  We have performed two-dimensional special-relativistic magnetohydrodynamic
simulations of non-equilibrium over-pressured relativistic jets in cylindrical
geometry. Multiple stationary recollimation shock and rarefaction structures
are produced along the jet by the nonlinear interaction of shocks and
rarefaction waves excited at the interface between the jet and the surrounding
ambient medium. Although initially the jet is kinematically dominated, we have
considered axial, toroidal and helical magnetic fields to investigate the
effects of different magnetic-field topologies and strengths on the
recollimation structures. We find that an axial field introduces a larger
effective gas-pressure and leads to stronger recollimation shocks and
rarefactions, resulting in larger flow variations. The jet boost grows
quadratically with the initial magnetic field. On the other hand, a toroidal
field leads to weaker recollimation shocks and rarefactions, modifying
significantly the jet structure after the first recollimation rarefaction and
shock. The jet boost decreases systematically. For a helical field, instead,
the behaviour depends on the magnetic pitch, with a phenomenology that ranges
between the one seen for axial and toroidal magnetic fields, respectively. In
general, however, a helical magnetic field yields a more complex shock and
rarefaction substructure close to the inlet that significantly modifies the jet
structure. The differences in shock structure resulting from different field
configurations and strengths may have observable consequences for disturbances
propagating through a stationary recollimation shock.
