  In the paradigm of magnetic acceleration of relativistic jets, one of the key
points is identifying a viable mechanism to convert the Poynting flux into the
kinetic energy of the plasma beyond equipartition. A promising candidate is the
kink instability, which deforms the body of the jet through helical
perturbations. Since the detailed structure of real jets is unknown, we explore
a large family of cylindrical, force-free equilibria to get robust conclusions.
We find that the growth rate of the instability depends primarily on two
parameters: (i) the gradient of the poloidal magnetic field; (ii) the Lorentz
factor of the perturbation, which is closely related to the velocity of the
plasma. We provide a simple fitting formula for the growth rate of the
instability. As a tentative application, we use our results to interpret the
dynamics of the jet in the nearby active galaxy M87. We show that the kink
instability becomes non-linear at a distance from the central black hole
comparable to where the jet stops accelerating. Hence (at least for this
object), the kink instability of the jet is a good candidate to drive the
transition from a Poynting-dominated to a kinetic-energy-dominated flow.
