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We have investigated the influence of velocity shear and a radial densityprofile on the spatial development of the current driven kink instability alonghelically magnetized relativistic jets via three-dimensional relativisticmagnetohydrodynamic simulations. In this study, we use a non-periodiccomputational box, the jet flow is initially established across thecomputational grid, and a precessional perturbation at the inlet triggersgrowth of the kink instability. If the velocity shear radius is located insidethe characteristic radius of the helical magnetic field, a staticnon-propagating current driven kink is excited as the perturbation propagatesdown the jet. Temporal growth disrupts the initial flow across thecomputational grid not too far from the inlet. On the other hand, if thevelocity shear radius is outside the characteristic radius of the helicalmagnetic field, the kink is advected with the flow and grows spatially down thejet. In this case flow is maintained to much larger distances from the inlet.The effect of different radial density profiles is more subtle. When thedensity increases with radius, the kink appears to saturate by the end of thesimulation without apparent disruption of the helical twist. This behaviorsuggests that relativistic jets consisting of a tenuous spine surrounded by adenser medium with a velocity shear radius outside the radius of maximumtoroidal magnetic field have a relatively stable configuration.

Spatial Growth of the Current-Driven Instability in Relativistic Jets