Nonlinear kinetic formulation of gravitationally modified electron Bernstein waves in magnetized plasmas

Electron Bernstein waves are electrostatic waves that play a fundamental role in wave-particle interactions, plasma heating,and energy transport in magnetized plasmas. Although the kinetic theory of EBWs has been extensively investigated under various plasma conditions, the influence of gravitationally induced drift on their nonlinear propagation has received comparatively little attention. In this work, we develop a nonlinear kinetic framework that self-consistently incorporates the gravitationally induced $$\vec{g}\times \vec{B}$$ drift into the equilibrium electron dynamics and the dielectric response of EBWs in an inhomogeneous magnetized plasma. Starting from the Vlasov Poisson system, a modified equilibrium distribution function is formulated to account for both the equilibrium density gradient and the gravitational drift. A nonlinear dispersion relation is then derived within the plasma maser formalism by including the direct and polarization nonlinear coupling terms arising from low-frequency drift wave turbulence. To illustrate the influence of gravity on the reactive wave dispersion, numerical calculations are performed using the linear dielectric function. The results demonstrate that the gravitational drift systematically modifies the Bernstein-wave resonance condition through the $${K}_{\perp }\vec{{V}_{g}}$$ term, producing perturbative shifts in the dielectric response and resonance frequencies. For the representative astrophysical plasma parameters considered in this study, these frequency shifts remain modest, consistent with the condition $$\vec{{V}_{g}}\parallel {v}_{g}$$ . However, the derived kinetic formulation establishes the fundamental mechanism through which gravity influences EBW propagation and provides a general theoretical framework applicable to magnetized plasma environments where gravitational effects become comparatively more important. The present work therefore extends the conventional kinetic theory of EBWs by incorporating gravitationally induced drift effects within a unified nonlinear kinetic description.