Electromagnetic fields with electric and chiral magnetic conductivities in heavy ion collisions

TL;DR

This paper derives explicit formulas and numerical solutions for electromagnetic fields in conducting media with electric and chiral magnetic conductivities, relevant for understanding fields in heavy ion collisions.

Contribution

It provides the first compact algebraic expressions for electromagnetic fields with both conductivities, including analytic and numerical solutions applicable to heavy ion collision scenarios.

Findings

Analytic formulas recover Lienard-Wiechert fields at zero conductivity.

Numerical solutions match analytic results across conductivity ranges.

Electromagnetic field profiles in non-central Au+Au collisions are characterized.

Abstract

We derive analytic formula for electric and magnetic fields produced by a moving charged particle in a conducting medium with the electric conductivity $\sigma$ and the chiral magnetic conductivity $\sigma_{\chi}$. We use the Green function method and assume that $\sigma_{\chi}$ is much smaller than $\sigma$. The compact algebraic expressions for electric and magnetic fields without any integrals are obtained. They recover the Lienard-Wiechert formula at vanishing conductivities. Exact numerical solutions are also found for any values of $\sigma$ and $\sigma_{\chi}$ and are compared to analytic results. Both numerical and analytic results agree very well for the scale of high energy heavy ion collisions. The space-time profiles of electromagnetic fields in non-central Au+Au collisions have been calculated based on these analytic formula as well as exact numerical solutions.