The Study of Thermal Conditions on Weibel Instability

Weibel electromagnetic instability has been studied analytically in relativistic plasma with high parallel temperature, where |α=(mc²/T_∥)(1+p^{^}_⊥²/m²c²)^1/2|≪1 and while the collision effects of electron-ion scattering have also been considered. According to these conditions, an analytical expression is derived for the growth rate of the Weibel instability for a limiting case of |ζ=√(α/2)(ω^′/ck)|≪1, where ω^′ is the sum of the wave frequency of instability and the collision frequency of electrons with background ions. The results show that in the limiting condition α≪1 there is an unusual situation of the Weibel instability so that T_∥≫T_⊥, while in the classic Weibel instability T_∥≪T_⊥. The obtained results show that the growth rate of the Weibel instability will be decreased due to an increase in the number of collisions and a decrease in the anisotropic temperature by the increasing of plasma density, while the increase of the parameter γ^{^}_⊥=(1+p^{^}_⊥²/m²c²)^1/2 leads to the increase of the Weibel instability growth rate