Effect of collisions on Weibel instability with anisotropic electron distributions

Using kinetic approach, the effect of electron–ion collisions on Weibel instability has been investigated for three different types of anisotropic distribution functions (i.e., bi-kappa, bi-Maxellian, and product bi-kappa). It is found that the presence of electron–ion collisions has a negative effect on the growth rate of Weibel instability. By using analytical analysis, it has been found that the growth rate of the collisional plasma becomes negative if the electron–ion collision frequency becomes higher than the growth rate of the Weibel instability for a collisionless plasma while keeping all the other parameters same. The impact of electron–ion collisions has also been studied on the temperature anisotropy parameter τ(=T⊥/T||) threshold required for making the growth rate of the Weibel instability positive for all the three distribution functions. The illustrations show that for higher spectral index κ||=κ>4, the temperature anisotropy threshold is same for all the three distribution functions; however, for lower κ||=κ<4, the threshold conditions are different for the bi-kappa as compared to those found for the other two distribution functions. The boundaries between the stable and unstable regions of bi-kappa and product bi-kappa distributions have been found in the presence of collisions. In the presence of collisions, the boundary curve for product bi-kappa is similar to that we get in the absence of collisions. However, the temperature anisotropy threshold parameters are higher for collisional plasma as compared to those obtained for the collisionless plasma. The boundary curve for bi-kappa distribution function in the presence of collisions is significantly different from the boundary curve formed in the absence of collisions. In the presence of collisions, the temperature anisotropy threshold increases very rapidly when the spectral index is <2.