  Several observations of astrophysical jets show evidence of a structure in
the direction perpendicular to the jet axis, leading to the development of
"spine & sheath" models of jets. Most studies focus on a two-component jet
consisting of a highly relativistic inner jet and a slower - but still
relativistic - outer jet surrounded by an unmagnetized environment. These jets
are believed to be susceptible to a relativistic Rayleigh-Taylor-type
instability, depending on the effective inertia ratio of the two components. We
extend previous studies by taking into account the presence of a non-zero
toroidal magnetic field. Different values of magnetization are examined, to
detect possible differences in the evolution and stability of the jet. We find
that the toroidal field, above a certain level of magnetization $\sigma$,
roughly equal to 0.01, can stabilize the jet against the previously mentioned
instabilities and that there is a clear trend in the behaviour of the average
Lorentz factor and the effective radius of the jet when we continuously
increase the magnetization. The simulations are performed using the
relativistic MHD module from the open source, parallel, grid adaptive,
MPI-AMRVAC code.
