  We have investigated the development of current-driven (CD) kink instability
through three-dimensional relativistic MHD simulations. A static force-free
equilibrium helical magnetic configuration is considered in order to study the
influence of the initial configuration on the linear and nonlinear evolution of
the instability. We found that the initial configuration is strongly distorted
but not disrupted by the kink instability. The instability develops as
predicted by linear theory. In the non-linear regime the kink amplitude
continues to increase up to the terminal simulation time, albeit at different
rates, for all but one simulation. The growth rate and nonlinear evolution of
the CD kink instability depends moderately on the density profile and strongly
on the magnetic pitch profile. The growth rate of the kink mode is reduced in
the linear regime by an increase in the magnetic pitch with radius and the
non-linear regime is reached at a later time than for constant helical pitch.
On the other hand, the growth rate of the kink mode is increased in the linear
regime by a decrease in the magnetic pitch with radius and reaches the
non-linear regime sooner than the case with constant magnetic pitch. Kink
amplitude growth in the non-linear regime for decreasing magnetic pitch leads
to a slender helically twisted column wrapped by magnetic field. On the other
hand, kink amplitude growth in the non-linear regime nearly ceases for
increasing magnetic pitch.
