Relativistic jets naturally occur in astrophysical systems that involve accretion onto compact objects, such as core collapse of massive stars in gamma-ray bursts (GRBs) and accretion onto supermassive black holes in active galactic nuclei (AGN). It is generally accepted that these jets are powered electromagnetically, by the magnetised rotation of a central compact object. However, how they produce the observed emission and survive the propagation for many orders of magnitude in distance without being disrupted by current-driven non-axisymmetric instabilities is the subject of active debate. We carry out time-dependent 3D relativistic magnetohydrodynamic simulations of relativistic, Poynting flux dominated jets. The jets are launched self-consistently by the rotation of a strongly magnetised central compact object. This determines the natural degree of azimuthal magnetic field winding, a crucial factor that controls jet stability. We find that the jets are susceptible to two types of instability: (i) a global, external kink mode that grows on long time scales and causes the jets to bodily bend sideways. Whereas this mode does not cause jet disruption over the simulated distances, it substantially reduces jet propagation speed. We show, via an analytic model, that the growth of the external kink mode depends on the slope of the ambient medium density profile. In flat density distributions characteristic of galactic cores, an AGN jet may stall, whereas in stellar envelopes the external kink weakens as the jet propagates outward; (ii) a local, internal kink mode that grows over short time scales and causes small-angle magnetic reconnection and conversion of about half of jet electromagnetic energy flux into heat. Based on the robustness and energetics of the internal kink mode, we suggest that this instability is the main dissipation mechanism responsible for powering GRB prompt emission.
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