3-D twisted flux-tube in a linear force-free equilibrium

It is now commonly accepted that prominence plasma is supported in magnetic dips, in particular in twisted flux tubes. But present two-dimensional models are unable to explain the observed presence and structure of prominence feet. This requires three-dimensional models. We modelled the field using linear force-free field equations. Combining a small number of harmonics, and using observational constraints, we have found the area in the parameter space where prominences are likely to be present. Then, adding 3-D harmonics, we show that feet appear periodically underneath the prominence body. For great helicity, the parameter space is mostly fulfilled by configurations which have feet alternating between both sides of the prominence axis, as observed. The lateral feet are formed by dips in the vicinity of small magnetic polarities, that are located in a low field corridor where the prominence stands. The modelled configurations show in a natural fashion many observational aspects of prominences, such as the vector magnetic field measurements in prominences and the chirality patterns.