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A plasma wave dominated by a longitudinal electric field. The leading dispersion relation is $\mathbf{k}\cdot \mathbf{ϵ}\cdot \mathbf{k}=0$. In a cold magnetized plasma, this becomes $k_{\perp }^{2}S+k_{\parallel }^{2}P=0$. An exactly longitudinal finite-wavenumber solution must also satisfy the full Maxwell equations; the oblique electrostatic condition is usually an asymptotic large-refractive index approximation.