Kinetic-scale diagnostics of destabilization of electromagnetic electron whistler-cyclotron modes in the presence of hybrid non-thermal non-extensive electrons

Temperature anisotropies exist in all the solar terrestrial regions and act as a source of free energy that plays a pivotal role for the destabilization of various plasma modes, one of them is the electromagnetic electron whistler-cyclotron instability. In this paper, the kinetic-scale diagnostic of parallel propagating electromagnetic electron whistler-cyclotron instability is numerically investigated in hybrid non-thermal non-extensive non-collisional magnetized plasmas. The dielectric response function (DRF) of right handed circularly polarized whistler instability (WI) is derived by the incorporation of Vlasov–Maxwell model for both super-extensive ($q<1$, $\alpha \ne 0$) and sub-extensive ($q>1$, $\alpha \ne 0$) bi-Cairns–Tsallis distributed plasma (bi-CTDP) systems. The unstable solutions of WI are obtained through the exact numerical analysis of DRF to compute the oscillatory/real frequency and growth rate. The dependence of pertinent parameters, i.e., non-thermality ($q$), non-extensivity ($\alpha$), temperature anisotropy ratio (${\delta }_e$) and ($\alpha ,q$)-dependent plasma beta (${\beta }_{\parallel e}^{\alpha ,q}$), on the destabilization of whistler mode are examined in detail. The prevalence of hybrid non-thermal non-extensive electrons population plays a substantial role in altering the characteristics of whistler-cyclotron instability in bi-CTDP system as compared to other non-thermal/non-equilibrium plasma systems. The nature and characteristics of the instabilities and waves are substantially influenced by the shape of particle velocity distributions, particularly on kinetic scale. The hybrid non-thermal non-extensive character of electrons distribution remarkably support the instability growth. We observed the highest growth rate of WI in super-extensive bi-CTDP in contrast to other non-thermal plasma distributions. A detailed comparison of the present findings with the other models, e.g. bi-Cairns, bi-nonextensive, and bi-Maxwellian plasmas is also unveiled in the present research.