The Semi-Relativistic Weibel Instability

In this work, we have analyzed the Weibel instability (IW) in the semi-relativistic case, when assuming the modified isotropic Jüttner-Maxwell distribution function taking into account relativistic effects. For this we consider an inhomogeneous plasma in the presence of a high laser field. From the semi-relativistic Fokker-Planck equation and Maxwell's equations we have established the dispersion relations and deduced the growth rate of WI. As a result, the effect of collision frequency and high plasma density under anisotropic temperature conditions decrease the spectrum of the growth rate of Weibel modes, this result clearly shows that previous analyses of WI due to temperature anisotropy, collision effect and choice of plasma density can be estimated the values of the growth rate of WI.