Self-similar evolution of interplanetary magnetic clouds and Ulysses measurements of the polytropic index inside the cloud
A self similar model for the expanding flux rope is developed for a magnetohydrodynamic model of interplanetary magnetic clouds. It is suggested that the dependence of the maximum magnetic field on the distance from the sun and the polytropic index gamma has the form B = r exp (-1/gamma), and that the ratio of the electron temperature to the proton temperature increases with distance from the sun. It is deduced that ion acoustic waves should be observed in the cloud. Both predictions were confirmed by Ulysses observations of a 1993 magnetic cloud. Measurements of gamma inside the cloud demonstrate sensitivity to the internal topology of the magnetic field in the cloud.