Toroidal magnetic clouds in the interplanetary space

In-situ magnetic and plasma measurements allow us to determine the size and orientation of clouds near the Earth’s orbit based on the formulae proposed by Romashets and Vandas (Geophysical Research Letters, 2003). Marubashi et al. (Solar Physics, 2015) applied this approach for finding the shape and speed of 53 toroidal clouds near the Earth's orbit. We utilize their findings to several events and analyze the motion and expansion of the clouds. We offer a more detailed look to the geomagnetic storm on May 15, 1997. In this case, the maximum speed of the cloud at 3 solar radii is close to 2500 km/s. The cloud’s arrival time (about 74 hrs) and speed near the Earth’s orbit (of 423 km/s) are in good agreement with observations (within +/- 7%).  Temperature of solar wind is assumed constant or slowly variable on the trajectory of the cloud, while the major and minor radii are defined mostly by the interplanetary magnetic field magnitude, which depends on heliodistance as 1/r. The density of solar wind meets continuity requirement and velocity of solar wind is set such a way that it equals to the measurements at 1 AU, and is below 70 km/s close to the Sun. Density of the magnetic cloud is calculated from the condition of constant mass. It remains lesser than that of solar wind for most of travel time. The profiles of the density, magnetic field, and the size of the cloud versus heliodistance will be presented. Similarly, conditions in the solar wind outside of the cloud are available from modeling, as well. The quiet conditions in solar wind are determined in the period of one day prior to arrival of the cloud, given that the period provides almost constant values of density, velocity, and magnetic field. The average values inside the cloud are taken from measurements within the interval of Marubashi's list.