The shape of twisted, line-tied coronal loops

The magnetostatic equilibrium of a coronal loop in response to slow twisting of the photospheric footpoints is investigated. A numerical code is used to solve the full nonlinear two-dimensional axisymmetric problem, extending earlier linearized models which assume weak twist and large aspect ratio. It is found that often the core of the loop tends to contract into a region of strong longitudinal field while the outer part expands. It is shown that, away from the photospheric footpoints, the equilibrium is very well approximated by a straight one-dimensional cylindrical model. This idea is used to develop a simple method for prescribing the footpoint angular displacement and calculating the equilibrium.