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Context: Detailed hydrodynamic modeling explained several features of a fragment of the core of a Coronal Mass Ejection observed with SoHO/UVCS at 1.7 Rsun on 12 December 1997, but some questions remained unsolved.Aims: We investigate the role of the magnetic fields in the thermal insulation and the expansion of an ejected fragment (cloud) traveling upwards in the outer corona.Methods: We perform MHD simulations including the effects of thermal conduction and radiative losses of a dense spherical or cylindrical cloud launched upwards in the outer corona, with various assumptions on the strength and topology of the ambient magnetic field; we also consider the case of a cylindrical cloud with an internal magnetic field component along its axis.Results: We find that a weak ambient magnetic field (β ˜ 20) with open topology provides both significant thermal insulation and large expansion. The cylindrical cloud expands more than the spherical one

MHD evolution of a fragment of a CME core in the outer solar corona