Instabilities in Cylindrical Geometry Using the Minimalist Approach: Formalism and Rotational Instabilities

Abstract

The minimalist approach for linear stability analysis is applied to fluids and magnetized ideal plasmas in cylindrical geometry. In this approach, the dispersion relation is obtained by integrating a single first-order differential equation - referred to as the principal equation - subject to appropriate boundary conditions. We first derive the principal equation for a general unperturbed state with radially varying density and pressure, axial and azimuthal components of both the velocity and magnetic field, and a radially directed gravitational field. We then use this formulation to analyze rotating flows with axial magnetic fields, addressing both wall-bounded and interface-driven axisymmetric instabilities. In addition to exact results for selected unperturbed states, we obtain approximate dispersion relations using the WKBJ method in the incompressible and compressible limits. The analysis encompasses centrifugal, magnetorotational, and buoyancy-driven instabilities as special cases, and it clarifies how compressibility modifies their stability properties.

arXiv commentAccepted for publication in Universe

References in corpus (10)

• The Stability of Magnetized Rotating Plasmas with Superthermal Fields
• Magnetohydrodynamic Instabilities in Shearing, Rotating, Stratified Winds and Disks
• Waves and Instabilities in Accretion Disks: MHD Spectroscopic Analysis
• Relativistic Centrifugal Instability
• Linear stability analysis of magnetized jets: the rotating case
• Legolas: a modern tool for magnetohydrodynamic spectroscopy
• Linear Stability Analysis of Relativistic Magnetized Jets: Methodology
• Linear Stability Analysis of Relativistic Magnetized Jets: The Minimalist Approach
• The Schwarzian Approach in Sturm-Liouville Problems
• Classical waves and instabilities using the minimalist approach