Whistler instability in a semi-relativistic bi-Maxwellian plasma

Employing linearized Vlasov–Maxwell system of equations, the whistler instability is discussed for a semi-relativistic bi-Maxwellian distribution. The dispersion relations are analyzed analytically along with the graphical representation and the estimates of the growth rate and instability threshold condition are also presented in the limiting cases i.e., _ξ±=(ω?Ω)/_k∥vt‖?1${\xi }_{\pm }=(\omega ?\Omega )/k_{\parallel }{v}_{t_{\Vert }}?1$ (resonant case) and _ξ±?1${\xi }_{\pm }?1$ (non-resonant case). Further for field free case i.e., _B0=0$B_0=0$, the growth rates for Weibel instability in a semi-relativistic bi-Maxwellian plasma are presented for both the limiting cases.