Whistler-Mode Waves with Latitudinal variation drive by Loss-Cone Beams and a Parallel DC Electric Field in Jupiter’s Magnetosphere

We derive the dispersion relation and growth rates of parallel-propagating whistler-mode waves in a collisionless Jovian plasma containing relativistic hot beams and a parallel DC electric field. Using a generalized loss-cone distribution, we obtain analytical expressions for the real frequency and dimensionless growth rate as functions of temperature anisotropy, relativistic factor, beam density and DC field strength, and compute results for conditions representative of Jupiter at L ≈ 17 R _J . Compared to earlier studies, our analysis on Jupiter’s magnetosphere (1) incorporates a generalized unperturbed distribution with an explicit loss-cone index, (2) quantifies the combined influence of a parallel DC electric field and relativistic beam effects on growth rates for both electron and ion beams, and (3) presents latitudinal variations using an empirical magnetic field model Jupiter’s magnetosphere. Our results demonstrate that temperature anisotropy and magnetic latitude strongly modulate whistler growth, while relativistic factor and beam density suppress it — implications that can be tested against Juno wave and particle data.