Development of an Analytical Model for Whistler Branch Wave Instability and Propagation in Inhomogeneous Magnetized Plasma

The generation and propagation of whistler waves mediates energy transfer from localized transverse electric fields and resulting sheared plasma flows to particle acceleration and heating, causing cross-scale transport and dissipation of flow and electromagnetic energy in both space and fusion plasmas. To study their spatio-temporal structure, we develop a linear analytical model for wave modes in slab and cylindrically symmetric magnetized plasmas, focusing on the lower right-handed (whistler) branch of the dispersion surface in the overdense regime. Closed-form solutions are obtained for square-well and parabolic plasma density profiles, in analogy to the Klein-Gordon and Schrödinger equations. We then introduce background velocity and temperature gradients to break the Hermitian symmetry of the system to obtain the resulting unstable modes. Model predictions are compared with experimental data from the U.S. Naval Research Laboratory's Space Simulation Chamber for validation.