A sequence of in situ measurements points the presence of non-thermal species in the profile of particle distributions. This study highlights the role of such energetic electrons on the wave-spectrum. Using Vlasov–Maxwell’s model, the dispersion relations of the parallel propagating modes along with the space scale of damping are discussed using non-relativistic bi-Maxwellian and bi-Kappa distribution functions under the weak field approximation, i.e., ω − k . v > Ω 0 $\left\vert \omega -\mathbf{k}.\mathbf{v}\right\vert { >}{{\Omega}}_{0}$ . Power series and asymptotic expansions of plasma dispersion functions are performed to derive the modes and spatial damping of waves, respectively. The role of these highly energetic electrons is illustrated on real frequency and anomalous damping of R and L-modes which is in fact controlled by the parameter κ in the dispersion. Further, we uncovered the effect of external magnetic field and thermal anisotropy on such spatial attenuation. In global perspective of the kinetic model, it may be another step.

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.

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The dispersion relations of parallel propagating modes (Langmuir mode, right and left handed circular polarized waves) in the weak magnetic field limit |ω − 𝑘 • 𝑣| Ω are considered for ultra-relativistic arbitrary degenerate electron plasma. The results are presented in terms of moments of Fermi-Dirac distribution. The increase in the electron equilibrium number density from negative large (weakly degenerate) to positive large (highly degenerate) values of µ/T e is observed (where µ is the electron chemical potential and T e is the electron thermal energy). As a result, shifting of the cutoff points in all the real dispersion branches towards the higher values and increasing in the band gap between unmagnetized longitudinal and transverse modes in k-space are examined. Also, the suppression of the weak magnetic field effects in weakly magnetized right handed and left handed circular polarized waves and a decrease in the longitudinal and transverse screening effects are observed in the graphical patterns due to an increase in the equilibrium number density.