Stability of Relativistic Force-free Jets

We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylindrical radius R j. We find that equilibria in which the Lorentz factor γ(R) increases monotonically with increasing radius R are stable. On the other hand, equilibria in which γ(R) reaches a maximum value at an intermediate radius and then declines to a smaller value γ j at R j are unstable. The most rapidly growing mode is an m = 1 kink instability which has a growth rate ∼ (0.4/γ j)(c/R j). The e-folding length of the equivalent convected instability is ∼ 2.5γ jR j. For a typical jet with an opening angle θ j ∼ few/γ j, the mode amplitude grows weakly with increasing distance from the base of the jet, much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion. Subject headings: instabilities – MHD – galaxies: jets