MHD Equilibria and Triggers for Prominence Eruption

Magneto-hydrodynamic (MHD) simulations of the emergence of twisted magnetic flux tubes from the solar interior into the corona are discussed to illustrate how twisted and sheared coronal magnetic structures (with free magnetic energy), capable of driving filament eruptions, can form in the corona in emerging active regions. Several basic mechanisms that can disrupt the quasi-equilibrium coronal structures and trigger the release of the stored free magnetic energy are discussed. These include both ideal processes such as the onset of the helical kink instability and the torus instability of a twisted coronal flux rope structure and the non-ideal process of the onset of fast magnetic reconnections in current sheets. Representative MHD simulations of the non-linear evolution involving these mechanisms are presented.