Model of the effect of collisions on QCD plasma instabilities

We study the effect of including a Bhatnagar-Gross-Krook (BGK) collisional kernel on the collective modes of a QCD plasma which has a hard-particle distribution function which is anisotropic in momentum space. We calculate dispersion relations for both the stable and unstable modes and show that the addition of hard-particle collisions slows the rate of growth of QCD plasma unstable modes. We also show that for any anisotropy there is an upper limit on the collisional frequency beyond which no instabilities exist. Estimating a realistic value for the collisional frequency for alpha(s)similar to 0.2-0.4 we find that for the large-anisotropy case which is relevant for the initial state of matter generated by free streaming in heavy-ion collisions that the collisional frequency is below this critical value.