Stability properties of magnetohydrodynamic cylindrical flows

A normal‐mode stability analysis is performed on a set of stationary equilibrium configurations, originally introduced by Chiuderi, Pietrini, and Torricelli‐Ciamponi (Astrophys. J., in press) to describe the structure of extragalactic jets. The examined equilibria are characterized by three parameters that allow the magnetic field configuration and the magnitude of the flow speed to be changed. Moreover, two different cases for the equilibrium velocity field are considered, namely v₀∥B₀, and a purely longitudinal v₀. Thus the instability properties of a wide range of magnetic and flow structures are studied numerically and the growth rates as a function of the longitudinal wavenumber k are derived for the azimuthal mode numbers m=0,+1,−1. The aim is both to analyze the behavior of the instability growth rates as a function of the equilibrium parameters and the flow structure and to look for the existence of regions in the equilibrium parameter space corresponding to stable equilibria. A restricted ‘‘stable’’ region for the two considered flow patterns has been identified: configurations characterized by a predominantly longitudinal magnetic field and a velocity smaller or comparable to the Alfvén speed turn out to be stable.