sun. They are generally modeled as a static flux rope traveling in the solar wind, though they can present signatures of expansion. We analyze three expanding MCs using a self-similar free radial expansion model with a cylindrical linear force-free field (i.e., Lundquist solution) as the initial condition. We derive expressions for the magnetic fluxes, the magnetic helicity and the magnetic energy per unit length along the flux tube. We find that these quantities do not differ more than 25%25% when using the static or expansion model.