A Self-similar Solution of Expanding Cylindrical Flux Ropes for any Polytropic Index Value

Physics

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7513 Coronal Mass Ejections, 7524 Magnetic Fields, 2111 Ejecta, Driver Gases, And Magnetic Clouds, 2134 Interplanetary Magnetic Fields, 2164 Solar Wind Plasma

Scientific paper

We found a new solution for MHD equations that satisfies the condition that cylindrical flux ropes can expand self-similarly even when the polytropic index γ is larger than 1. We achieved this by including the effects of elongation along the symmetry axis as well as radial expansion and assuming that the radial expansion rate is the same as the elongation rate. Previous studies (Osherovich et al., 1993; 1995) showed that cylindrical flux ropes self-similarly expand only in the medium where γ is less than 1. We compare the models including elongation and excluding elongation observationally by using the WIND key parameters for the year 1995. Approximately half of the flux ropes were fitted better to the model including elongation and the remainder were fitted better to the model excluding elongation, but the differences were slight. This new exact solution to a time-dependent two-dimensional MHD problem can also be used to test numerical codes.

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