Linear Ideal-MHD Waves in Cylindrical Geometry with Transverse Inhomogeneity: A Comprehensive Scientific Review

Abstract

Linear ideal-MHD waves in cylindrical geometries with transverse density and magnetic field inhomogeneities represent a fundamental class of plasma waves critical to understanding energy transport and heating mechanisms in astrophysical plasmas. This review synthesizes current theoretical and computational advances in characterizing wave propagation, mode coupling, and resonant absorption phenomena in magnetized plasma cylinders. The cylindrical geometry naturally supports diverse wave modes including fast and slow magnetoacoustic waves, Alfvén waves, surface waves, and their mixed-property counterparts. Transverse inhomogeneity fundamentally alters wave behavior through coupling mechanisms, leading to complex spatial eigenfunctions, mode conversion, and energy dissipation through resonant absorption. Key findings demonstrate that inhomogeneous plasma cylinders exhibit mixed wave properties where traditional mode classification breaks down, with waves simultaneously displaying characteristics of both Alfvénic and magnetosonic modes. Surface waves at density discontinuities and resonant layers play crucial roles in wave energy dissipation. Applications to solar coronal loop oscillations and laboratory plasma confinement demonstrate the practical importance of understanding these wave phenomena. Critical challenges include accurately modeling the transition from uniform to strongly inhomogeneous systems, quantifying energy transfer rates, and developing comprehensive mode identification techniques. Future research directions emphasize multi-dimensional modeling, advanced spectroscopic diagnostics, and integration with observational data to validate theoretical predictions and enhance predictive capabilities for plasma heating and stability applications.