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 . Equilibria in which the Lorentz factor γ(R) increases monotonically with increasing radius R are found to be 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. A feature of these unstable equilibria is that poloidal field line curvature plays a prominent role in maintaining transverse force balance. 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_j R_j . For a typical jet with an opening angle θ_j few/γ_j, the mode amplitude grows only weakly with increasing distance from the base of the jet. The growth is much slower than one might expect from a naive application of the Kruskal-Shafranov stability criterion.