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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    &gt;    Ω    0$\left\vert \omega -\mathbf{k}.\mathbf{v}\right\vert { &gt;}{{\Omega}}_{0}$. 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.

Impact of non-thermal electrons on spatial damping: a kinetic model for the parallel propagating modes