  We have investigated the influence of jet rotation and differential motion on
the linear and nonlinear development of the current-driven (CD) kink
instability of force-free helical magnetic equilibria via three-dimensional
relativistic magnetohydrodynamic simulations. In this study, we follow the
temporal development within a periodic computational box. Displacement of the
initial helical magnetic field leads to the growth of the CD kink instability.
We find that, in accord with linear stability theory, the development of the
instability depends on the lateral distribution of the poloidal magnetic field.
If the poloidal field significantly decreases outwards from the axis, the
initial small perturbations grow strongly, and if multiple wavelengths are
excited non-linear interaction eventually disrupts the initial cylindrical
configuration. When the profile of the poloidal field is shallow, the
instability develops slowly and eventually saturates. We briefly discuss
implications of our findings for Poynting dominated jets.
