On the Chiral imbalance and Weibel Instabilities

TL;DR

This paper investigates the simultaneous occurrence of chiral-imbalance and Weibel instabilities in plasmas with quantum anomalies, analyzing their dependence on anisotropy, angle, and chemical potential differences.

Contribution

It introduces a unified kinetic framework incorporating Berry curvature to study both instabilities and explores their interplay under various plasma conditions.

Findings

Weibel instability depends on momentum anisotropy and angle, with maximum growth at $ heta_n=0$.

Chiral-imbalance instability occurs in isotropic plasma, influenced by chiral chemical potential difference.

Conditions identified where either instability dominates based on anisotropy, angle, and chemical potential ratios.

Abstract

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 $\xi$ and the angle ($\theta_n$) between the propagation vector and the anisotropy direction. It has maximum growth rate at $\theta_n=0$ while $\theta_n=\pi/2$ 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 $\theta_n=0$, only for a very small values of the anisotropic parameter $\xi\sim \xi_c$, growth rates of the both instabilities are comparable. For the cases $\xi_c<\xi\ll1$, $\xi\approx 1$ or $\xi \geq 1$ at $\theta_n=0$, the Weibel modes dominate over the chiral-imbalance instability if $\mu_5/T\leq1$. However, when $\mu_5/T\geq1$, it is possible to have dominance of the chiral-imbalance modes at certain values of $\theta_n$ for an arbitrary $\xi$.