In the paradigm of magnetic launching of astrophysical jets , instabilities in the MHD flow are a good candidate to convert the Poynting flux into the kinetic energy of the plasma .
If the magnetised plasma fills the almost entire space , the jet is unstable to helical perturbations of its body .
However , the growth rate of these modes is suppressed when the poloidal component of the magnetic field has a vanishing gradient , which may be the actual case for a realistic configuration .
Here we show that , if the magnetised plasma is confined into a limited region by the pressure of some external medium , the velocity shear at the contact surface excites unstable modes which can affect a significant fraction of the jet ’ s body .
We find that when the Lorentz factor of the jet is \Gamma \sim 10 ( \Gamma \sim 100 ) , these perturbations typically develop after propagating along the jet for tens ( hundreds ) of jet ’ s radii .
Surface modes may therefore play an important role in converting the energy of the jet from the Poynting flux to the kinetic energy of the plasma , particularly in AGN .
The scaling of the dispersion relation with ( i ) the angular velocity of the field lines and ( ii ) the sound speed in the confining gas is discussed .