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 { d } U _ { B \phi } / { { 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 .