On the chiral imbalance and Weibel instabilities

We study the chiral-imbalance and the Weibel instabilities in presence of the quantum anomaly using the Berry-curvature modified kinetic equation. We argue that in many realistic situations, e.g. relativistic heavy-ion collisions, both the instabilities can occur simultaneously. The Weibel instability depends on the momentum anisotropy parameter ξ   and the angle (θnθn) between the propagation vector and the anisotropy direction. It has maximum growth rate at θn=0θn=0 while θn=π/2θn=π/2 corresponds to a damping. On the other hand the pure chiral-imbalance instability occurs in an isotropic plasma and depends on difference between the chiral chemical potentials of right and left-handed particles. It is shown that when θn=0θn=0, only for a very small values of the anisotropic parameter ξ∼ξcξ∼ξc, growth rates of the both instabilities are comparable. For the cases ξc<ξ≪1ξc<ξ≪1 or ξ≳1ξ≳1 at θn=0θn=0, the Weibel modes dominate over the chiral-imbalance instability if μ5/T≤1μ5/T≤1. However, when μ5/T≥1μ5/T≥1, it is possible to have dominance of the chiral-imbalance modes at certain values of θnθn for an arbitrary ξ.