[Paper Review] Pressure- and magnetic shear- driven instabilities in rotating MHD jets

Evy Kersalé, Pierre‐Yves Longaretti+1 more|arXiv (Cornell University)|Oct 25, 2000

Solar and Space Plasma Dynamics3 citations

TL;DR

This paper derives new stability criteria for pressure- and magnetic shear-driven instabilities in rotating magnetohydrodynamic (MHD) jets using the ballooning ordering expansion. Surprisingly, it identifies a linear term in magnetic shear that can destabilize jets—contrary to Suydam's criterion, which predicts magnetic shear always stabilizes. The instability is particularly relevant for jets with vanishing current density on axis, such as those from accretion disks, and may power particle acceleration in AGN jets.

ABSTRACT

We derive new stability criteria for purely MHD instabilities in rotating jets, in the framework of the ballooning ordering expansion. Quite unexpectedly, they involve a term which is linear in the magnetic shear. This implies that cylindrical configurations can be destabilized by a negative magnetic shear as well as by a favorable equilibrium pressure gradient, in distinction with the predictions of Suydam's stability criterion, which suggests on the contrary that the shear is always stabilizing. We have used these criteria to establish sufficient conditions for instability. In particular, the magnetic shear can always destabilize jets with vanishing current density on the axis, a feature which is generically found in jets which are launched from an accretion disk. We also show that standard nonrotating jet models (where the toroidal field dominates the poloidal one), which are known to be unstable, are not stabilized by rotation, unless the plasma $β$ parameter and the strength of the rotation forces are both close to the limit allowed by the condition of radial equilibrium. The new magnetic shear-driven instability found in this paper, as well as the more conventional pressure-driven instability, might provide us with a potential energy source for the particle acceleration mechanisms underlying the high energy emission which takes place in the interior of AGN jets.

Motivation & Objective

• To derive new stability criteria for purely MHD instabilities in rotating jets under the ballooning ordering approximation.
• To investigate the role of pressure and magnetic shear in driving instabilities, especially in configurations with vanishing current density on the axis.
• To assess whether rotation stabilizes known unstable jet models, particularly those dominated by toroidal magnetic fields.
• To explore the potential link between these instabilities and particle acceleration mechanisms in AGN jets.

Proposed method

• The study employs the ballooning ordering expansion to analyze local, quasi-perpendicular MHD perturbations in rotating, cylindrical jet equilibria.
• It derives exact expressions for perturbed magnetic field and tension forces using the WKB-like approximation, retaining key geometric and field curvature effects.
• The momentum equations are derived from the perturbed MHD force balance, incorporating magnetic tension, Coriolis, and entrainment inertial terms.
• The total pressure perturbation is shown to cancel in the quasi-perpendicular propagation limit, simplifying the force balance.
• The divergence of the displacement field is expressed in terms of field-aligned derivatives and geometric factors, reducing the system to ordinary differential equations for the field-aligned and azimuthal components of displacement.
• Stability criteria are derived by analyzing the resulting eigenvalue problem under radial equilibrium constraints.

Experimental results

Research questions

• RQ1 Can magnetic shear destabilize rotating MHD jets, contrary to the conventional Suydam criterion?
• RQ2 What conditions allow magnetic shear to drive instability in jets with vanishing current density on the axis?
• RQ3 To what extent does rotation stabilize or destabilize standard nonrotating jet models with dominant toroidal fields?
• RQ4 How do pressure and magnetic shear instabilities compare in growth rate and physical mechanism?
• RQ5 Can these instabilities provide a viable energy source for particle acceleration in AGN jets?

Key findings

• A linear term in magnetic shear appears in the stability criterion, indicating that negative magnetic shear can destabilize jets—contrary to Suydam’s prediction of always stabilizing shear.
• Jets with vanishing current density on the axis are always susceptible to magnetic shear-driven instability, a feature common in disk-launched jets.
• Standard nonrotating jet models with dominant toroidal fields remain unstable under rotation unless both plasma β and rotation forces are near their radial equilibrium limits.
• The new magnetic shear-driven instability, combined with pressure-driven modes, may serve as a sustained energy source for particle acceleration in AGN jet interiors.
• The instability mechanism is robust in the ballooning ordering framework and arises from field line curvature and shear effects, not from current-driven kink modes.
• The analysis shows that slow and Alfvénic perturbations are quasistatic in the field line direction, and fast perturbations are compressional, justifying the WKB-like approximation.