Plasma Waves in MHD Model

This lecture covers the general formulation of ideal MHD waves, starting from the ideal MHD equations and adding small perturbations to a uniform and static equilibrium. The linearized system of equations is obtained by applying Fourier transform to derive the wave dispersion relation. The lecture discusses the choice of geometry for MHD waves and focuses on transverse waves like the shear Alfvén wave, which is non-compressional. The dispersion relation for the shear Alfvén wave is derived, and its importance in fusion plasmas and space observations is highlighted. Additionally, the lecture explores ideal MHD waves with a longitudinal component, deriving the dispersion relation for compressional waves. The conclusion summarizes the different types of ideal MHD waves and their representation through the wave dispersion relation surface.