The effect of poloidal velocity shear on the local development of current-driven instabilities

TL;DR

This paper analyzes how poloidal velocity shear influences local current-driven instabilities in relativistic magnetized plasma columns, revealing new unstable modes that could impact energy dissipation and jet dynamics in astrophysical phenomena.

Contribution

It introduces the identification of overstable modes driven by velocity shear in relativistic MHD, expanding understanding of jet stability and energy conversion mechanisms.

Findings

Velocity shear reduces growth rates of exponential modes.

High shear induces dominant overstable modes.

Instabilities may facilitate energy dissipation in astrophysical jets.

Abstract

We perform a local (short-wavelength) linear stability analysis of an axisymmetric column of magnetized plasma with a nearly toroidal magnetic field and a smooth poloidal velocity shear by perturbing the equations of relativistic magnetohydrodynamics. We identify two types of unstable modes, which we call 'exponential' and 'overstable', respectively. The exponential modes are present in the static equilibria and their growth rates decrease with increasing velocity shear. The overstable modes are driven by the effects of velocity shear and dominate the exponential modes for sufficiently high shear values. We argue that these local instabilities can provide an important energy dissipation mechanism in astrophysical relativistic jets. Strong co-moving velocity shear arises naturally in the magnetic acceleration mechanism, therefore it may play a crucial role in converting Poynting-flux-dominated jets into matter-dominated jets, regulating the global acceleration and collimation processes, and producing the observed emission of blazars and gamma-ray bursts.