  Extragalactic jets are inferred to harbor dynamically important, organized
magnetic fields which presumably aid in the collimation of the relativistic jet
flows. We here explore by means of grid-adaptive, high resolution numerical
simulations the morphology of AGN jets pervaded by helical field and flow
topologies. We concentrate on morphological features of the bow shock and the
jet beam behind the Mach disk, for various jet Lorentz factors and magnetic
field helicities. We investigate the influence of helical magnetic fields on
jet beam propagation in overdense external medium. We use the AMRVAC code,
employing a novel hybrid block-based AMR strategy, to compute ideal plasma
dynamics in special relativity. The helicity of the beam magnetic field is
effectively transported down the beam, with compression zones in between
diagonal internal cross-shocks showing stronger toroidal field regions. In
comparison with equivalent low-relativistic jets which get surrounded by
cocoons with vortical backflows filled by mainly toroidal field, the high speed
jets demonstrate only localized, strong toroidal field zones within the
backflow vortical structures. We find evidence for a more poloidal, straight
field layer, compressed between jet beam and backflows. This layer decreases
the destabilizing influence of the backflow on the jet beam. In all cases, the
jet beam contains rich cross-shock patterns, across which part of the kinetic
energy gets transferred. For the high speed reference jet considered here,
significant jet deceleration only occurs beyond distances exceeding ${\cal
O}(100 R_j)$, as the axial flow can reaccelerate downstream to the internal
cross-shocks. This reacceleration is magnetically aided, due to field
compression across the internal shocks which pinch the flow.
