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Description
The present work aims to analytically determine the dispersion relations of the primary fundamental modes of wave propagation in cold plasmas. Additionally, it seeks to obtain normalized graphical representations of these equations for comparison with established literature. The methodology employed is based on theoretical analysis, focusing on the linearization of Maxwell's equations in a vacuum using the cold plasma approximation.
We considered the propagation of electromagnetic waves in plasma, analyzing scenarios where the wave propagation (wave vector $\mathbf{k}$) occurs both parallel and perpendicular to the magnetic field $\mathbf{B}_0$. The research incorporates the influence of a constant magnetic field $\mathbf{B}_0$ and utilizes linear perturbation theory, where the physical quantities are divided into unperturbed and perturbed components.
The results demonstrate that normalizing the frequencies by the plasma frequency $\omega_{pe}$ simplifies the mathematical expressions, allowing for a clearer identification of the various propagation modes and their physical characteristics. Ultimately, we concluded that the approach employed validated the cold plasma model for the examined modes, showing good agreement with the anticipated theoretical results, particularly regarding the magnetic field’s impact on the extraordinary and circularly polarized modes.
This study underscores the significance of the cold plasma model in understanding wave phenomena in magnetized plasmas, with potential applications in space weather, plasma astrophysics, and laboratory plasma diagnostics.
