  We performed relativistic magnetohydrodynamic simulations of the hydrodynamic
boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006)
using the RAISHIN code. Simulation results show that the presence of a magnetic
field changes the properties of the shock interface between the tenuous,
overpressured jet ($V^z_j$) flowing tangentially to a dense external medium.
Magnetic fields can lead to more efficient acceleration of the jet, in
comparison to the pure-hydrodynamic case. A ``poloidal'' magnetic field
($B^z$), tangent to the interface and parallel to the jet flow, produces both a
stronger outward moving shock and a stronger inward moving rarefaction wave.
This leads to a large velocity component normal to the interface in addition to
acceleration tangent to the interface, and the jet is thus accelerated to
larger Lorentz factors than those obtained in the pure-hydrodynamic case.
Likewise, a strong ``toroidal'' magnetic field ($B^y$), tangent to the
interface but perpendicular to the jet flow, also leads to stronger
acceleration tangent to the shock interface relative to the pure-hydrodynamic
case. Overall, the acceleration efficiency in the ``poloidal'' case is less
than that of the ``toroidal'' case but both geometries still result in higher
Lorentz factors than the pure-hydrodynamic case. Thus, the presence and
relative orientation of a magnetic field in relativistic jets can significant
modify the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).
