The dispersion characteristics of obliquely propagating electrostatic Bernstein wave in a relativistic degenerate electron plasma is markedly different from perpendicular one. Employing linearized Vlasov-Maxwell model, the dispersion relation of obliquely propagating Bernstein wave in a relativistic degenerate electron plasma is derived. In particular, the results are obtained in the propagation range kz > kx with kx≠0. In the high frequency (ω > > k.v) and weak propagation (Ω>>k.v or k → 0) limiting cases, the generalized results reduce to the Upper hybrid wave for θ′ = 00 and Langmuir wave for θ′ = 900 (where Ω is the gyro-frequency and θ′ is the propagation angle of k with respect to x-axis). Graphical analysis is also performed to highlight the new trends in wave spectra.

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (TeTFe≈1) comprising arbitrary electron degeneracy, where Te and TFe, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

Using Vlasov-Maxwell's equations, the spectra of the perpendicular propagating Bernstein wave and Extraordinary wave in ultra-relativistic fully degenerate electron plasma are studied. The equilibrium particle distribution function is assumed to be isotropic Fermian. The analysis of high frequency spectra of the waves is carried out in the weak propagation limit Ω≫k.v and in the weak magnetic field limit |ω−k.v|≫Ω and graphically observed.

The study of relativistic degenerate plasmas is important in many astrophysical and laboratory environments. Using linearized relativistic Vlasov–Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. Employing Fermi-Dirac distribution at zero temperature, the dispersion relation of the extraordinary mode in a relativistic degenerate electron plasma is investigated. The propagation characteristics are examined in different relativistic density ranges. The shifting of cutoff points due to relativistic effects is observed analytically and graphically. Non-relativistic and ultra-relativistic limiting cases are also presented.

Higher levels of solar wind temperatures are reported to be constrained. Microinstabilities play a key role under dilute space plasma conditions. The present study highlights the role of proton firehose instability in defining parallel temperatures of protons. Considering reality, we chose a bi-Maxwellian model for core protons, while halo protons are best modeled with kappa distribution. Taking different sets of input parameters like temperature anisotropy, plasma beta, and kappa index into account, the growth rate levels and associated domains for an unstable firehose mode are investigated.