Stability of Relativistic Force-Free Jets

TL;DR

This paper analyzes the stability of relativistic force-free jets, finding that jets with monotonically increasing Lorentz factor profiles are stable, while those with a maximum Lorentz factor at an intermediate radius are unstable, with specific growth rates for kink instabilities.

Contribution

It introduces a stability analysis of cylindrical force-free jet equilibria, identifying conditions for stability and instability, and quantifies growth rates of kink modes in relativistic jets.

Findings

Monotonically increasing (R) profiles are stable.

Profiles with a maximum (R) are unstable.

Kink instability growth rate is approximately 0.4/_j times c/R_j.

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 R_j. We find that equilibria in which the Lorentz factor \gamma(R) increases monotonically with increasing radius R are stable. On the other hand, equilibria in which \gamma(R) reaches a maximum value at an intermediate radius and then declines to a smaller value \gamma_j at R_j are unstable. The most rapidly growing mode is an m=1 kink instability which has a growth rate ~ (0.4 / \gamma_j) (c/R_j). The e-folding length of the equivalent convected instability is ~2.5 \gamma_j R_j. For a typical jet with an opening angle \theta_j ~ few / \gamma_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.