  We study the evolution of kink instability in a force-free, non-rotating
plasma column of high magnetization. The main dissipation mechanism is
identified as reconnection of magnetic field-lines with various intersection
angles, driven by the compression of the growing kink lobes. We measure
dissipation rates ${\rm d} U_{B\phi}/{{\rm d}t} \approx -0.1 U_{B\phi}/\tau$,
where $\tau$ is the linear growth time of the kink instability. This value is
consistent with the expansion velocity of the kink mode, which drives the
reconnection. The relaxed state is close to a force-free Taylor state. We
constraint the energy of that state using considerations from linear stability
analysis. Our results are important for understanding magnetic field
dissipation in various extreme astrophysical objects, most notably in
relativistic jets. We outline the evolution of the kink instability in such
jets and derive constrains on the conditions that allow for the kink
instability to grow in these systems.
