Kink instability: evolution and energy dissipation in Relativistic Force-Free Non-Rotating Jets

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 ${\rm d} U_{Bφ}/{{\rm d}t} \approx -0.1 U_{Bφ}/τ$, where $τ$ 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.