Lyapunov stability of flowing MHD plasmas surrounded by resistive walls

TL;DR

This paper derives a general Lyapunov stability condition for flowing MHD plasmas with resistive walls, showing that stability depends on potential energy sign and not on gyroscopic effects, especially in ideal, non-dissipative conditions.

Contribution

It introduces a new stability criterion for plasma-vacuum systems with resistive walls using the Frieman Rotenberg formulation, emphasizing the role of potential energy sign.

Findings

Lyapunov stability limit depends on potential energy sign.

Flow cannot stabilize the system without plasma dissipation.

Stability condition is independent of gyroscopic effects.

Abstract

A general stability condition for plasma-vacuum systems with resistive walls is derived by using the Frieman Rotenberg lagrangian stability formulation [Rev. Mod. Phys. 32, 898 (1960)]. It is shown that the Lyapunov stability limit for external modes does not depend upon the gyroscopic term but upon the sign of the perturbed potential energy only. In the absence of dissipation in the plasma such as viscosity, it is expected that the flow cannot stabilize the system.