Ionization-Driven Instabilities of Circularly Polarized Electromagnetic Modes in Dense Plasmas

Abstract Circularly polarized (CP) electromagnetic waves in the dense, degenerate plasmas of white dwarfs and neutron-star envelopes are relevant to the interpretation of their emission, yet the influence of ionization on their stability has received little attention. We use a linearized quantum hydrodynamic model that includes electron and ion Fermi pressure and an ionization source term to derive the dispersion relation and analytical growth-rate expressions for the CP and right-circularly polarized (RCP) modes. In the ionization-dominated regime described by these expressions, both growth rates are approximately equal to half the ionization frequency, and their small deviations from this value depend on the plasma frequency, the Fermi velocities, the propagation angle and the wavenumber. For the CP branch, this deviation grows quadratically with the product of the wavenumber and the Thomas--Fermi screening length and is largest for propagation closest to the reference axis. For the RCP branch, we show that part of the growth-rate expression cancels identically and that the remaining expression exhibits two narrow, sign-reversing singular features, associated with the electron and ion Fermi velocities, whose positions scale linearly with the ionization frequency and inversely with the cube root of the density. We give closed-form conditions for these positions, verify them numerically, and discuss the validity range of the model and the extensions required for a quantitative comparison with observations of compact objects.