By employing quantum Vlasov–Maxwell set of equations, we have derived a general dispersion relation for perpendicularly propagating electrostatic waves in a degenerate anisotropic quantum plasma. Specifically, we discuss the Bernstein mode and examine how the effects of quantum diffraction and degenerate anisotropy influence its propagation characteristics. We find that the spectrum of the mode becomes more oscillatory. Further, we observe that while the anisotropy significantly affects the mode for β = ωpe/ωce > 1, the quantum effect prevails for β < 1. These effects become more prominent at higher harmonics. It is also pointed out that our results may prove helpful to understand the phenomena of plasma heating and particle acceleration in astrophysical environments like white dwarf.
Employing the linearized Vlasov-Maxwell equations, a generalized dispersion relation for the ordinary mode is derived by employing the Cairns distribution function. The instability of the mode and its threshold condition is investigated. It is found that the temperature anisotropy χ = T‖/T⊥ > 1 required to excite the instability varies with density values whereas the growth rate is dependent on various parameters like non-thermality Λ, equilibrium number density n0 and temperature anisotropy. It is found that with the increase in the values of any of the parameters Λ, n0 and χ, the growth rate is enhanced and the k-domain is enlarged. The results are applicable for space plasma environments like solar wind.
Using the linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. The dispersion relation for the O-mode in a relativistic degenerate electron plasma is investigated by employing the Fermi-Dirac distribution function. The propagation characteristics of the O-mode (cut offs, resonances, propagation regimes, harmonic structure) are examined by using specific values of the density and the magnetic field that correspond to different relativistic dense environments. Further, it is observed that due to the relativistic effects the cut off and the resonance points are shifted to low frequency values, as a result the propagation regime is reduced. The dispersion relations for the non-relativistic and the ultra-relativistic limits are also presented.
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