Stability of Relativistic Force-Free Jets

Abstract

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 Rj. 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 γj at Rj 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/γj )(c/Rj ). The e-folding length of the equivalent convected instability is ∼2.5γjRj . For a typical jet with an opening angle θj ∼ few/γj , 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.