Evolution of Toroidal Magnetic Clouds

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It was shown by numerical MHD simulation (Detman et al., JGR, 1991, Vandas et al., JGR, 1997, 1998) that spherical spheromaks can evolve into toroidal ones. In terms of toroid's aspect ratios the phenomenon can be treated as transformation from less than unity value to greater than unity. Until recently, there were no linear force-free solutions known for very small aspect ratios. It was found by Romashets and Vandas (A&A, 2009) and used for interpretation of solar flux ropes instabilities (Romashets, Vandas, and Poedts, Solar Phys., 2010). The shape is of a toroidal form, but it is not an ideal toroid, since its cross-section is not circular. It is a tear drop shape for some parameters. The solution of Tsuji (Phys. Fluids, 1991) is an ideal toroid, on the other hand it is applicable only for aspect ratio more than 1. We shall demonstrate that the magnetic structure in the range 0.5-2.5 transforms from a sphere into a toroid.

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