Dynamics of Field Line Mappings in Magnetic Flux Tubes

We study the topological constraints on the dynamics of magnetic field lines in flux tubes. Our approach is based on the application of the topological invariant: fixed point index. We consider periodic flux tubes and find various restrictions on the field lines that come from the sequence of fixed point indices of iterations. We also analyze the case of a tube with a cylindrical obstacle, deducing some special dynamical properties of the field line mapping from geometrical properties of the tube and the additional assumptions put on the field.