Collisional effect on the Weibel instability in a semi-relativistic anisotropic plasma

Abstract

The detailed properties of the classical electromagnetic Weibel instability in a semi-relativistic anisotropic plasma are investigated for Maxwellian distribution. In this article, the effects of one particular factor affecting the growth rate of Weibel instability, Coulomb collision effect of electrons and ions, is studied and discussed based on the equilibrium semi-relativistic Maxwellian distribution function, in a dense and unmagnetized anisotropic plasma. An analytical expression is derived for the growth rate of the Weibel instability. The two limiting cases ( $\left| \xi\right| \ll1$ and $\left| \xi\right| \gg1$ ) are considered. It is shown that in the limit $\left| \xi\right| \ll 1$ , the quantity η, which is due to the collision term, will appear in the growth and in the conditions of the rate of the Weibel instability. The quantity χ symbolizes the contribution from relativistic terms which becomes unity as we approach the non-relativistic Maxwellian case, leading to the standard Weibel instability scenario. The increasing of η leads to decreasing of the growth rate, and with the decreasing of η the growth rate will increase.