Finding the arrival times of toroidal magnetic clouds from solar active regions to Earth's orbit

We report a parameter-based model for predicting the arrival times of the magnetic clouds produced by solar activities and apply it to the solar flare released in May 1997 (Romashets E. et al. 2025, JASTP, 267, 106416). The characteristics of the cloud, such as its size, shape, magnetic field, mass, speed, and expansion rate are estimated. The shape of this cloud is toroidal, with minor and major radii changing at different rates with the cloud's propagation. The effects on cloud’s motion due to the helical structure of the interplanetary magnetic field and solar wind plasma and especially due to the helisopheric current sheet crossing (Romashets E. et.al S., 2007, A&A, 466, 357) were not considered. The maximum speed measured in Earth's orbit during the cloud passage was 460 km/s, which was relatively low, enabling comparison with existing literature (Corona-Romero P. and Riley P., 2020, AnGeo, 38, 657). We use the published diamagnetic force expression (Romashets E. P., Vandas M., 2001, JGR, 106, 10615), but the calculation is now different. We added the conservation of total helicity in the cloud and the continuity equation for solar wind plasma flow. Also, the compression of the cloud by solar wind is not considered when we apply the model to the real event of May 1997.